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This article considers the nonlinear dynamics of coupled oscillators featuring strong coupling in 1:2 internal resonance. In forced oscillations, this particular interaction is the source of energy exchange, leading to a particular shape of the response curves, as well as quasi-periodic responses and a saturation phenomenon. These main features are embedded in the simplest system which considers only the two resonant quadratic monomials conveying the 1:2 internal resonance, since they are the proeminent source allowing one to explain these phenomena. However, it has been shown recently that those features can be substantially modified by the presence of non-resonant quadratic terms. The aim of the present study is thus to explain the effect of the non-resonant quadratic terms on the dynamics. To that purpose, the normal form up to the third order is used, since the effect of the non-resonant quadratic terms will be transferred into the resonant cubic terms. Analytical solutions are detailed using a second-order mutliple scale expansion. A thorough investigation of the backbone curves, their stability and bifurcation, and the link to the forced–damped solutions, is detailed, showing in particular interesting features that had not been addressed in earlier studies. Finally, the saturation effect is investigated, and it is shown how to correct the detuning effect of the cubic terms thanks to a specific tuning of non-resonant quadratic terms and resonant cubic terms. This choice, derived analytically, is shown to extend the validity of the saturation effect to larger amplitudes, which can thus be used in all applications where this effect is needed e.g. for control.

Synchronization of audio-tactile stimuli represents a key feature of multisensory interactions. However, information on stimuli synchronization remains scarce, especially with virtual buttons. This work used a click sensation produced with traveling waves and auditory stimulus (a bip-like sound) related to a virtual click for a psychological experiment. Participants accomplish a click gesture and judge if the two stimuli were synchronous or asynchronous. Delay injection was performed on the audio (haptic first) or the click (audio first). In both sessions, one stimulus follows the other with a delay ranging from 0−700ms . We use weighted and transformed 3-up/1-down staircase procedures to estimate people's sensitivity. We found a threshold of 179ms and 451ms for the auditory first and haptic first conditions, respectively. Statistical analysis revealed a significant effect between the two stimuli' order for threshold. Participants' acceptable asynchrony decreased when the delay was on the haptic rather than on the audio. This effect could be due to the natural experience in which the stimuli tend to be first tactile and then sonorous rather than the other way around. Our findings will help designers to create multimodal virtual buttons by managing audio-tactile temporal synchronization.

In this article, we propose a new concept for tuning a resonant piezoelectric shunt absorber thanks to the use of a nonsmooth electronic component. It consists in adding a voltage source in the resonant shunt circuit, which is a bilinear function of the voltage across the piezoelectric patch. The main advantage is the ability to change the electrical resonance frequency with the bilinear component gain, enabling a tuning as well as a possible reduction in the required inductance value. Furthermore, because of the intrinsic nonlinear nature of the bilinear component, a multi-harmonic response is at hand, leading to a nonlinear coupling between the mechanical and electrical modes. Two particular tunings between the electrical and the mechanical resonance frequencies are tested. The first one is one-to-one, for which the electrical resonance is tuned close to the mechanical one. It is proved to be similar to a classical linear resonant shunt, with the additional tuning ability. The second case consists in tuning the electrical circuit at half the mechanical resonance, leading to a two-to-one (2:1) internal resonance. The obtained response is also found to be similar to a classical resonant shunt near the main resonance. In either case, the shunt performances are analytically and numerically studied, leading to optimal values of the design parameters as well as an estimation of the amplitude reduction provided by the shunt. Finally, experimental validation is proposed, targeting the damping of the twisting mode of a hydrofoil structure, in which the bilinear component is realized with a diode.

In this study, we present a theoretical and experimental analysis of an antiresonance detuning correction for a nonlinear piezoelectric shunt absorber based on a two-to-one internal resonance. Thanks to this purely nonlinear feature, the oscillations of the primary system become independent of the forcing at a particular antiresonance frequency, thus creating an efficient reduction of the vibration. Past works of the literature present the design of the piezoelectric shunt and show that it is subjected to a softening behavior that detunes the antiresonance frequency as a function of the amplitude and thus degrades the performance. It is also shown that this softening behavior is caused by some non-resonant terms present in the equations, linked to the piezoelectric coupling. To counteract this undesired effect, we propose in this work to add a cubic nonlinearity in the shunt circuit, in addition to the quadratic one already present. Its tuning is based on a normal form analysis already published, which shows how cubic nonlinearities can cancel the effect of quadratic non-resonant terms. The present article describes the main features of the theory and focuses on the experimental proof of concept of this antiresonance detuning correction as well as the analysis of its range of validity. It is applied to the damping of the first bending mode of a hydrodynamic foil structure.

