Minimization of Sound Pressure Levels in Vibro-Acoustic Systems Using Optimal Distribution of a Viscoelastic Damping Layer

An efficient damping layout optimization method of structural-acoustic systems is proposed to minimize acoustic responses using a gradient-based optimization algorithm. To analyze vibro-acoustic systems, a hybrid model that uses finite elements for the structures and boundary element for the cavity is developed. The four-parameter fractional derivative model is used to represent the dynamic characteristics of viscoelastic materials with respect to frequency and temperature. Using the equivalent stiffness for the structure with an unconstrained damping layer, a finite element is developed and a nonlinear eigenvalue problem is solved. Responses of the structure are calculated by using the modal superposition method and plugged into the velocity boundary conditions of boundary integral equation for the cavity. The acoustic design sensitivity information is obtained from the discrete boundary element equations using the direct differentiation method. The design sensitivity formula of the structure response is also derived and inserted into the acoustic boundary sensitivity equation as a boundary condition, which consists of eigenvalue and eigenvector sensitivity expressions. A two-dimensional numerical example is introduced to validate the proposed method. To obtain the optimal damping layer layout that gives a minimum sound pressure level over a specified frequency range, the area of the sound pressure level graph in decibel scale is introduced as an objective function. The optimal damping layer layout is identified according to temperatures and the amount of damping material. The numerical results show that the proposed optimization formulation systematically gives the damping treatment layout that minimizes acoustic responses