中文摘要：

研究了计及剪切变形的复合材料梁的刚-柔耦合的动力学特性.从复合材料梁的应变能表达式出发,考虑了几何非线性,用虚功原理建立了Timoshenko梁的动力学变分方程,并用假设模态法将其离散,建立了中心刚体/悬臂梁的刚/柔耦合动力学方程.对中心刚体/悬臂梁仿真计算结果表明,剪切变形对复合材料梁动力学特性的影响大于各向同性材料.在此基础上,研究了Timo-shenko梁和Euler-Bernoulli梁模型的频率差异,根据频率误差研究了Euler-Bernoulli梁模型对于复合材料梁的适用性.

英文摘要：

Coupling dynamical characteristics of composite beam experiencing free motions with shear deformation were investigated. Based on the strain energy of composite beam, considering geometrical nonlinearity, variation equations of a composite Timoshenko beam were derived by means of the principle of virtual work. The assumed mode method was used to discrete the variation equations to obtain the rigid- flexible coupling dynamic equations for hub-cantilevered-beam system. The numerical results demonstrate that the influence of shear deformation on dynamical characteristics of composite beams is more significant than isotropic beams. Furthermore, the frequency difference between Euler-Bernoulli model and Timosh- enko model was investigated. According to the frequency error, the applicability of the Euler-Bernoulli model to a composite beam was investigated.