In this paper, a semi-passive nonlinear piezoelectric shunt absorber is presented, aiming at attenuating the vibration of a resonant elastic structure under external excitation. This is done by connecting the elastic structure to a nonlinear shunt circuit via a piezoelectric patch. The nonlinear shunt circuit consists of resonant circuit that includes a quadratic non-linearity. A particular tuning of the natural frequency of the shunt enables to create a two to one internal resonance. This generates a strong coupling between the mechanical mode and the electrical mode, leading to replace the mechanical resonance with a nonlinear antiresonance associated with an amplitude saturation, thus leading to an efficient vibration reduction. In this paper, we first propose a theoretical model that is expanded onto a suitable electromechanical modal basis and reduced to the two modes of interest, nonlinearly coupled by quadratic terms. Then, analytical solutions are obtained by the multiple scale method and compared to a reference numerical solutions stemming from the harmonic balance method. This enables to investigate the performance of the system in term of vibration absorption as well as giving design rules to tune the nonlinear shunt and to choose the free parameters of the system.

In this article, several modes are controlled simultaneously both in phase and amplitude on an haptic display. To achieve this, modulation/demodulation control combined with mixed spatial/frequency filters is developed. It is then applied to produce a predefined velocity field both in space and time on a plate. The experimental results show good agreement with theory.

Parametrically excited oscillators are used in several domains, in particular to improve the dynamical behaviour of systems like in the case of the parametric amplification or parametric energy harvesting. Although dry friction is often omitted during system modelling due to the complexity of its nonsmooth nature, it is sometimes necessary to account for this kind of damping to adequately represent the system motion. In this paper, it is proposed to investigate the effect of dry friction on the dynamical behaviour of a nonlinear parametric oscillator. Using the pendulum case as example, the problem is formulated according to a Mathieu-Duffing equation. Semi-analytical developments using the harmonic balance method and the method of varying amplitudes are used to find the solutions of this equation and their stability. These results are validated thanks to a comparison with time integration simulations. Effects of initial conditions on the basins of attractions of the solutions are also studied using these simulations. It is found that trivial and non-trivial solutions of the oscillator including dry friction are not connected, giving birth to isolated periodic solutions branches.Thus, both initial displacement and phase between the excitation and the oscillator displacement must be carefully chosen to reach periodic solutions. Finally, a method based on the energy principle is used to find the critical forcing amplitude and frequency needed to obtain the birth of nontrivial solutions for the nonlinear parametric oscillator including dry friction.

n experimental proof of concept of a new semi-passive nonlinear piezoelectric shunt absorber, introduced theoretically in a companion article, is presented in this work. This absorber is obtained by connecting, through a piezoelectric transducer, an elastic structure to a resonant circuit that includes a quadratic nonlinearity. This nonlinearity is obtained by including in the circuit a voltage source proportional to the square of the voltage across the piezoelectric transducer, thanks to an analog multiplier circuit. Then, by tuning the electric resonance of the circuit to half the value of one of the resonances of the elastic structure, a two-to-one internal resonance is at hand. As a result, a strong energy transfer occurs from the mechanical mode to be attenuated to the electrical mode of the shunt, leading to two essential features: a nonlinear antiresonance in place of the mechanical resonance and an amplitude saturation. Namely, the amplitude of the elastic structure oscillations at the antiresonance becomes, above a given threshold, independent of the forcing level, contrary to a classical linear resonant shunt. This paper presents the experimental setup, the designed nonlinear shunt circuit and the main experimental results.

Friction reduction using ultrasonic longitudinal surface vibration can modify the user perception of the touched surface and induce the perception of textured materials. In the current paper, the mechanisms of friction reduction using longitudinal vibration are analyzed at different finger exploration velocities and directions over a plate. The development of a non-Coulombic adhesion theory based on experimental results is evaluated as a possible explanation for friction reduction with vibrations that are non-collinear with the finger displacement. Comparison with experimental data shows that the model adequately describes the reduction in friction, although it is less accurate for low finger velocities and depends on motion direction.

The design and closed loop control of a device able to produce both longitudinal mode and transverse mode vibration, at about the same resonance frequency (60 kHz) are presented in this article. The structure uses an array of piezo-ceramics. A dynamic analysis is performed on the obtained modes, and their dynamic lumped parameters are identified. A closed loop control is performed to maintain the desired vibration amplitude in the presence of a finger. Longitudinal and transverse motion cartographies show that the objective of achieving and controlling pure modes independently has been achieved. Using this device, tribological, psychophysical and energetic analyses are carried out. The analyses show that in terms of friction measurements and perception, both modes produce equivalent results. In terms of active power losses, an advantage of the longitudinal mode over the transverse mode is observed due to the interaction with the finger.

