干摩擦振动系统响应计算方法研究

运用Ｆｏｕｒｉｅｒ级数分析技巧和谐波平衡法，提出了一种三次非线性粘性阻尼双线性滞迟振子强迫振动响应计算方法，并通过四阶Ｒｕｎｇｅ－Ｋｕｔｔａ数值积分对近似解析方法的精确性进行了验证。根据Ｆｌｏｑｕｅｔ理论，对定常解的稳定性和鞍结分叉现象进行了讨论。

Study on Response Computation of Dry Friction Damped Vibration System

By the harmonic balance method in nonlinear theory and Fourier analysis, response computation for the forced vibration of viscous damping bilinear hysteretic oscillator with cubic restoring force is studied. To obtain a frequency response curve of the system, a nonlinear transcendental algebraic equation should be resolved firstly. The approach is examined by forth order Runge Kutta numerical integration. At the same time the stability of periodic solutions and the saddle node bifurcation are discussed based on Floquet theory. Through the numerical and theoretical investigation, a conclusion that the saddle node bifurcation due to the cubic nonlinear will happen under higher level exciation.