A method for the parametric frequency sensitivity of interior acousto-structural coupled systems

This paper presents an algorithm to compute the derivatives of natural freq uencies of undamped acousto-structural interior coupled systems. The uncoup led modal bases of the structural and acoustic system are used to derive th e modal equations for sound-structure interaction. The governing equations are coupled through velocity terms. This approach allows derivation of a se cond order matrix form with the same characteristics of undamped gyroscopic systems: two diagonal modal mass and stiffness matrices and a skew-symmetr ic coupling one, The eigensolutions of this system possess mathematical fea tures that can be used to compute the derivatives of the coupled frequencie s versus a design parameter in a closed form. As an example, the formulatio n is applied to compute the parametric sensitivities of natural frequencies of a system composed of a rectangular closed cavity coupled to a simply su pported square plate. The design variables are the thickness of the plate a nd the width of the rectangular cavity. The computed derivatives are then c ompared to the sensitivity curves obtained by a Finite Element calculation on an analogous model. (C) 1999 Elsevier Science Ltd. All rights reserved.