One way to enhance the performance of vibration control with piezoelectric shunt is to use a negative capacitance in the shunt circuit. This component is very effective and pro- vides good results in terms of attenuation improvement without significantly increasing the complexity of the shunt network. However, negative capacitances are built using oper- ational amplifiers and, in some applications, the risk of saturation of the outputs of the operational amplifier exists. This constitutes a non-negligible aspect since it leads to a non-proper functioning of the control system which significantly deteriorates the control performance or even triggers instability phenomena. In light of this limitation, this paper proposes strategies to decrease the outputs of the operational amplifier in order to reduce the risk of saturation acting just on the values of the circuit components, without worsen- ing the attenuation performance. However, when the achievable reduction is not sufficient, it is also possible to act on other components accepting a deterioration of the attenuation performance. Guidelines are provided for properly choosing the best shunt circuit configu- ration accounting for both the extent of the operational amplifier outputs and the control performance. The paper also evidences that the mechanical part of the system cannot be neglected in the analysis when assessing the operational amplifier outputs. Furthermore, two different circuit types used to build the negative capacitance are compared in terms of output requirements. This analysis shows that there is no circuit always less demanding than the other and that the choice of the circuit is not always straightforward. Therefore, a multi-degree of freedom model is presented, which is essential to understand which con- figuration of the negative capacitance has to be used in a given engineering application. All the presented outcomes are validated through an experimental campaign.

When a finger touches an ultrasonic vibrating plate, a non-sinusoidal contact force is produced. This force is called acoustic finger force. In a setup where closed-loop control is performed on the vibration amplitude, a component of the acoustic finger force can be measured at the fundamental vibration frequency of the plate. This calculation is obtained from the measurement of the variation of the controller voltage between the no-load case and when a finger is present. This calculation is made for a group of twelve participants. From these results a PCA (Principal Component Analysis) model is created. This model permits estimation of the acoustic finger force response of a participant at any vibration amplitude, based on a one or two point measurement. Finally, a linear relation between the PCA coefficients and the friction reduction is proposed. The objective of this relation would be to ultimately provide the means to create an amplitude reference calibration based on the desired friction reduction level, and thus be able to produce a standardized tactile feedback for each user, despite the biomechanical differences in finger pad properties between subjects.

This article proposes a novel mean for tuning the natural frequency of an electromagnetic resonant shunt, using a pulse-width modulation (PWM) circuit. It is used to modulate the value of the capacitance of the shunt, and the electrical frequency is shown to be proportional to the command parameter of the PWM, the duty cycle. An easy and efficient strategy to tune the resonant shunt in real time is then proposed, thus obtaining a low powered and always stable vibration control device. The article proposes the theory of PWM, giving a robust method to predict the dynamics of the system. Then, an accurate multi-mode theoretical model of the tunable resonant shunt coupled to an elastic structure is proposed and experimentally validated on an elastic multi-mode structure, in the case of two different control strategies. The first one is a standard resonant shunt with both the electrical frequency and damping optimized to reduce a given resonance peak. The second one is based on a resonant shunt with the electrical damping as low as possible, which creates an antiresonance and a “notch” type mechanical response at the driving frequency. Both strategies are experimentally validated with real time variation and adaptation of the electrical frequency, obtaining an efficient vibration control device, able to reduce by a factor 40 the vibration level.

Piezoelectric devices with integrated actuation and sensing capabilities are often used for the development of electromechanical systems. The present paper addresses experimentally the nonlinear dynamics of a fully integrated circular piezoelectric thin structure, with piezoelectric patches used for actuationand other for sensing. A phase-locked loop control system is used to measure the resonant periodic response of the system under harmonic forcing, in both its stable and unstable parts. The single-mode response around a symmetric resonance as well as the coupled response around an asymmetric resonance, involving two companion modes in 1:1 internal resonance, is accurately measured. For the latter, a particular location of the patches and additional signal processing is proposed to spatially discriminate the response of each companion mode. In addition to a hardening behavior associated with geometric nonlinearities of the plate, a softening behavior predominant at low actuation amplitudes is observed, resulting from the material piezoelectric nonlinearities.

In this study, we address the reduction of structural vibrations by means of an electromagnetic shunt damper (EMSD) combined with a mechanical dynamic vibration absorber (DVA). Two architectures, that differs in the placement of the EMSD with respect to the DVA, are tested, showing that one of them enhances the vibration control. In parallel, three shunt architecture are tested: a resistive shunt, a resonant conservative shunt and a resonant dissipative shunt. Optimal values of the EMSD and DVA parameters are obtained; then, the performances of all architecture, according to relevant criteria, are estimated and compared to a single DVA or a single EMSD. The case of a conservative DVA, that creates an anti-resonance, is particularly targeted. It is shown that the performances rely on two free parameters only: the mass ratio for the DVA and the electromagnetic coupling factor for the EMSD, thus giving generic abacuses that can be applied to any practical cases. Finally, experiments are proposed and a good agreement with the theoretical results is obtained, thus validating them.

Modulated-Demodulated control (or vector control) allows to simultaneously impose amplitude and phase of a resonator. Moreover, the working frequency in the case of discrete-controller is substantially lower than the resonance frequency. However, the design of a such controller can be complex. In this paper, we outline a design directly in the baseband. To do so, the oscillator is modelled as a non-dimensional Multi-Input-Multi-Output system. An optimal control (Linear Quadratic Regulator) framework can then be used to design the controller. Thanks to ad hoc performances criteria, the weighting matrices are systematically specified according to the desired closed-lop time response. The methodology is validated by an experimental results on a plate actuated using piezoelectric patches.

