计及剪切变形的Timoshenko梁的刚-柔耦合动力学

Coupling dynamics of Timoshenko beam with shear deformation

研究带中心刚体的Timoshenko梁的刚-柔耦合动力学问题。从力学的基本原理出发,基于Timoshenko梁假设,用虚功原理建立了带中心刚体的柔性梁的刚-柔耦合动力学方程。仿真计算结果表明,随着梁的惯量矩和横截面积比逐渐增大,剪切变形对梁的刚-柔耦合动力学性态产生了一定的影响。此外,本文还对不计剪切变形的Euler-Bernoulli梁假设的适用性进行了研究。

In this paper, the coupling dynamics of a Timoshenko beam attached to a central rigid body is investigated. Based on continuum medium mechanics and Timoshenko beam assumption, the coupling dynamic equations of flexible beam attached to a central rigid body are derived by using virtual work principle and nonlinear strain-displacement theory. Simulation results show that the shear effect is significant with the increase of the proportion of the inertia moment to the cross-section area and the increase of the rotation speed of the beam has no effect on the difference between the two models of the beam. Furthermore, the applicability of the Euler-Bernoulli assumption in which the shear effect is ignored is investigated.