Michel Brissaud

Modelling of a cantilever non-symmetric piezoelectric bimorph

The aim of this paper is the modelling of a non-symmetric bimorph constituted by a piezoelectric material deposited on an alumina substrate and used either as an actuator or a sensor. Theoretical modelling based on the flexural modes of the structure is carried out and the influence of the electrode characteristics (geometrical dimensions and elastic parameters) is introduced in the modelling for calculating the bimorph bending displacement. In actuator mode, the electrical admittance of the cantilever non-symmetric bimorph is stated and the intrinsic electromechanical coupling factor linked to the bimorph bending motion is deduced and compared with that defined in IEEE Standards. The analytical modelling was used for characterizing a cantilever bimorph constituted by a piezoelectric thick film deposited on an alumina substrate. A trial and error fitting method is described for determining the elastic, piezoelectric and dielectric constants of the piezoelectric material. The influence of the electrode parameters is calculated and the measurement uncertainty is deduced. In sensor mode the open voltage delivered by the bent piezoelectric layer and the electrical equivalent circuit of the bimorph are given. Theoretical results are compared with those obtained by the finite element method, and discussed.

Magnetostrictive pulse-echo device for non-destructive evaluation of cylindrical steel materials using longitudinal guided waves

A magnetostrictive device for the low-frequency (<500 kHz) ultrasonic testing of elongated ferromagnetic structures is presented. The device consists of two transducers, one transmitter and one detector, and operates in pulse-echo mode. The axisymmetric geometrical arrangement of the device is designed for the generation and detection of longitudinal mechanical waves. From experimental observations, the non-linear behaviour of the magnetostrictive transduction versus the polarizing current intensity and amplitude of the driving current is illustrated for different material samples. Concurrently, according to the non-contact nature of the magnetostrictive transducers, the device is used for the study of guided wave propagation in structures. Hence, operating on the experimental data set with a signal processing technique, good agreement of predicted and experimental group velocities of multimodal longitudinal waves in axisymmetric cylindrical structure is achieved. Finally, a pulse-compression technique is applied to defect detection.

Modelling of non-symmetric piezoelectric bimorphs

This paper deals with the modelling of non-symmetric piezoelectric bimorphs used in micromechanics or microsystems (MEMs). An analytical modelling including the elastic and geometric parameters of the substrate, bonding material, piezoelectric layer and electrodes is carried out. This model has been applied to bimorphs having different types of boundary conditions, that is clamped edges (CC), clamped and free edges (CF) or simply supported edges (SS). When the bimorph is used as an actuator, the resonance frequency and displacement of different types of bimorphs are calculated. Open circuit voltage, displacement and resonance frequency are determined when the bimorph is used as a sensor. The influence of the parameters of the bonding layer has been determined. A new method for calculating the global quality factor of bimorphs versus the quality factor of each layer is given. This method can easily be applied to all types of bimorphs (CC, CF, SS). The analytical form of the evolution of the resonance frequency and the sensitivity is deduced from the general modelling and theoretical models and are compared to those given by the finite element method and discussed.

Three-dimensional modeling of piezoelectric materials

This paper deals with 3-D modeling of piezoelectric materials. The model is based on an exact description of the potential and electric field inside a material. Moreover, coherent piezoelectric equations are used. Modeling has been applied to rectangular and cylindrical elements. In each case, the exact equations of the displacements along the three coordinate axes and the corresponding electric impedance are calculated. The general resonance conditions are stated for these two geometries. It is shown that, contrary to the 1-D models, a unique equation describes lateral and thickness vibrations, or radial and thickness vibrations. These properties enable us to analytically calculate the frequency spectrum of rectangular elements, thick disks, or cylinders and also thick rings or hollow cylinders versus the width to thickness ratio. It is then very easy to determine the corresponding dispersion diagram related to each geometry sample. These resonance conditions are similar to those deduced from the 1-D model described in the IEEE standard but are more general and necessitate no cancelling out assumptions. In addition, contrary to 1-D models, the wave velocities and the permittivity are independent of the element geometry (parallelepiped or cylindrical). The wave velocities are equal to those stated for the wave propagation in infinite medium and measured with pulse-echo techniques. It is the coupling inside the material which modifies the resonance conditions and not the geometrical dimensions of the vibrating element. 3-D modeling and 1-D radial mode of the admittance of a thick disk are calculated and compared with experimental measurements. Theoretical and measured admittances are compared and discussed.