In the field of tactile feedback, researchers try to generate localized stimulations on screens. Some solutions such as time reversal or phased array use vibration induced in the screen equipped with piezoelectric ceramics. We propose to use the modal basis to reproduce a specified velocity field on such devices. We explain the theory and propose a methodology to practically synthesize the voltages to achieved a controlled focusing in a given time. Experiments on a simple demonstrator are in good agreement with the theory for various velocity fields and a reduced number of modes.

In this paper, we address the problem of pull out and stalling of the vector control of the piezo-actuator drive. The model presented reveals the similarities with synchronous machine and therefore we propose the vector control to solve the problem and to enhance its performances. The implementation using a position sensor is tested. Experimental results show that the vector control avoids pull out and reduces dramatically the voltage applied to achieve the same performances. Speed up to 2.5 times the maximum rated speed at full load could be achieved without loss of synchronization.

In this article, we address the model identification of nonlinear vibratory systems, with a specific focus on systems modeled with distributed nonlinearities, such as geometrically nonlinear mechanical structures. The proposed strategy theoretically relies on the concept of nonlinear modes of the underlying conservative unforced system and the use of normal forms. Within this framework, it is shown that without internal resonance, a valid reduced order model for a nonlinear mode is a single Duffing oscillator. We then propose an efficient experimental strategy to measure the backbone curve of a particular nonlinear mode and we use it to identify the free parameters of the reduced order model. The experimental part relies on a Phase-Locked Loop (PLL) and enables a robust and automatic measurement of backbone curves as well as forced responses. It is theoretically and experimentally shown that the PLL is able to stabiliz the unstable part of Duffing-like frequency responses, thus enabling its robust experimental measurement. Finally, the whole procedure is tested on three experimental systems: a circular plate, a chinese gong and a piezoelectric cantilever beam. It enable to validate the procedure by comparison to available theoretical models as well as to other experimental identification methods.

This paper presents the implementation of a novel vibration amplitude control and resonant frequency tracking for Piezoelectric Transducers (PT) and Ultrasonic Motors (USM). It is based on a generalization of the Vector Control Method (VCM) to PT and USM that is explained in the first part. We show that two independent controllers with similar structure are required : one tracks the resonant frequency and the second controls the amplitude.We then present the implementation into a low cost DSP controller with a 200μsec sampling period. Experimental results on a Langevin Transducer achieved a time response of 20msec approximately, and the generality of the method is further demonstrated on a 2D Tactile stimulator at the end of the paper.

This work demonstrates the ability of a torsion-based shear-mode energy harvester to power a sensor module by integrating a temperature sensor circuit with a purpose developed piezoelectric energy harvester. A 10-cm3 energy harvester was developed for this application and was found to produce over 200 µW of maximum power through an optimal load resistance under 0.25 gpk acceleration excitation at its resonant frequency of 237 Hz. This harvester was then tested with two interface circuits: a standard interface diode bridge rectifier and a nonlinear synchronous electrical charge extraction circuit that were compared for their suitability in powering the sensor module. Through this, the synchronous electrical charge extraction nonlinear conditioning circuit was found to have superior performance when charging a capacitor and with DC loads at low voltages and was capable of providing a maximum power output of 37 µW under 0.25 gpk acceleration at 237 Hz. This output power was then used to successfully power a temperature sensor module consisting of a temperature sensor, a microcontroller, and a radio-frequency identification memory chip at a sensing frequency of 0.5 Hz.

In Variable Friction Tactile Displays, an ultrasonic standing wave can be used to reduce the friction coefficient between a user’s finger sliding and a vibrating surface. However, by principle, the effect is limited by a saturation due to the contact mechanics, and very low friction levels require very high vibration amplitudes. Besides, to be effective, the user’s finger has to move. We present a device which uses a travelling wave rather than a standing wave. We present a control that allows to realize such a travelling wave in a robust way, and thus can be implemented on various plane surfaces. We show experimentally that the force produced by the travelling wave has two superimposed contributions. The first one is equal to the friction reduction produced by a standing of the same vibration amplitude. The second produces a driving force in the opposite direction of the travelling wave. As a result, the modulation range of the tangential force on the finger can be extended to zero and even negative values. Moreover, the effect is dependant on the relative direction of exploration with regards to the travelling wave, which is perceivable and confirmed by a psycho-physical study.

This paper deals with vibration control by means of piezoelectric patches hunted with electrical impedances made up by a resistance and a negative capacitance. The paper analyses most of the possible layouts by which a negative capacitance can be built and shows that a common mathematical description is possible. This allows closed formulations to be found in order to optimise the electrical network for mono- and multi-mode control. General analytical formulations are obtained to estimate the performance of the shunt in terms of vibration reduction. In particular, it is highlighted that the main effect of a negative capacitance is to artificially enhance the electromechanical coupling factor, which is the basis of performance estimation. Stability issues relating to the use of negative capacitances are especially addressed using refined models for piezoelectric patch capacitance. Furthermore, a new circuit based on a couple of negative capacitances is proposed and tested, showing a better performance than those provided by the usual layouts with a single negative capacitance. Finally, guidelines and analytical formulations to deal with the practical implementation of negative capacitance circuits are provided.

