A differential quadrature procedure for free vibration of circular membranes backed by a cylindrical fluid-filled cavity

This paper presents a numerical procedure using the differential quadrature method (DQM) to study the free vibration of circular membranes backed by a cylindrical fluid-filled cavity. The governing differential equation of the circular membrane and that of the circular cylindrical fluid cavity are first discretized using the DQM. By applying the fluid–membrane interface boundary condition, the governing eigenvalue equations of the coupled system are then obtained which can be solved for the eigenvalues of the system. Computational issues related to the singularity of the stiffness matrices of the membrane and fluid are also addressed. Two different new approaches are proposed to overcome these issues. The applicability of the proposed approaches is shown herein through the numerical simulations. The results generated by the proposed approaches are compared with the analytical and numerical results available in the literature. Numerical results prove that the proposed approaches are highly accurate and reliable.