Vibration response of perforated thick beam under moving load

Abstract

This manuscript aims to investigate the dynamic responses of thick Timoshenko perforated beams under a moving load using Ritz method for the first time. The beam is perforated by equally spaced square holes arranged in array form. The perforated geometrical parameters of beam are presented as a function of full beam, hole number throughout the cross section, and filling ratio. The governing equation is derived by using the Lagrange procedure using the kinematic assumption of Timoshenko shear deformation theory to include the rotation of the thickness effect. Therefore, the transverse-shear strain and rotary inertia are considered through analysis. Ritz method is exploited to solve the governing equation and transform it to ordinary differential equation in time domain. Newmark average acceleration method is adopted to solve the dynamic equation of motion to obtain the time response. The effects of moving load parameter, filling ratio, and the number of holes throughout the cross section on the dynamic responses of the perforated beam are investigated and analyzed. The proposed model can be used in many civil and mechanical perforated structures to reduce the vibration amplitudes. © 2021, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.