Tactile interfaces are intuitive but lack of haptic feedback. One method to provide tactile feed- back is to change the friction coefficient of the touch surface. Several small-size tactile devices have been developed to provide programmable friction coefficient based on the squeeze air film effect. This effect is produced by ultrasonic vibration of the tactile plate thanks to piezoceramics. In order to design larger embedded tactile feedback areas, a key issue is the power consumption. In this paper, we present the power analysis of a tactile device which is based on the squeeze film effect. We first investigate the source of power consumption by a series of measurements. Then, an analytical model is developed to estimate the power, which gives the conclusion that, when the vibration amplitude is constant, the power consumption is not related to the number of piezoelectric actuators. According to this result, we design a large area (198 mm × 138 mm) tactile plate with only eight piezoelectric actuators. Experimental results show that the power consumption of the large tactile plate is less than 2 W. Moreover, we also find that the power consumption of the large tactile plate was predictable with the measurement results from small plates with an average error of less than 10%.

When the frequency of the source of vibration of a piezolectric generator is significantly different from its eigenfrequency, the dielectric power losses become prominent and decrease the amount of power which is practically harvested. For off-resonance vibrating frequencies, the optimal operating conditions can be obtained with a Maximum Power Point Tracking method. This paper introduces complex phasors in the study of power conversion for piezoelectric generators. These complex phasors are used to describe three strategies which help simplify the tracking of the optimal generator output power for vibration frequencies which are away from resonance. Experimental results obtained on a prototype illustrate and confirm the approach with the phasor approaches illustrate and confirm the success of the proposed optimal power tracking strategies. Finally, we show that the efficiency results of each strategy depend on whether they are used inside or outside a frequency bandwidth around the eigenfrequency, and that the length of this bandwidth depends on the excitation amplitude.

This paper presents the modeling of forging processes assisted by vibrations. A piezoelectric actuator is used to generate specific low-frequency vibration waveforms superimposed to the forging motion. Experimental results show a reduction of the forging load during upsetting tests. However, the appropriate waveforms and their influence on the forging load are still poorly understood. Moreover, the requirements of actuators and the design of the control should be known in advance. Therefore, there is a need for simulation to predict those issues. Due to the complexity of the interactions between the different components of the system, a complete model of the process is proposed. It is developed using an energetic macroscopic representation to preserve causality throughout themodeling. Simulation results are then compared with representative experimental results.

This paper presents the closed-loop control of exciters to produce a traveling wave in a finite beam. This control is based on a dynamical modeling of the system established in a rotating reference frame. This method allows dynamic and independent control of the phase and amplitude of two vibration modes. The condition to obtain the traveling wave is written in this rotating frame, and requires having two vibration modes with the same amplitude, and imposing a phase shift of 90?? between them. The advantage of the method is that it allows easy implementation of a closed loop control that can handle parameter drift of the system, after a temperature rise, for example. The modeling is compared with measurement on an experimental test bench which also implements real-time control. We managed to experimentally obtain a settling time of 250 ms for the traveling wave, and a standing wave ratio (SWR) of 1.3.

A piezoelectric generator converts mechanical energy into electricity and is used in energy harvesting devices. In this paper, synchronisation conditions in regard to the excitation vibration are studied. We show that a phase shift of ninety degrees between the vibration excitation and the bender’s displacement provides the maximum power from the mechanical excitation. However, the piezoelectric material is prone to power losses; hence the bender’s displacement amplitude is optimised in order to increase the amount of power which is converted into electricity. In the paper, we use active energy harvesting to control the power flow, and all the results are achieved at a frequency of 200 Hz which is well below the generator’s resonant frequency.

When the finger interacts with a surface where a purely lateral ultrasonic vibration occurs, a vibration attenuation is produced. An added force is therefore needed in order to maintain the vibration amplitude in closed loop control. In this article we explore whether the friction reduction in lateral ultrasonic surface haptic devices may be predicted using static measurements of this additional force.

Friction attenuation using ultrasonic lateral surface haptic devices (ULSHD) can modify the user perception of the touched surface and induce the perception of textured materials. In the current paper, the mechanisms of friction attenuation using lateral vibration are analyzed at different finger exploration velocities and directions over a plate. A development of a non-Coulombic friction function based on experimental results is proposed and evaluated.

