夹层椭圆形板的1/3亚谐解

研究了夹层椭圆形板的非线性强迫振动问题。在以5个位移分量表示的夹层椭圆板的运动方程的基础上,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和派生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了椭圆板的1/3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了比较。并且讨论了1/3亚谐解的渐近稳定性。

1/3 Subharmonic Solution of Elliptical Sandwich Plates

The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components,the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force is derived.A superpositive-iterative harmonic balance(SIHB)method is presented for the steady-state analysis of strongly nonlin-ear 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 fundamental differential equation with fundamental harmonics and incremental differential equation with derived harmonics.The 1/3 subharmonic solu-tion of an elliptical sandwich plate is investigated by using the methods of SIHB.The SIHB method is compared with the numerical integration method.Finally,asymptotical stability of the 1/3 subhar-monic oscillations is inspected.