Inclined Boundary Inertial Vibration Absorber for Elastic Beam

本文提出了一种在弹性梁两边加载斜置式惯性边界进行减振的方法。在谐波激励下，对具有斜置式惯性边界的弹性梁进行动力学分析。首先建立弹性梁的动力学控制方程。采用Galerkin方法离散连续偏微分方程，将谐波平衡法与伪弧长算法相结合得到梁的非线性稳态动态响应，并采用Runge-Kutta方法进行数值验证。基于最大幅值减振百分比展示了斜置式惯性边界对弹性梁振动的减振性能。结果表明，斜置式惯性边界在保证承载力的同时又有很好的减振效果。另外，讨论了斜置式惯性边界各项参数变化对其减振性能及系统响应非线性特性的影响。随着惯性增大，系统幅频特性曲线由右侧弯曲向左侧弯曲发生转变，使弹性梁的硬特性转化为软特性。In this paper, a method of damping an elastic beam with diagonally placed inertial boundaries loaded on both sides of the beam is proposed. The dynamics of the elastic beam with oblique inertia boundaries will be analysed under harmonic excitation. The controlling equations for the dynamics of the elastic beam are first established. The Galerkin method is used to discretize the continuous partial differential equations, and the nonlinear steady-state dynamic response of the beam is obtained by combining the harmonic balance method with the pseudo arc-length algorithm, and numerically verified by the Runge-Kutta method. The damping performance of the inclined placed inertia boundary for elastic beam vibration is demonstrated based on the maximum magnitude damping percentage. The results show that the inclined inertia boundary has a good vibration damping effect while ensuring the load carrying capacity. In addition, the effects of the variation of the parameters of the inclined inertia boundary on the vibration damping performance and the nonlinear characteristics of the system response are discussed. With the increase of inertia, the amplitude-frequency characteristic curve of the system is transformed from the right side bending to the left side bending, so that the hard characteristic of the elastic beam is transformed to the soft characteristic.