Dynamic inhomogeneous finite element method for dynamic response analysis of the 1D inhomogeneous media with the variable section area

Dynamic response problem in the inhomogeneous media is a hot topic. In this paper, dynamic inhomogeneous finite element formulations are given for dynamic response analysis of 1D inhomogeneous medium with variable section area. The dynamic equilibrium equation is given first. Then, the equation's weak formation is derived by weight residual method. The expressions of inhomogeneous element stiffness and mass matrices are observed. Then, two equivalent relationships about stiffness and mass are presented. The same equivalent coefficients, initial and boundary conditions lead to the same response solution. In addition, the results of the example show that this dynamic inhomogeneous finite element approach has a high degree of accuracy and high efficiency.