Analytical solutions on dynamic response of a thin-walled curved beam subjected to two-axle moving load with variable speed

This paper proposes the analytical solutions involving damping effects for the dynamic response of a simply supported thin-walled curved beam under uniformly variable two-axle moving loads in four directions: vertical, torsional, radial, and axial. The warping stiffness and damping of the thin-walled beam were comprehensively considered in the vibration control equations. Unlike traditional one-axle load cases, this study employs a more realistic two-axle vehicle load model. Based on the modal superposition method, the control vibration equations for thin-walled curved beams in-plane and out-of-plane under variable speed moving loads were solved using a combination of the Fourier sine transform method, the Galerkin method, and the Laplace transform method. Analytical solutions for the dynamic responses were derived in integral form, facilitating direct numerical computation. The proposed computational method’s effectiveness and accuracy were validated against published research. Subsequently, the dynamic responses of the thin-walled curved beam under one-axle and two-axle moving load models were compared, and the effects of initial load velocity, load acceleration, and center angle of the curved beam on the dynamic responses were investigated through extensive parameter research. The research results provide valuable insights into the structural behavior of thin-walled curved beams under the moving loading with variable speed.