二次非线性粘弹性圆板的2/1⊕3/1超谐解

2/1⊕3/1Superharmonic Solution of A Circular Plate With Quadratic Nonlinear Viscoelastic Material

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 21 31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 叠代谐波平衡法。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 21 31超谐解。对叠加迭代谐波平衡法和数值积分法进行了比较 ,两者结果吻合很好。并且讨论了 21

The nonlinear dynamic equation of a circular plate under the action of a harmonic force is derived with consideration of the viscoelastic effects. A superpositive iteration harmonic balance method (SIHB) is presented for the steady state analysis of the strong nonlinear oscillations. 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 hasmonics and incremental differential equation with bifurcate harmonics. The 2131 superharmonic solution for a circular plate is investigated by the superpositive iteration harmonic balance method. The results indicated that the results of the superpositive iteration harmonic balance method are very similar to the numerical results. Finally, asymptotical stability of the 2131 superharmonic oscillations is inspected.