【摘要】 计及材料的非线性弹性和粘性性质,研究了圆板在简谐载荷作用下的2/1超谐解,导出了相应的非线性动力方程。提出一类强非线性动力系统的叠加迭代谐波平衡法。将描述动力系统的二阶常微分方程,化为基本解为未知函数的基本微分方程;及分岔解为未知函数的增量微分方程。通过叠加迭代谐波平衡法得出了圆板的2/1超谐解。同时,对叠加迭代谐波平衡法和数值积分法的精度进行了比较。并且讨论了2/1超谐解的渐近稳定性。更多还原

【Abstract】 The nonlinear dynamic equation of a circular plate under a harmonic force is derived under the consideration of the viscoelastic effects. A superimposing iteration harmonic balance method (SIHB) is presented for the steady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system, which is described as a second order ordinary differential equation, can be expressed to be a basic differential equation with basic harmonics and incremental differential equation with bifurcate harmonics. The 2/1 superharmonic solution for a circular plate is investigated by the superimposing iteration harmonic balance method. The results of the superimposing iteration harmonic balance method are in good agreement with those of numerical integration. In addition, the asymptotical stability of the 2/1 superharmonic oscillations is examined.更多还原