Implementation of time-weighted residual method for simulation of flexural waves in multi-span Timoshenko beams subjected to various types of external loads: from stationary loads to accelerating moving masses, Archive of Applied Mechanics Vol 92, (2022)

In this paper, a recently introduced method has been implemented for the forced vibration analysis of multi-span Timoshenko beams subjected to a wide range of external loads. To this end, the time-weighted residual approach has been developed for the vibration analysis of Timoshenko beams for the first time. Through a simplifying assumption, the governing system of the differential equations is firstly converted to two decoupled equations in terms of the vertical displacement and the rotation of the beam section. Next, the displacement and the rotation fields are considered as a series of exponential basis functions. Storing the information of the solution at each time step on the coefficients of these series plays a vital role in the proposed method. With such a feature, the solution advances in time through a set of recursive relations. The innovative concept of source functions has also been introduced and employed to direct both shear and flexural waves, tailored to the vertical displacement and the rotation of the beam section, toward the beam’s ends. A new dynamic index is also proposed to investigate the validity of Bernoulli assumption for different ranges of the moving object’s velocities. Compared with the results of some available common methods, the accuracy and efficiency of the proposed method have been appraised in the solution of five sample problems of single- and multi-span beams subjected to stationary or moving load/mass, including an overhead crane-suspended payload system.