The Vector Control Method applied to piezoelectric transducers is a promising way to track the resonance fre-quency as well as to control the vibration speed. Similar to the modulation-demodulation techniques, the (d,q) transformation applied here takes advantage of the recent advances in microcontrollers. Moreover, engineers can make a bridge between the control of brushless DC motors and piezoelectric actuators and two simple PI controllers, one for each axis are tuned in order to precisely control the vibration amplitude components in axis d and axis q. This paper presents the procedure to tune the PI controllers. First, the model in the rotating reference frame is given. A procedure, based on the LQR approach, is used to calculate the parameters of the PI controllers based on the desired closed loop response time. In the (d,q) reference frame, the second order type response of the system becomes two first order systems, coupled if the system is operated outside its resonance. By taking into account these couplings, the closed loop system can be accelerated, yet ensuring stable operation. In addi-tion to the control, environment’s acoustic impedance can be derived, on line. Finally, we present experimental results, obtained on a haptic display. The model and the measures are consistent, and confirms the approach: the vibration amplitude can be tuned with a response time less than 10ms.

In this paper, we propose a new device in order to produce normal and lateral ultrasonic vibrations in a plate, using an array of piezoelectric ceramics. This setup serves to continue the comparative analysis between the two vibration modes for tactile feedback rendering, by including an energetic characterization. With the help of a tribological analysis, this study will help to examine the energy performance of each vibration mode in terms of active power consumption against friction contrast (which is linked to perception). Using a simplified second order plate model, the energetic results are analyzed. The results show a better energy efficiency for the lateral vibration for low exploration speeds. The tribological analysis helps as well to evaluate the effect of frequency increase in terms of friction reduction vs. vibration amplitude for both vibration modes

In this paper, we present a method to observe the fundamental of the acoustical finger force for the case of a friction reduction based haptic interface. The capability of the method to be achieved on-line, in a small micro-controller is established. We show a correlation between this measurement and the friction when sliding the finger. A model that predicts the friction coefficient and the friction contrast is laid down; it gives consistent output for 10 participants out of 12 having different biomechanical parameters of the skin.

The influence of the vibration frequency on the friction reduction of an ultrasonic haptic surface has been reported in the literature. The models predict that increasing the frequency of the vibration leads to higher friction reduction at constant vibration amplitude, but this has not been reported experimentally. In this paper, we study the friction reduction on a prototype which can vibrate at low (66kHz) and high (225kHz) frequency. By estimating the Point of Subjective Equivalence between a standard at low frequency with a sample at high frequency, we have found that high frequencies can indeed reduce the friction, with the advantage of much smaller vibration amplitude. Moreover, we show that the invariant between the two frequency conditions is not the vibration amplitude. Our conclusion is that the invariant could be the acceleration instead.

The multimodal control of a 2D controlled-Friction Device is presented. We use the Vector control method because the phase and amplitude of two vibration modes at a same frequency can be precisely set. The closed loop response time of 10msec is achieved. The device is then associated with a finger position sensor. The algorithm of the multimodal approach is then tested. In spite of the inevitable limitations of the system - saturation of amplifiers, low sampling frequency of the sensor - low friction could be imposed under one finger and high friction on a second one in the same time. This confirms the validity of the modal approach to create multi touch interactions.

In this study, we develop and implement a method for superimposing two vibration modes in order to produce different tactile stimuli on two fingers located in different positions. The tactile stimulation is based on the squeeze film effect which decreases the friction between a fingertip and a vibrating plate. Experimental test have been conducted on a 1D tactile device. They show that it is possible to continuously control the friction on two fingers moving independently. Then, we developed the design of a 2D device based on the same principle, which gives rise to the design of a two-fingers tactile display. Evaluations were conducted using a modal analysis with experimental validation.

Among human senses, touch is much less understood than hearing or sight. However, today, new emerging technologies are placing tactile interaction at the heart of the communication with smart devices (smartphones, tablets,…). Hence, studying the sense of touch is now very important, in order to better understand the mechanisms induced from the mechanical excitation of skin to the feeling experienced by a user. Also, being able to detect and measure tactile disabilities, and to propose rehabilitation is a challenge; otherwise, numerous people can drift away from these objects as they can't be used easily by them. In the paper, we present Dtact, a device which stimulates the finger pulp with a calibrated stimulation. It is designed to be used during experimental studies aiming at recording nerves and brain activity of a user touching its surface. It will be used to detect tactile disabilities …

The PAD motor has remarkable abilities for ultra-precise positioning at very low speed. Recent works have shown the possibility to extend its speed range, but some challengess remain such as pull-off. This paper proposes a model that highlights the parameters of the voltage supply that act on the torque and the contact, and can be used for control. Experimental results demonstrate the role of higher vibration modes, and show that typical signature of the imminence of pull-off can be detected thanks to some of the harmonic of the displacement of the actuators, giving some indications on means to address this problem.

In this paper, the control of the vibration amplitude of a Langevin transducer is obtained simultaneously with the tracking of its resonant frequency. Vector control method is applied to achieve this. The result of this study is illustrated with experimental and simulation results.

This paper presents a method to control ultrasonic waves on a beam, allowing to obtain a Multi-touch ultrasonic tactile stimulation in two points, to give the sensation to two fingers, from two piezoelectric transducers. The multi-modal approach and the vector control method are used to regulate the vibration amplitude, in order to modulate the friction coefficient with the fingers. An analytical modelling is presented, with experimental validation. Finally a psychophysical experiment shows that a multi-touch ultrasonic tactile stimulation is possible.

