具有非线性能量阱的弹性边界约束轴向载荷梁结构动力学行为研究

A study of dynamic behavior of axially loaded beams with nonlinear energy sink and elastic boundary restraints

近年来,非线性能量阱作为一种高效的被动控制手段受到国内外学者广泛关注。本文采用Galerkin截断法(GTM)预报弹性边界约束轴向载荷梁结构动力学响应,研究非线性能量阱对梁结构振动行为影响规律。在Galerkin截断法中,选取具有线性边界条件轴向载荷Euler-Bernoulli梁模态函数作为权函数和试函数,之后利用Galerkin条件建立梁结构振动系统的残差方程,结合4阶龙格-库塔算法对上述残差方程进行求解。采用谐波平衡法对Galerkin截断法所得结果进行验证并研究了Galerkin截断法截断数对结果稳定性的影响。在此基础上,研究外部激励位置、非线性能量阱参数对该梁结构系统动力学响应、减振性能的影响规律。结果表明,外部激励位置与非线性能量阱参数对梁结构动力学响应影响显著。适当的非线性刚度、阻尼参数能够有效抑制梁结构端点处的振动响应幅值。

As an efficient passive control means,the nonlinear energy sink has received extensive attention from various scholars all over the word in recent years.In this work,the Galerkin truncated method(GTM)was employed to predict the system dynamics of an axially loaded beam with elastic boundary restraints,and the influence of nonlinear energy sink on vibration behavior of such beam structure was investigated.In the Galerkin truncated method,mode functions of the axially loaded Euler-Bernoulli beam with linear boundary conditions were selected as the trail and weight functions.The Galerkin condition was used to establish the residual equations of the beam structure.The fourth-order Runge-Kutta method was utilized to solve the residual equations directly.The harmonic balance method was also used to verify the results obtained by GTM,and the influence of truncated number on the stability of the results was also studied.Based on this,the influence of excitation position and nonlinear energy sink on dynamic behavior and vibration suppression of the beam structure was explored.Results show that the excitation position as well as parameters of the nonlinear energy sink have significant influence on dynamic behavior of the beam structure.The appropriate nonlinear stiffness and damping parameters can effectively suppress the vibration response amplitude at the both ends of the beam structure.