【摘要】 给出了确定一般二阶强非线性非自治系统周期解的能量迭代方法。该方法给出了二阶强非线性非自治系统主谐波共振和超谐波、次谐波共振周期解存在的必要条件,求得了这些周期解的近似解析表达式,并且得出了解的稳定性判据。近似解析解表达式由计算机辅助推导,计算程序集推导、计算、数值解以及绘图于一体。例子表明,该方法不仅有效而且结果精度较高。更多还原

【Abstract】 A energy iteration method for periodic solutions to second order strongly nonlinear non-autonomous systems is suggested.Using this method not only the necessary condition of existence and the approximate analytic expressions of the periodic solutions for primary-harmonic,super-harmonic and sub-harmonic resonances can be obtained,but the criteria of stability for these solutions can also be gained.The approximate analytic expressions can be derived out by computer aided method.Examples show that the energy iteration method is both effective and high accurate to second order strongly nonlinear non-autonomous systems.更多还原