An efficient differential quadrature methodology for free vibration analysis of arbitrary straight-sided quadrilateral thin plates

Abstract

In this paper, a new differential quadrature (DQ) methodology is employed to study free vibration of irregular quadrilateral straight-sided thin plates. A four-nodded super element is used to map the irregular physical domain into a square domain in the computational domain. Second order transformation schemes with relative ease and less computation are employed to transform the fourth order governing equation of thin plates between the two domains. The only degree of freedom within the domain is the displacement, whereas along the boundaries, the displacement as well as the second order derivative of the displacement with respect to associated normal co-ordinate variable in computational domain are the two degrees of freedom. Implementing the method, the formulation for the DQ method for the free vibration analysis of plates of straight-sided shapes was presented together with the implementation procedure for the different boundary conditions. To demonstrate the accuracy, convergency and stability of the new methodology, detail studies are made on isotropic plates at acute angles with different geometries, boundary and loading conditions including DQ free-edge boundary condition implementations. Accurate results even with fewer degrees of freedom than for those of comparable numerical algorithms were achieved.