Integrated Dynamic Analysis of Thin-Walled Beams: Coupled Bidirectional Bending, Torsion, and Axial Vibrations Under Axial Loads

This paper proposes a beam model integrating the Timoshenko beam theory with Vlasov beam theory to capture the coupled behavior of bidirectional bending, torsion, and axial vibration in thin-walled beams subjected to axial loads. Our model incorporates the effects of shear deformation, rotational inertia, and axial loads, offering a comprehensive approach to complex dynamic behaviors. By utilizing Hamilton's principle, we derived a complete set of coupled dynamic equations and boundary conditions. The highlight of this model is its capacity to accurately predict the dynamic response of thin-walled beams under multifaceted loading conditions, surpassing traditional models by integrating coupled axial vibrations. This research significantly advances the understanding of the dynamic behavior of thin-walled beams, providing a precise analytical tool for structural design and safety assessment. The robustness and accuracy of the proposed model were validated through extensive theoretical analysis and empirical validation, equipping engineers with critical insights to optimize the design of engineering structures subjected to complex dynamic loads.