Roger Ohayon

New Thin Piezoelectric Plate Models

Early investigations on piezoelectric plates were based on a priori mechanical and experimental considerations. They assume plane stress and consider only transverse components of electric displacement and field. Beside, these were supposed constant in the plate thickness. Through an asymptotic analysis, this paper shows that mechanical hypotheses follow Kirchhoff-Love theory of thin plates. However, electric assumptions are found to be strongly dependent on the electric boundary conditions. That is, two regular problems should be distinguished: (1) the short circuited plate, for which only transverse electric displacement and field have to be considered-the electric potential is then found to be the sum of a known part, which depends on prescribed potentials, and an unknown part, which represents an induced potential and cannot be a priori neglected; the mechanical and electrical problems may be uncoupled; (2) the insulated plate, for which only in-plane electric displacement and field components are to be considered; the mechanical and electrical problems may be uncoupled for orthorhombic plates but not in general. Based on the above asymptotic analysis, two variational and local two-dimensional static models are presented for heterogeneous anisotropic plates. They are then applied to homogeneous and orthorhombic piezoelectric plates. For homogeneous orthorhombic piezoelectric plates, the electromechanical problem can be uncoupled. Hence, a mechanical problem is first solved for the mechanical displacement, then electric potentials are explicitly deduced from this displacement. Classical finite element codes having multilayer plate facilities can be used for solving the plate problems obtained.

A Fractional Derivative Viscoelastic Model for Hybrid Active-Passive Damping Treatments in Time Domain - Application to Sandwich Beams

This work presents a finite element formulation for the dynamic transient analysis of a damped adaptive sandwich beam composed of a viscoelastic core and elastic-piezoelectric laminated faces. The latter are modeled using the classical laminate theory, which takes the electromechanical coupling into account by modifying the stiffness of the piezoelectric layers. For the core, a fractional derivative model is used to characterize its viscoelastic behavior. Equations of motion are solved using a direct time integration method based on the Newmark scheme in conjunction with the Grunwald approximation of fractional derivatives. Emphasis is given to the finite element implementation of the fractional derivative model and to the influence of the electromechanical coupling.

Structural-Acoustic Vibration Reduction Using Switched Shunt Piezoelectric Patches: A Finite Element Analysis

In this paper, we present a finite element formulation for vibration reduction in structural-acoustic systems using passive or semipassive shunt techniques. The coupled system consists of an elastic structure (with surface-mounted piezoelectric patches) filled with an inviscid linear acoustic fluid. An appropriate finite element formulation is derived. Numerical results for an elastic plate coupled to a parallelipedic air-filled interior acoustic cavity are presented, showing the performances of both the inductive shunt and the synchronized switch shunt techniques.

Advanced Computational Dissipative Structural Acoustics and Fluid-Structure Interaction in Low-and Medium-Frequency Domains. Reduced-Order Models and Uncertainty Quantification

This paper presents an advanced computational method for the prediction of the responses in the frequency domain of general linear dissipative structural-acoustic and fluid-structure systems, in the low-and medium-frequency do¬mains, including uncertainty quantification. The system under consideration is constituted of a deformable dissipative structure, coupled with an internal dissipative acoustic fluid including wall acoustic impedances and surrounded by an infinite acoustic fluid. An efficient reduced-order computational model is constructed using a finite element discretization for the structure and the internal acoustic fluid. The external acoustic fluid is treated using an appropriate boundary element method in the frequency domain. All the required modeling aspects for the analysis of the medium-frequency domain have been introduced namely, a viscoelastic behavior for the structure, an appropriate dissipative model for the internal acoustic fluid including wall acoustic impedance and a model of uncertainty in particular for modeling errors. This advanced computational formulation, corresponding to new extensions and complements with respect to the state-of-the-art, is well adapted for developing new generation of software, in particular for parallel computers.

Semi-active control using magneto-rheological dampers for payload launch vibration isolation

This paper presents some preliminary results concerning semi-active vibration isolation of a spacecraft during its launch using Magneto-Rheological (MR) dampers. In order to evaluate the isolation performance of such smart structures, a single degree of freedom isolation system was studied and the extension to a soft hexapod configuration is currently carried out. Semi-active isolation is known to offer appreciable improvement over passive isolation for tonal vibration. As regards broadband vibration, semi-active control leads to a conflict between the demand for damping, which induces less good isolation performance than for tonal vibration. This paper focuses on semi-active isolation of broadband vibration. In the single degree of freedom configuration, it is demonstrated experimentally that, for an example of broadband disturbance, band-passed white-noise, semi-active isolation using MR dampers performs better than passive isolation for various damping, when using a clipped-continuous skyhook control scheme. Then, a semi-active hexapod prototype using MR dampers is shown. The dynamic modelling of the hexapod as well as the investigated control strategy, a clipped-continuous version of the integral force feedback law are presented. Finally, some preliminary open-loop transmissibilities for a piston motion are measured.

