非高斯激励下带附加质量的悬臂梁响应研究

Responses of the cantilever beam with a lumped mass under non-Gaussian excitation

大多数悬臂梁的研究都是基于确定性振动分析或将外部激励假定为高斯过程,鲜少涉及非高斯激励。针对非高斯激励下带附加质量的悬臂梁的响应特征进行研究。首先,通过Lagrange方程建立考虑曲率非线性的悬臂梁振动方程;然后,通过指数多项式闭合法求解结构响应的概率密度函数,并分析了平均到达速率、激励强度及附加质量对结构响应的影响;同时分析了非平稳非高斯激励下非线性结构参数对响应的影响。计算结果表明,指数多项式闭合法与模拟解吻合很好,平均到达速率越大,结构响应的概率密度函数曲线收缩越明显。

Most of the research on cantilever beam is based on deterministic analysis or the assumed Gaussian excitation,non-Gaussian excitation is rarely involved.Stochastic responses of cantilever beam with lumped mass subjected to non-Gaussian random excitation are studied in this paper.Motion equation of the structure is established by the Lagrange s equation which considers curvature nonlinearity,approximate transient solutions of responses of structure are obtained by exponential polynomial closure(EPC)method.Effects of average arrival rate,excitation intensity and lumped mass on the structural response are analyzed.Meanwhile,the influence of nonlinear structural parameters on structural response under non-stationary and non-Gaussian excitation is also analyzed.Numerical results show that results obtained by the EPC method agree well with simulation solution.With the increase of the average arrival rate,the probabi-lity density function curve of structural response presents centralization.