非白噪声激励的二自由度非线性系统及碰撞振动系统的响应

【作者】 高李霞；

【导师】 黄志龙；

【作者基本信息】 浙江大学 ， 固体力学， 2003， 硕士

【摘要】 本文首先应用基于广义谐和函数的强非线性系统的随机平均法研究了宽带随机激励下单自由度碰撞振动系统的平稳响应，分别讨论了单边碰撞与双边碰撞两种情况，将随机平均法所得结果与数字模拟结果进行比较，证明了该方法具有很高的精度。然后研究宽带随机激励下耦合强非线性振子的平稳响应及谐和与高斯白噪声联合激励下的耦合Duffing-van der Pol振子的随机跳跃与分叉，应用随机平均法分别导出了系统的随机平均方程，近似得到了其平均漂移与扩散系数的解析表达式，并用有限差分法求解了稳态FPK方程，将所得结果与数字模拟结果进行比较，证实了该法的有效性。当耦合Duffing-van der Pol振子受到谐和与白噪声联合激励时，随着系统参数的变化，详细讨论了该系统的随机跳跃与分叉现象。指出了随机跳跃与确定性跳跃的区别并给出了合理的解释。更多还原

【Abstract】 The stationary response of single-degree-of-freedom (SDOF) vibro-impact system under wide-band random excitation is studied. The approximate stationary responses of the system are obtained by using the stochastic averaging method for strongly non-linear SDOF system under wide-band random excitation. Two examples with both side constraints and with right hand side constraint only are given to illustrate the application and accuracy of the proposed procedure. It is shown that the analytical stationary probability densities of the system agree well with those from digital simulation of the original equation of motion. Then a stochastic averaging procedure for coupled Duffing-van der Pol oscillators subject to wide-band random excitations or to combined harmonic and white noise excitations is proposed and the averaged Fokker-Plank-Kolmogorov(FPK) equation is solved by using the finite difference method. It shown that the analytical results are in very good agreement with those from digital simulation of the original equation of motion. The stochastic jump of the coupled Duffing-van der Pol oscillators under combined harmonic and white noise excitations and its bifurcation as the system parameters change are examined. The differences between the deterministic bifurcation and stochastic bifurcation are pointed out and the reasonable explanation of the phenomena to given.更多还原