基于非线性模态和一种数值迭代法的陀螺连续体参数振动研究

以脉动流输流管为例,利用非线性模态技术和一种数值迭代法研究陀螺连续体的非线性参数振动响应问题. 通过谐波平衡法将系统非线性非自治控制方程转化为拟自治方程,并在状态空间上利用不变流形法构造系统的非线性模态. 以对应自治系统的解为初值,采用一种数值迭代法来求解拟自治控制方程的模态系数,结果证明了该迭代法的快速收敛性. 在频域分析中得到了幅频响应和相空间上的不变流形,而在时域复模态分析中则发现了参激陀螺系统的正交相位差和行波振动现象.

STUDY OF PARAMETRIC VIBRATION OF GYROSCOPIC CONTINUA BASED ON NONLINEAR NORMAL MODES AND A NUMERICAL ITERATIVE APPROACH

The nonlinear normal mode technique and a numerical iterative approach are applied to study the nonlinear parametric vibrations of pipes conveying pulsating fluid as an example of gyroscopic continua. The nonlinear non-autonomous governing equations are transformed into a set of pseudo-autonomous ones by employing the harmonic balance method. The nonlinear normal modes are constructed by the invariant manifold method in the state space and a numerical iterative approach is adopted to obtain the modal coefficients, in which the modal solutions of the corresponding autonomous system are taken as the initial values. The results obtained see a fast convergence. The frequency-amplitude responses and the invariant manifolds are both obtained in the frequency-domain study, while the quadrature phase difference and the traveling waves are found in the time-domain complex modal analysis.