An efficient time-space formulation for dynamic transient analyses: application to the beam assemblies subjected to moving loads and masses, Applied Mathematical Modelling, 2021

In this study, the formulation of a time marching method has been developed for the dynamic analysis of beam-type structures in the presence of moving loads/masses. By considering each flexural member of the system as a beam element, the introduced idea of the time-weighted residual method in our recent study “Int. J. Numer. Methods Eng., Vol. 114(7); pp. 719–748″, has been evoked to express the beam response in terms of a series of exponential basis functions. The solution advances in time by modifying the series coefficients through employing a pre-integration process as well as the governing equilibrium equation. The presented method needs neither discretization of the members nor any numerical integration processes so the solution can be obtained by the minimum numbers of required degrees of freedom. Six sample problems have been provided to show the capabilities of the proposed method in the solution of a variety of single and multi-spans beam under constant and accelerated moving loads/masses.