Modal control of beam flexural vibration

An active control system was developed to control the flexural vibrations of a beam with a modal filtering with only one secondary actuator. Segmented piezoelectric actuators and sensors were used for driving and sensing the bending beam vibrations. The primary actuator was fed by a broadband random disturbance signal in order to excite the first five modes of the structure. However, only the second to fifth modes were controlled. The control algorithm was implemented on a DSP board and the input and output signals were filtered using high order low pass filters. These filters, implemented on the DSP board avoid the degrading effect on the control performances of the higher order modes and which are not controlled. The modal filtering was achieved by computing. To this end, it is based on a previous identification procedure. This latter models, in one step, the dynamics of the structure and also the transfer function of the electronic circuits of the controller. The identified filtered modes were then used to compute the gain matrix using a LQR technique (linear quadratic regulator). Simulations of the active control were carried out and practical implementation of the control algorithms was performed. Experimental and simulation results were then compared and discussed.

Spatial analysis of torsional wave propagation in a cylindrical waveguide. Application to magnetostrictive generation

A spatial analysis of the generation and propagation of torsional waves in a cylindrical rod is presented. Starting from the classical linear equation of propagation and assuming a linear medium of propagation, the eigenfunctions of the propagation operator are calculated. Under the hypothesis of separation-of-variables type of solution, two ways of deriving the associated modes are performed. Given the normal mode basis, the behavior of a wavefront generated into the rod is examined. The application to the magnetostrictive generation of torsional waves is studied. Including the influence of eddy currents on the excitation and the geometry waveguide effects on the wave propagation, an analytical expression of mechanical losses during the first steps of propagation is given. A basic model of the interaction between a defect and the torsional guided waves is also proposed.

Theoretical modelling of non-symmetric circular piezoelectric bimorphs

This paper deals with the theoretical modelling of non-symmetric and symmetric circular bimorphs. The model is restricted to the study of flexural vibration modes having radial symmetry (axisymmetry), as is often the case for piezoelectric devices such as MEMs. The calculation of the resonance frequencies and the displacement of the non-symmetric circular bimorph has been carried out and the influence of the elastic and geometric parameters of the cement layer has been introduced into the model. As is shown, the modelling of non-symmetric and symmetric circular bimorphs reduces to the determination of two global quantities: the global rigidity DG and the global Poisson ratio σG of the bimorph which is then equivalent to a homogenous element. Consequently, the results obtained with elastic and homogeneous circular plates can be applied to non-symmetric and symmetric bimorphs with the only condition of using the global DG and σG. The new modelling was applied to bimorph functioning either as an actuator or as a sensor and having a simply supported or clamped edge. The electromechanical coupling factor of flexure modes has been calculated and compared to the radial mode. Comparison between analytical models and simulations using the finite-element method is given and discussed.

Piezoelectric actuator for pulsating jets

Recent researches in aeronautics showed that fluidic actuator systems could offer possibilities for drag reduction and lift improvement. To this end many actuator types were designed. This paper deals with the design, fabrication and test of piezoelectric actuator in order to generate pulsated jets normal to a surface and control air flow separation. It is based on the flexural displacement of a rectangular metal plate clamped on one of its large edge. Piezoelectric patches cemented on the plate were used for driving into vibration the actuator. Experimental measurements show that pulsed flow velocities are adjustable from 1.5m/s to 35m/s through a 100x1mm2 slit andwithin a 100 to 400 Hz frequency range. Prototype provides the jet performances classically required for active control flow.

Characterization of rectangular and cylindrical piezoceramics using three dimensional modelling

ABSTRACT This paper is devoted to piezoceramic characterization using 3D-modelling. It is applied on Navy III and Navy II elements. The influence of coupling on resonance frequencies is analysed. It is shown that velocities are independent of the element dimensions and coupling is asymmetrical because it is generated by elastic constants . Characterization is described and the determination of six elastic constants (), two piezoelectric coefficients () and permittivity is explained. Calculation needs only one element: parallelepiped or cylindrical. The error made on resonance frequencies using 1D-models is deduced and can reach 20% when certain element shapes are employed.

Active-control headset protector using piezoceramic material actuator

This paper describes the achievement of active control headset protector using piezoceramic actuators leading to a noise attenuation of about 20 dB within a 1 kHz frequency span located at around 1 to 2 kHz. To this end, several types of piezoceramic transducers or actuators have been designed and tested. They are based on flexural modes of bimorphs constituted by a thin piezoelectric ceramic disk cemented on a metallic plate. The main problems encountered are the spurious frequency regenerations which mask the noise reduction in the expected frequency range. Thus only a few of them meet the above specifications and can be used for reducing the noise inside the headset protector.