Liquid Sloshing Damping in an Elastic Container

It is proposed to investigate in this paper the damped vibrations of an incompressible liquid contained in a deformable tank. A linearized formulation describing the small movements of the system is presented. At first, a diagonal damping is introduced in the reduced equations of the hydroelastic sloshing problem. We obtain a nonclassically damped coupled system with a damping matrix that is not symmetric. Then, by projecting the system onto its complex modes, the frequency and time responses for different type of loads are built. A numerical application is illustrated on a test case.

Modeling of Plate Structures Equipped with Current Driven Electrostrictive Actuators for Active Vibration Control

The study here reported is focused on active vibration control applications performed on plate host structures equipped with electrostrictive patches. In such applications the design of controllers requires to simulate the behavior of the coupled structure. These simulations can then be performed through a Finite Element Method which implies the elaboration of electrostrictive finite elements. The purpose of the present paper is to use the electrostrictive plate finite element elaborated in a previous paper such as to simulate active vibration control of a cantilever beam equipped with current driven or voltage driven electrostrictive actuators. From these numerical results it is shown that a linear controller is as efficient as a nonlinear one in terms of vibration absorption, whatever the driving input used. An experimental implementation of the current driving input is moreover presented. Based on experimental measurements, it is proved that current driving electrostrictive actuators induce a decrease of electric energy consumption compared to a classical voltage driving input.

PAYLOAD/LAUNCHER VIBRATION ISOLATION: MR DAMPERS MODELING WITH FLUID COMPRESSIBILITY AND INERTIA EFFECTS THROUGH CONTINUITY AND MOMENTUM EQUATIONS

During launching, a payload is submitted to large vibrations, which may damage it. To get rid of the problem, a solution would be to put an appropriate vibration isolator at the payload/launcher interface. Thus, a soft Isolating Payload Attach Fitting (IPAF) using Magneto-Rheological (MR) dampers is envisaged. In a pre-design phase for the launcher application, a preliminary study of the behaviour of a commercial MR damper (RD-1005-3) and its use in a 1-dof vibration isolator is carried out. In this paper, we report the MR damper behaviour analysis based on fluid and solid mechanics equations. In particular, we investigate chambers fluid compressibility and inertia effects. Then the damper model is used to evaluate the performance of a MR isolator in terms of equivalent transmissibility in passive mode and using skyhook control. The theoretical results will be soon compared to those from an experimental bench in construction.

Active control of sound transmission using a hybrid/blind decentralized control approach

This paper presents a theoretical and experimental analysis of broadband sound transmission control of an aluminum panel in the frequency range between 30 Hz and 1 kHz. Based on the analysis of characteristics of sensor-actuator pairs, piezoelectric patches bonded on the structure are used as actuators, and collocated accelerometers are used as sensors. Then a hybrid decentralized control law is derived, which has a broad control band and puts more control authority on the most sound radiation effective mode. This control law comprises two parts: one is the direct velocity feedback controller, and the other one, relatively new, is called the negative acceleration feedback (NAF) controller. The control architecture is decentralized, which means each controller works independently. Due to the second-order dynamic property of the NAF controller and the fact that the structure’s frequencies may shift, the Hilbert-Huang method is used for quick and automatic identification of the natural frequency. Finally, open loop and closed loop experiments are presented to support the theoretical analysis. The active control results demonstrate that the panel’s vibration level can be suppressed by 16.7 dB and the broadband sound pressure level could be lowered by more than 7 dB.

Effect of internal liquids on the vibrations of aerospace structures

The case of structures partially filled with liquids (propellants, cooling liquids, etc.) is very common and many industrial domains are interested in this issue, especially the aerospace industry (for aircrafts, liquid propelled launchers, satellites, etc.). We propose here a linearized formulation to deal with the vibrations of such fluid-structure coupled systems. As our main interest is for weakly damped fluid-structure problems, the study of the conservative (undamped) associated system will be at the center of the method, and the liquid will be considered in a first step as inviscid. Taking into account this assumption, the linearized local equations describing the coupling between a sloshing liquid and a deformable tank will be reminded. Once the variational formulation is established, the integral operators will be discretized by a classical Rayleigh-Ritz Finite Element approach. An a posteriori damping model for the liquid will be introduced in this formulation by assigning to each sloshing mode a damping coefficient that can be evaluated experimentally or numerically. To simplify the construction and the implementation of this sloshing liquid model in a CSM code, a representation of the fluid dynamical loads on the structure wall by an impedance mass matrix will be proposed. In the case where the tank own deformations can be neglected with respect to the global deformations of the main structure, the size of the liquid impedance model will be drastically reduced to ensure low CPU-time and memory consumptions. The versatility of this approach will be illustrated by an application example.