多自由度耦合强非线性振动系统的规范形方法

The normal form method in strongly nonlinear vibration with three degrees of freedom and coupled in its linear parts

采用改进后的规范形理论研究一个线性耦合的三自由度强非线性振动系统。介绍了多自由度耦合强非线性系统的复规范形方法,利用一个恒等的矩阵变换将方程解耦,求出解耦后系统的规范形表达式。通过对一个实际振动系统的分析,用数值仿真方法验证了该方法在研究多自由度耦合强非线性问题中的有效性。

The complex normal form method has been used to analysis the strongly nonlinear oscillation system with three-degree of freedom and coupled in its linear parts.The complex normal form method in view of this melt-degree of freedom is introduced and the expression of normal form is also offered here.The validity of the complex normal form theory will be testified in a more complicated actual system by comparing the asymptotic solutions with the numerical imitation.