FREE VIBRATION ANALYSIS OF ARBITRARILY SHAPED PLATES WITH CLAMPED EDGES USING WAVE-TYPE FUNCTIONS

The basic idea related to the non-dimensional dynamic influence (Greenʹs) function defined in an infinite membrane has been applied to the free vibration analysis of arbitrarily shaped plates with clamped edges. Another non-dimensional dynamic influence function newly defined in the paper exactly satisfies the governing homogeneous differential equations of plates and is regular in the entire domain. The proposed method uses the boundary discretization scheme similar to that of the boundary element method but does not require any interpolation function between the nodes distributed along the boundary. As a result, the method has a significant advantage in its simplicity and accuracy. Although the method uses no interpolation function, it gives very accurate eigenvalues and mode shapes compared with the exact solutions or FEM results. It should be also noted that particular attention is given to reduce the size of the system matrix whose determinant equation yields eigenvalues, and to overcome the functional dependence problem of the non-dimensional dynamic influence functions.