中文摘要：

以中间层为基体材料、上下层为对称的功能梯度材料组成的层合板为研究对象,根据大挠度理论和薄板变形理论,利用Hamilton原理和Rayleigh-Ritz法推导出了在简谐机械力作用下功能梯度层合薄板的非线性振动方程。利用多尺度法对非线性振动方程进行求解,得到了层合板的幅频响应方程。利用Matlab探讨了不同边界条件下的层合板的主共振问题,通过改变阻尼、机械力等的大小来分析这些因素对主共振的影响。

英文摘要：

Taking laminated plate co the middle layer as the substrate material and the upper/lower as symmetrical mposed of functionally graded materials as the research object, and according to the theory of large deflection and deformation plate theory, we used Hamilton principle and Rayleigh-Ritz method to derive the action of harmonic mechanical force of FGM laminated thin plate nonlinear vibration equation. The nonlinear vibration equation is solved by using multi-scale method, and the amplitude-frequency response equations of laminated plates are obtained. Matlab was used to study the different boundary conditions of laminated plates of primary resonance the impact of these factors on the primary resonance by mechanical strength and so on. changing the problem, and we analyzed size of the damping, the