APPLICATION OF FREE VIBRATION ANALYSIS OF MEMBRANES USING THE NON-DIMENSIONAL DYNAMIC INFLUENCE FUNCTION

In this paper, the multi-domain method of subdividing the membranes of interest into several domains is presented for applications of free vibration analysis of arbitrarily shaped membranes. The method is especially effective for concavely shaped membranes with high concavity and multi-connected membranes with a hole, compared with the single-domain method. The frequency equations of these membranes are given by the determinants of the system matrices obtained when the compatibility conditions are considered on the common boundaries along which the sub-domains adjoin each other. Although many boundary nodes are distributed along the fixed boundaries on which transverse displacements are prescribed to be zero, the number of boundary nodes has no effect on the order of the system matrix. The order is determined to be equal to the value corresponding to twice the number of interior nodes distributed on the common boundaries. Thus, eigenvalues, the roots of the frequency equation, may be obtained from the determinant of the system matrix of a small order. The case studies presented in the paper reveal that the eigenvalues calculated by this method are in good agreement with those obtained by the FEM program, ANSYS.