The control of the vibration amplitude, and the resonance frequency tracking for ultrasonic transducer have been established. However, some applications require to control the vibration amplitude and its relative phase at a fixed frequency as the generation of travelling wave. In this paper, the transducer is modelled in rotating frame, and the decoupling according to two-axis allows to obtain a double independent closed loop control to address this issue. It is possible to control the transducer vibration amplitude and its relative phase, in steady state even in transient by acting on the amplitude of the supply voltage. Thanks to vector control method. This approach will be confirmed with experimental and simulation results.

This paper presents a new method to produce and control the vibration amplitude and direction of a travelling wave in a finite beam, using multi-modal approach. A closed loop control of the transducer vibration is applied using vector control method. the modelling in rotating frame and the decoupling according to two-axis allows to obtain a double independent closed loop control. This allows to regulate the vibration amplitude of the travelling wave directly. An analytical modelling is presented, with experimental validation, showing good performances even in the presence of perturbations.

This paper presents the design of a mechatronic system integrating piezoelectric multi-actuators, which is used to generate low-frequency vibrations to assist the forging process.With the aim of controlling the complete system, modelling using Energetic Macroscopic Representation is performed. A prototype with an electrical system is developed in a short term to validate the design. Finally, the preliminary experiments are presented with the corresponding simulation’s results.

The paper presents a serial architecture of an actuated manipulator which uses an ultrasonic motor. The serial architecture allows to modify the kinetic relationship between user’s input and a tool. The design of the device is presented. A load, which exhibits fine details, is used in order to show how a zooming effect of its haptic rendering can be achieved with the haptic magnifier. Finally, the design is validated through an experimental analysis.

We study the effect of feedback on an energy harvester for broadband applications. Using modal analysis we show that it has an influence on modal shape as a side effect of the resonance shifting. We show that the piezoelectric coupling can thus be reduced. Experimental results are in agreement and also reveal that non-linear effects are promoted in some cases.

Friction reduction based tactile devices use an ultrasonic vibration to create an overpressure between a user’s fingertip and the vibrating surface. This phenomenon is called "the squeeze film effect". This is an emerging technology to produce a haptic feedback on the touchscreen of handheld electronic devices. In this paper, we present the technology and the main technological issues to be improved.

We study the effect of feedback on an energy harvester for broadband applications. Using modal analysis we show that it has an influence on modal shape as a side effect of the resonance shifting. We show that the piezoelectric coupling can thus be reduced. Experimental results are in agreement and also reveal that non-linear effects are promoted in some cases.

This paper deals with an one-dimensional semi-analytical modelling of the vibratory behaviour of a rectangular beam excited by several piezoelectric ceramics glued on its lower face. The establishment of the equations of motion is guaranteed by the application of Hamilton’s principle. From this approach, it results an accurate knowledge on the mode shape in function of the geometry, the structure and the positions of the piezoelectric actuators. This approach deployed on a simple case falls within a general process of the tactile surfaces optimization. This article shows that there is a trade-off between the optimization of the homogeneity of the tactile stimulation and the electromechanical coupling factor.

In this paper, we propose a power supply for piezoelectric actuators that can generate arbitrary waveforms at frequencies ranging from low to medium frequency. The actuators are used in a forging process and require high voltage. The converter is based on an original combination of a boost DC-DC converter and a rectifier circuit, thus reducing the number of components needed. Moreover, no transformer is required. Experimental results on a single and three phase version are presented and validate the proposed converter.

This paper deals with the control of a haptic device which is used in a generator mode to produce electricity from a user’s walking movements in a handheld device, like a mobile phone for instance. We first present the design principle of such a device. Then, a design is presented, which allows haptic feedback and energy harvesting to be produced with a same device. It is based on a piezoelectric plate actuator. A causal modelling of the system is then developed, and inverted in order to obtain the key control algorithms. Compared to other energy harvesting system, HarTic is characterized by some interesting features like the accelerometer which is now embedded into most mobile phones, and its measurement can be used in the energy harvesting strategy. Our simulations show that 2mW can be harversted in our case study.

Ultrasonic vibrations are used to modulate the friction coefficient between a sliding surface and the vibrating object. In this paper an ultrasonic travelling wave is used to modulate the friction accordingly to the direction of motion of the finger. In its propagation direction, the travelling wave applies a net force on the sliding body reducing the friction whereas in the other increases it. The ability to obtain an asymmetric friction coefficient in function of the motion direction has made possible to induce different sensation on the finger accordingly to the controlled direction of travelling wave.

Use of vibration in the forming process has already shown numerous advantages in the improvement of mechanical and surface properties of workpiece such as good surface or less friction between die and workpiece. The aim of this work is to develop a mathematical model of a progressive wave in the lower die due to the vibration given by multi piezoelectric actuators to assist the forging process. Based on the mathematical model, simulations using finite element software Forge2011 have been performed to observe the presence of progressive wave in the workpiece due to the movement of the lower die. The simulations’ results conrm the existence of progressive wave in the workpiece and demonstrate the effect of progressive wave to reduce the forging load and improve the forging process.

