A New Mixed Finite Element–Differential Quadrature Formulation for Forced Vibration of Beams Carrying Moving Loads

In this paper, a new version of mixed finite element–differential quadrature formulation is presented for solving time-dependent problems. The governing partial differential equation of motion of the structure is first reduced to a set of ordinary differential equations (ODEs) in time using the finite element method. The resulting system of ODEs is then satisfied at any discrete time point apart and changed to a set of algebraic equations by the application of differential quadrature method (DQM) for time derivative discretization. The resulting set of algebraic equations can be solved by either direct methods (such as the Gaussian elimination method) or iterative methods (such as the Gauss–Seidel method). The mixed formulation enjoys the strong geometry flexibility of the finite element method and the high accuracy, low computational efforts, and efficiency of the DQM. The application of the formulation is then shown by solving some moving load class of problems (i.e., moving force, moving mass, and moving oscillator problems). The stability property and computational efficiency of the scheme are also discussed in detail. Numerical results show that the proposed mixed methodology can be used as an efficient tool for handling the time-dependent problems.