Element Differential Method for Vibro-Acoustic Problems in Time Domain

In this paper, a new numerical method, named element differential method (EDM), is developed to solve vibro-acoustic problems in time domain. The key methodology of the method is the direct differentiation of the shape functions of the isoparametric elements used to characterize the geometry and physical variables, which can be utilized to evaluate the spatial partial derivatives of the physical variables appearing in the governing equations and boundary conditions. Moreover, a unique collocation technique is proposed to form the system of equations, in which the corresponding governing equation is collocated at internal nodes of elements, and the acceleration/traction equilibrium equation is collocated at interface nodes between elements, outer surface nodes, and mechanics-acoustic domain interface nodes. Based on the Newmark difference technique, a time marching solution scheme is developed for solving the time-dependent system of equations. EDM is a strong-form numerical method that does not require a variational principle or a control volume to set up the computational scheme, and no integration is required during the solution process. Three numerical examples are given to demonstrate the correctness and application potential of the developed method.