The invention relates to a touch interface comprising, on the one hand, an interfacial surface able to generate a haptic-feedback effect in response to a touch of said surface by a user, and, on the other hand, at least one piezoelectric actuator configured to generate, in said interfacial surface, at least one wave of ultrasonic frequency able to endow the particles of this surface with an elliptical movement having a movement component tangential to said surface, which component is denoted ut(t), and a movement component normal to said surface, which component is denoted un(t), wherein said wave of ultrasonic frequency is chosen so that the amplitude Ut of the tangential component ut(t) and the amplitude Un of the normal component un(t) are substantially equal.

A system includes sensor-actuator units fixed onto a plate to be actuated according to at least one predetermined vibratory mode, each sensor-actuator unit having an electromechanical actuator and a deformation or vibratory speed sensor, wherein the electromechanical actuator and the sensor are colocated on the surface, that is to say that the measurement by the sensor is performed in immediate proximity to the electromechanical actuator, this proximity being such that the actuator and the sensor can respectively actuate and measure the same predetermined vibratory mode.

Les vibrations, ou plus généralement les oscillations dans un système sont un champ d'études et de préoccupations important en physique et en ingénierie. Dans ce domaine, les résonances occupent naturellement une place particulière soit pour leurs conséquences potentiellement catastrophiques, soit au contraire pour leurs propriétés d'amplification. Ainsi à côté des techniques d'atténuation des vibrations bien connues en acoustique ou en génie mécanique et civil, nombreuses sont les applications qui à l'inverse les exploitent dans les procédés (soudage par ultrason de plastiques, "defouling"), le médical (échographies, destruction de calcul rénaux ou de tumeurs, réactions chimiques localisées par sonochimie), les MEMS (accéléromètres, détection moléculaires), ou l'instrumentation (microscope à force atomique). Dans ces exemples, la vibration à la résonance est recherchée, et il peut s'avérer nécessaire de les immuniser vis à vis de perturbations extérieures. \\ A des échelles centimétriques et des vibrations de l'ordre du micromètre, les matériaux piézoélectriques possèdent des propriétés particulièrement intéressantes en particulier en terme de bande passante. Cependant du fait qu'ils soient partie intégrante d'une structure, leur utilisation demande une expertise spécifique, que ce soit au stade de la conception mécanique ou de leur alimentation. Ainsi le praticien doit être attentif à des caractéristiques particulières tel que, par exemple, le facteur de couplage, ou encore les courants réactifs induits par la nature capacitive des céramiques. Dans ce contexte la modélisation est incontournable mais les outils obtenus doivent être exploitables et interprétables pour une utilisation efficace. Avec une vision plus large, à l'échelle du système, les performances de tels dispositifs peuvent bénéficier des apports de la commande. Il est alors nécessaire de disposer de modèles adaptés, tout en assurant une cohérence et une hiérarchie des modèles en terme de précision et de simplicité dans une démarche mécatronique. Dans ce cadre, une approche développée dans notre équipe consiste à exploiter l'approche modale en s'appuyant sur la généralisation basée sur des modes électromécaniques. Grâce à cette description, la proposition adoptée dans l'activité "dispositifs piézoélectriques" du L2EP pour la réalisation d'interface tactile a été de généraliser la commande vectorielle des machines au vibration, qui s'apparente aux commandes par modulation/démodulation rencontrées dans la littérature, en l'enrichissant par une connaissance de la physique du système. Depuis, nous avons proposé une extension à la commande simultanée de plusieurs modes.\\ La transposition de la génération de stimuli par superposition de modes à l'élimination de modes de vibrations d'une structure se fait alors naturellement en conservant le principe. Cette voie a été à l'origine de travaux communs avec le LISPEN. Cette collaboration a depuis évoluée par une influence mutuelle des visions et une mise en commun des outils de nos communautés respectives. Ainsi, il a été identifié que l'électronique de puissance, en modifiant les flux d'énergie dans des systèmes électromécaniques permettait d'introduire volontairement des non-linéarités pour tirer profit de leur comportement particuliers et conférer des fonctionnalités nouvelles. En s'appuyant sur certaines propriétés spécifiques de certains modes non-linéaires, la commande permet d'en étendre le domaine d'application en introduisant des capacités d'adaptation et en améliorant leur robustesse

This chapter presents a preliminary overview of the state-of-the art in the field of piezoelectric actuators. Starting from the material, and describing its manufacturing process, we present several ways to exploit the energy conversion in order to obtain the displacement of a mechanical load. The basic principles of some widely used piezoelectric actuators and motors are presented, and illustrated with typical applications. The chapter also discusses the variability of the operating point of the piezoelectric actuators, and explains why a closed-loop control is needed. The chapter ends with the basics of the control theory, which are used in later chapters to design controllers.