计及剪切变形的Timoshenko梁的刚-柔耦合动力学

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。

Coupling dynamics of Timoshenko beam with shear deformation

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.