非线性振动中周期与振幅和能量关系的级数表达式

The series expressions of relations between period and amplitude and energy for nonlinear vibration

针对一般的一维非线性振动问题,讨论了周期与振幅和能量关系的级数解法,给出了直到4阶的表达式和相关结果,并用单摆和中心力场的严格解进行了验证.

The series expressions of relations between period and amplitude and energy are discussed for general one-dimensional nonlinear vibration,and solutions up to the fourth order are obtained.They are checked by the rigorous solution of two examples,i.e.,simple pendulum and central force.