FREE VIBRATION ANALYSIS OF RIBBED SKEW PLATES WITH A MESHFREE METHOD

Based on the first-order shear deformation theory (FSDT), a meshfree method for solving the free vibration problem of ribbed skew plates is proposed. The plates and ribs are discretized with a series of points to obtain a meshfree model of the stiffened plate. The FSDT and the moving least-squares approximation are used to establish the displacement field. The total dynamic energy and total potential energy of the stiffened plate are obtained by simulating the ribs as beams. The governing equation for the free vibration of the stiffened plate is derived by the Hamilton principle. The boundary condition is introduced by the full transformation method, and the free vibration frequencies are solved. Several examples are calculated, and the results given by the proposed method are compared with those from other researches or ABAQUS. The results show that the method can effectively analyze the free vibration problem of ribbed skew plates and can avoid the redistribution of plate nodes when the rib position changes.