摘要
考虑几何非线性和均匀静态温度的影响,研究了具有初挠度的双层金属薄板在周期时变横向载荷作用下的混沌运动。采用Galerkin法得到含二次和三次非线性项的动力学方程,利用Melnikov函数法,从理论上给出系统发生混沌运动的临界条件。借助于计算机代数系统Maple进行定量搜索与模拟,并利用Poincaré映射和相平面轨迹以及时程曲线加以判断。结果表明,受热双层板在强迫振动时存在复杂的混沌运动。
The chaotic motion of a bimetallic thin circular plate with transverse periodic excitation was investigated considering the effect of geometric nonlinearities and uniformly distributed stationary temperature. The dynamic equation with both quadratic and cubic nonlinearities was derived for a bimetallic plate by employing Galerkin's technique. The theoretical critical conditions for chaos were then determined using the Melnikov function method. Finally, the chaotic motions were simulated numerically with the Maple algebraic system, with the Poincaré map and phase curve along with the time-history diagram used to evaluate if chaotic motion occurs. The results identify conditions for which chaotic motion occurs in heated bimetallic plates.
出处
《清华大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2004年第8期1134-1137,共4页
Journal of Tsinghua University(Science and Technology)
关键词
非线性振动
混沌运动
双层薄板
初挠度
静态温度
MELNIKOV函数
nonlinear oscillation
chaotic motion
bimetallic plate
initial deflection
stationary temperature
Melnikov function
