中文摘要：

利用规范形理论与待定固有频率寻求改善Melnikov函数分析非线性振动系统混沌阈值的简单方法，着重讨论参数与周期激励联合作用下具有主参数共振的三阱势能系统，建立了其Melnikov函数积分式，引入由待定固有频率形成的时间尺度变换，从同宿及异宿分岔两个角度获取系统的混沌临界值，使得非线性扰动量对于基频的影响有效地体现于Melnikov函数表达式中，进而结合相应的分析过程提高所得结果的计算精度．作为算例，对解析解与数值积分结果进行了对比，以验证提出方法的有效性与可行性．

英文摘要：

The simple approach to improve the computational precision of Melnikov method is presented by using the undetermined fundamental frequency and normal form method. We construct the improved Meinikov expression for a triple-well nonlinear oscillator subject to principal parametric resonance and external excitation. For the occurrence of chaos, the approxime threshold values of chaotic motion are obtained from the Homoclinicity and Heteroclinicity points of view. It depends on the introduction of undetermined fundamental frequency, and adopting new time transformation for fulfilling the homoclinic and heteroclinic orbits, so that the effect of disturbing parameter can be easily detected and embodied in the Melnikov operation. As is illustrated, the explicit applications show that the improved results coincide very well with the results of numerical simulation.