Differential quadrature analysis of free vibration of rhombic plates with free edges

An accurate free vibration analysis of rhombic plates with free edges is presented by using the modified differential quadrature method (DQM). Fourteen combinations of boundary conditions with free edges and five skew angles for each plate are analyzed. It is found for the first time that the problem is extremely sensitive to grid spacing and the method to applying the multiple boundary conditions when the skew angle is very large. Various existing non-uniform grid spacing and methods for applying the multiple boundary conditions are tested. It is surprising to see that DQM with only one grid spacing can yield accurate and reliable solutions, besides applying boundary conditions correctly at free corners is also important for success. For verifications, the DQ results are compared with either existing accurate solutions or data obtained by finite element method. Due to bending stress singularities occurred at corners having obtuse angles, the rate of convergence is low for a few cases and quite different from rhombic plates without free edges. Some new results are presented and waiting for comparison with future data obtained by other investigators.