【摘要】 应用增量谐波平衡法(IHB法)研究轴向运动薄板横向非线性振动特性及其稳定性.通过Hamilton原理推导出了非惯性参考系下四边简支轴向运动薄板的横向振动微分方程,然后利用Galerkin方法离散运动方程.对离散后的非线性方程组应用IHB法进行非线性振动分析,研究了在固有频率之比ω20/ω10接近于3:1情况下,外激励频率ω在ω10附近的具有内部共振的基谐波响应.最后用多元Floquet理论分析了系统周期解的稳定性,其中采用Hsu方法来计算转移矩阵.通过对具体例子的数值计算,分别得到了自由振动和不同外激励下的频幅相应曲线,通过对比运动梁模型和运动薄板模型的计算结果,分析了各种模型的适用范围.更多还原

【Abstract】 The laterally nonlinear vibration of axially moving plates was analyzed by the incremental harmonic balance(IHB)method.Firstly,the motion equations of an axially moving plate were derived by Hamilton principle.Then,the Galerkin method was employed to discretize the governing equations,and the IHB method was applied to solve the nonlinear equations.Finally,the Floquet theory and Hsu’s method were used to investigate the stability of the solution.The free vibrations and the forced responses of an axially moving plate with internal resonance were studied.The effects of aspect ratio of plate were also discussed.更多还原