考虑剪切变形的自由阻尼悬臂梁瞬态响应近似解析解

Approximate analytical solutions for transient response of unconstrained damped cantilever beam considering shear deformation

考虑了阻尼层的剪切变形,利用Hamilton原理推导出了自由阻尼悬臂梁的控制方程,计算了自由振动的频率;然后根据模态叠加的方法构造悬臂梁的挠度函数,再利用虚功原理推导出集中力突然撤去的情况下的自由阻尼悬臂梁瞬态响应近似解析解,并和不考虑阻尼层剪切变形的计算结果进行了比较。分析发现,计算自由阻尼悬臂梁的瞬态响应时要考虑阻尼层的剪切变形。

Abstract：Shear deformation is considered. Based on Hamilton＇s principle, the vibration equations for un- constrained damped cantilever beam is derived, and the frequencies of vibration is obtained. And then de- flection of cantilever beam is established. Approximate analytical solutions for transient response of uncon- strained damped cantilever beam is obtained used the method of mode superposition when concentrated force is withdrew suddenly, that is compared with the result of calculation without regard to shear defor- mation. The analysis shows that the shear deformation of damping layer should be considered when tran- sient response of unconstrained damped cantilever beam is calculated.