中文摘要：

悬臂黏弹性夹层梁的随机振动抑制是一个重要的实际问题。采用性能可控黏弹性体的夹层梁具有无需改变结构设计的可优化性与对于较宽频带激励的适应性。关于两端约束可控黏弹性夹层梁的线性振动已有一定研究，而非线性振动仍有待于进一步讨论。悬臂黏弹性夹层梁高阶模态的求解是一个较为复杂的问题。高斯宽带随机激励下黏弹性夹层梁的非线性多模态耦合振动分析是一个较为困难的问题。考虑黏弹性体的物理非线性，首次建立悬臂黏弹性夹层梁的非线性运动微分方程，确定振动模态，根据伽辽金法将该方程离散化为多模态耦合的非线性振动方程；对于高斯平稳随机激励，运用统计线性化法推导等价拟线性系统，计算系统的随机响应，得到悬臂黏弹性夹层梁非线性随机振动的均方位移，及等价的频响函数和功率谱；通过数值分析结果说明，悬臂黏弹性夹层梁对非线性随机振动具有有效的抑制性能。

英文摘要：

Random vibration suppression of viscoelastic sandwich cantilever beams is an important subject in engineering.The sandwich beam with a controllable viscoelastic core can be optimized without structural change and has the suitability to wide-band excitation.The linear vibration of the controllable viscoelastic sandwich beams with both ends constrained has been studied.However,their nonlinear vibration needs to be studied further.The solution for high-order modes of the viscoelastic sandwich cantilever beams is a complicated problem.And the nonlinear multi-mode-coupling vibration analysis of the viscoelastic sandwich beams under Gaussian wide-band random excitation is a challenging problem.In this paper,the nonlinear viscoelastic constitutive relation is considered.The differential equations of motion of a viscoelastic sandwich cantilever beam under support excitations are derived.The vibration modes of the cantilever beam are determined by the constraint conditions at both ends.The partial differential equations are converted into nonlinear multimode-coupling vibration equations by using the Galerkin method.The equivalent quasi-linear system is derived for the Gaussian stationary random excitation by using the statistic linearization method.The random responses such as MS displacement,equivalent frequency response and power spectral density of the nonlinear random vibration of the cantilever beam are obtained.Numerical results illustrate the good suppression effectiveness of the nonlinear random vibration of the viscoelastic sandwich cantilever beams.