中文摘要：

针对对称铺设的复合材料层合薄板,用层合板的经典理论建立了相应的非线性动力学方程.采用多尺度法,导出了系统受前两阶模态间1：3 内共振及第1 阶模态主参激共振时的平均方程.采用石墨/环氧纤维复合材料层合板参数作为基础,进行数值计算,得到相应的幅频响应曲线.研究表明,系统阻尼的增大能够削弱系统的幅值,单层层合薄板厚度的微弱变化引起层合板整体拉伸刚度、弯曲刚度对应的变化,随厚度增加,整个系统偏离1：3 内共振.

英文摘要：

A set of nonlinear dynamic differential equations was established for a symmetric composite laminate plate.The multi-scale method was used to the nonlinear equations and the average equations for the principal parametric resonanceof the first mode and the1：3 internal resonance between the first two modes were derived respectively. Numerical simulationof a graphite/epoxy composite plate was done and the corresponding amplitude-frequency response curves were obtained.Results show that increase of system damping can reduce the response amplitudes, a small change of thickness can cause ahuge change of tensile stiffness and bending stiffness of the composite laminate plate and the change of thickness can also destroyinternal resonance. Thus, the 1：3 internal resonance of the laminate plate can be shifted with thickness increasing.