二次非线性圆板的1/2亚谐解

1/2 SUBHARMONIC SOLUTION OF A CIRCULAR PLATE WITH QUADRATIC NONLINEAR

计及材料的非线性弹性和粘性性质 ,研究圆板在简谐载荷作用下的 1 2亚谐解 ,导出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和分岔解为未知函数的增量微分方程。通过叠加—叠代谐波平衡法得出圆板的 1 2亚谐解。同时 ,对叠加—叠代谐波平衡法和数值积分法的精度进行比较。并且讨论了 1

The nonlinear dynamic equation of a circular plate subject to a harmonic force is derived, with the viscoelastic effects taken into account. A superpositive iterative 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 as basic differential equation with basic harmonics and the incremental differential equation with bifurcate harmonics. The 1/2 superharmonic solution for a circular plate is investigated by using SIHB. The SIHB is compared with the numerical integration method. Finally, asymptotical stability of the 1/2 subharmonic oscillations is inspected.