中文摘要：

黏弹性夹层梁的随机振动控制是一个重要的实际问题。基于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而倍受关注。虽然关于该可控黏弹性夹层梁的振动已有一定研究，但所用的动力学模型在几何或物理上是线性的，而对于较强激励情况则需要考虑非线性因素。首次考虑该黏弹性体的物理非线性，建立黏弹性夹层梁及其支承质量系统的非线性运动微分方程，并离散化为多模态耦合的非线性振动方程；对于平稳随机激励，运用统计线性化法推导等价拟线性系统，并计算系统的随机响应，得到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，用以评价可控黏弹性夹层梁的响应抑制性能。

英文摘要：

The random vibration control of viscoelastic sandwich beams is an important subject in engineering. The sandwich beams with property- controllable viscoelastic core are concerned since they can be optimized without structural change. There are some publications of studies on vibration responses of the controllable viscoelastic sandwich beams.However, the viscoelastic material dynamics in these studies were described by linear models only. Particularly, the physical nonlinearity of the viscoelastic core needs to be considered for vibration analysis under strong excitations. In this paper, a nonlinear dynamic model is employed for describing the viscoelastic constitutive relation. The differential equations ofmotion of a viscoelastic sandwich beam with supported mass under stationary random support excitations are derived andconverted into nonlinear multi-mode coupling vibration equations by using the Galerkin method. The equivalent quasi-linear system is derived by using the statistic linearization method. The random responses such as MS displacement, the equivalent frequency response function and power spectral density of the nonlinear random vibration are obtained, which are used for evaluating the vibration suppression efficiency of the viscoelastic sandwich beam.