Vibration Reduction of Structural-Acoustic Systems Using Synchronized Switch Damping Techniques

In this paper we present numerical results concerning vibration reduction of structural-acoustic systems using the synchronized switch control technique. In order to develop a general procedure to model the coupled system (composed by the fluid domain, the structure and the piezoelectric elements), the idea is to use the performances of a standard commercial code such as Nastran. A symmetric reduced order model is derived from a general finite element description through the extraction of appropriate system matrices. For sake of brevity, we just recall that depending upon the choice of fluid field variables, non symmetric formulations are usually obtained (so-called displacement-pressure formulations), the symmetrization can be derived through appropriate choice of fluid field variables [1, 2]. A simple fluid-structure system for which an analytic solution exists will be used to verify the finite element results and to demonstrate the capabilities of the control procedure. Referring to experimental tests [3], the system consists of a straight air-filled tube with a square cross section. The tube is a rigid cavity with an elastic plate at one end and a piezoelectric patch bonded in its centre. Firstly, the conservative structural-acoustic problem is presented. The symmetric variational and finite element formulations are then described. The model is constructed using Nastran software and the finite element matrices are then extracted and assembled in Matlab. In a second step, the electro-mechanical coupling matrices are built using three-dimensional finite elements in order to take into account local moments of the piezoelectric wafers according to the equivalent thermal coefficient theory [4, 5]. Finally, the reduced electro-mechanical fluid-structure system, obtained through a modal projection, is integrated in time using a Newmark type algorithm. Numerical results are then presented showing the performance of the synchronized switch damping for vibro-acoustic applications in the low frequency domain (low modal density).