Shape sensitivity analysis of sequential structural–acoustic problems using FEM and BEM
Abstract A shape design sensitivity formulation for structural–acoustic problems using sequential finite element and boundary element methods is presented. Frequency-response analysis is used to obtain the dynamic behavior of the structure, while boundary element analysis is used to solve for the pressure response of the acoustic domain. It is shown that the adjoint method, which takes the reverse direction to response analysis, provides a very efficient way of sensitivity calculation. In addition, it has been shown that the adjoint equation for the shape design problem is the same as that of the sizing design problem. The only difference is the numerical integration that evaluates the sensitivity coefficient. The combination of the semi-analytical method for the structure and the analytical differentiation method for the acoustic cavity yields a very practical approach for the shape design sensitivity formulation. The accuracy of the sensitivity information is compared with the analytical sensitivity as well as the sensitivity calculated using the finite difference method.
A numerical structure-borne noise prediction scheme based on the boundary element method, with a new formulation for the singular integrals
Abstract Predicting the noise radiated from vibrating structures is important in the automotive, aerospace, construction equipment, and defense industries. In this paper a numerical implementation of the boundary element method (BEM) in solving the Helmholtz equation for acoustic analysis is presented. The developed code can use the results from a structural dynamic analysis performed by a general-purpose structural finite element code like NASTRAN, to predict the noise emitted from the vibrating structure. A new approach is introduced in this paper to numerically treat the singularity problem inherent in the boundary element methodology for acoustics. The integration scheme and the overdetermination technique used in this development are also presented. The developed computer code is verified by comparison to available analytical solutions. Two practical applications, a vehicle interior noise analysis and a transmission cover noise radiation analysis are presented. Finally, the Rayleigh integral method which is suitable for analyzing plane structures in a baffle is implemented into computer code as an alternative to the BEM formulation, and some verification analyses are presented.
Investigations of dielectric gratings using electrodynamic models based on volume integral equations
Eigenmodes of planar and cylindrical dielectric gratings (DGs) and electromagnetic wave scattering from multiplayer DGs are investigated. The DG characteristics are calculated using numerical-analytical solution of integral equations (IEs).