Modified Vlasov beam model considering additional displacements induced by rotation deformation of asymmetric section beams

Vlasov theory of thin-walled beams neglects additional displacements induced by rotation of beam sections, which results in significant errors in calculating dynamic responses. In this study, additional lateral and vertical displacements and additional torques are introduced to modify Vlasov theory of thin-walled beams and a modified Vlasov beam model of asymmetric cross-sectional beams established. And then, a typical simply supported beam serves as a case in point to present a comprehensive analytical framework for the forced vibration analysis of beams with asymmetric sections. Subsequently, a beam element considering additional displacements is derived based on the principle of minimum potential energy. Notably, the proposed models and elements are versatile and applicable to various cross-sectional types. Finally, the impact of additional displacements on the forced vibration and the resonance of asymmetric cross-sectional beams is investigated under various boundary conditions. It is indicated that the impact of additional displacements becomes pronounced as boundary constraints are enhanced and should be considered in the dynamics analyses of beams. Moreover, as for an asymmetric cross-sectional beam, limiting torques can reduce its dynamic responses in the practical engineering. Additionally, additional displacements have a greater impact on torsional and lateral displacements instead of vertical displacements during vertical resonance.