The Generalized Differential Quadrature Method for Solving Initial-value Problems in Linear Dynamics

In this paper, the Generalized Differential Quadrature (GDQ) Method1-2 is applied to solve initial value problems in linear dynamics. By using the GDQ technique, the numerical statement of the problem does not pass through any variational formulation, but deals directly with the governing equations of motion3-7. The purpose is to obtain computationally efficient higher-order methods for solving time integration problems. The total time interval is discretized in time steps and the GDQ method is applied to solve the initial value problem within each time step. Various choices for the number of grid points and their distribution are analyzed and discussed. At each time interval, a linear algebraic equation system has to be solved. A simple and efficient implementation scheme is presented. To demonstrate the performance of the proposed algorithm, a wide numerical evaluation is carried out on typical test problems8-10. Accuracy and stability are studied when the number of sampling points and the grid distribution are varied.