二次非线性粘弹性圆板的2/1超谐解  

2/1 SUPERHARMONIC SOLUTION OF A CIRCULAR PLATE WITH QUADRATIC NONLINEAR VISCOELASTICITY

作　　者：李银山[1,2] 李欣业[1] 刘波[1] 崔锦华[3] 

机构地区：[1]河北工业大学机械工程学院 [2]太原理工大学应用力学研究所,太原030024 [3]辽宁师范大学化学系

出　　处：《工程力学》2003年第4期74-77,32,共5页Engineering Mechanics

基　　金：国家自然科学基金"九五"重大项目(19990510);山西省自然科学基金项目(20001007)

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。The nonlinear dynamic equation of a circular plate under a harmonic force has been derived under the consideration of the viscoelastic effects. A superimposing iteration harmonic balance method (SIHB) was 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.

关 键 词：一般力学 强非线性动力系统 叠加-迭代谐波平衡法 2/1超谐解 

分 类 号：O322[理学—一般力学与力学基础]