Time-domain analysis of transient structural acoustics problems based on the finite element method and a novel absorbing boundary element

This paper is concerned with the development of an efficient and accurate finite element procedure for the solution directly in the time domain of transient problems involving structures submerged in an infinite acoustic fluid. The central feature of the procedure is a novel impedance, or, absorbing boundary, element that is used to render the computational domain finite. This element is local in both time and space, and is completely defined by a pair of symmetric stiffness and damping matrices. It thus can be attached directly to the adjoining fluid elements within the computational domain using standard assembly procedures. Due to its local nature, it also preserves the overall structure of the global equations of motion, including symmetry and sparseness. Thus the new impedance element makes it possible to solve complex transient exterior structural acoustics problems via existing finite element software for interior problems by just incorporating this element into current finite element librafids. Standard step-by-step temporal integration techniques can then be used to solve the resulting equations of motion. Even though the focus is in the time domain, the same equations of motion can naturally be used to determine the solution under time-harmonic excitation directly in the frequency domain. In this paper the new methodology is presented in a two-dimensional setting, using as a model an infinite cylindrical thin elastic circular shell submerged in an acoustic fluid. The absorbing element, however, can be used equally well with any arbitrary (possibly nonlinear) two-dimensional structure. Explicit formulas for the element matrices are included, and numerical examples, involving both transient scattering and radiation model problems, are given for the homogeneous hell as well as for a shell with a concentrated mass to illustrate the validity and accuracy of the new procedure.