Abstract
本文基于欧拉–伯努利梁，考虑梁长度随时间变化，利用Hamilton原理，对附加非线性能量阱的轴向可伸缩各向同性矩形截面悬臂梁进行非线性动力学进行建模，得到其偏微分动力学控制方程。然后对控制方程无量纲化后，利用Galerkin方法对控制方程进行了截断，得到可伸缩悬臂梁横向振动的无量纲形式的常微分非线性动力学方程。设计非线性能量阱动力学参数，通过数值方法对模型在外伸和回收过程中的相关振动特性进行了时域分析，结果表明非线性能量阱具有良好的振动抑制效果。 In this paper, using the Hamilton principle, the nonlinear dynamics equation of an axially moving homogenous and isotropic beam with the additional nonlinear energy sink is derived. The beam, length changes with time, is based on the Euler Bernoulli beam model. Then, transforming the equations to dimensionless ones, using the Galerkin method, the governing equations are truncated. Meanwhile, the nonlinear ordinary differential equation, reflecting the transverse vibration of the telescopic cantilever beam, is obtained. The vibration characteristics of the model in the process of overhang and recovery are analyzed in time domain by numerical calculation method after appropriate nonlinear energy sink parameters were designed. The results show that the nonlinear energy sink has good effect on vibration suppression.
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