Forced vibration analysis of thin-walled beams under harmonic moving loads

Abstract

The coupled lateral-torsional vibration of thin-walled beams under moving harmonic loads holds critical engineering relevance. For example, vehicles traversing uneven roads induce vertical oscillations that translate into harmonic excitations on thin-walled beams. Based on Vlasov’s thin-walled beam theory, this study establishes closed-form time-domain solutions for the lateral-torsional displacements of mono-symmetric thin-walled beams by transforming the coupled partial differential equations into ordinary differential equations via modal expansion, and solving them through Laplace transform and its inverse. A finite element solution program based on the Newmark-β algorithm is created for validation purposes, with verification results demonstrating close alignment between analytical and numerical solutions. A key innovation involves representing a single vehicle load as two eccentric lateral forces in parameter analysis, enhancing the accuracy of simulating vehicle-induced dynamics. Furthermore, parametric studies quantitatively characterize the effects of critical control parameters (excitation frequency, moving speed, span length, load eccentricity, and warping stiffness) on lateral-torsional coupling displacements. Key conclusions are that torsional displacement is more velocity-sensitive; warping suppresses peak amplitudes. These findings provide a profound foundation for designing thin-walled bridges to avoid resonance.