Nonlinear torsional vibration differential equation of the nested arc-shaped short spring dual mass flywheel (DMF) is established, considering the piecewise linear stiffness and damping of the spring. The first-order approximate analytical solution under sinusoidal excitation and the amplitude–frequency characteristic function are obtained by means of the average method which verified by the Runge–Kutta (R–K) method. The effects of the parameters of input excitation, inertia, and piecewise linear stiffness and damping of DMF on the resonant amplitude, resonant frequency band, and equivalent linear natural frequency of the system are analyzed. The results show that the amplitude–frequency characteristic curve bending and jumping with the changes of excitation frequency and the peak of resonant amplitude can be obviously reduced by increasing the inertia of the primary flywheel and decreasing the inertia of the secondary flywheel. The complex nonlinear dynamic phenomena such as Period 1, quasi-periodic, and chaos are obtained by analyzing the forced vibration response under the different excitation frequencies.

中文翻译：

---

考虑分段线性刚度和阻尼的双质量飞轮非线性振动研究

考虑弹簧的分段线性刚度和阻尼，建立了嵌套弧形短弹簧双质量飞轮（DMF）的非线性扭转振动微分方程。采用平均法得到正弦激励下的一阶近似解析解和幅频特征函数，并经龙格-库塔（R-K）法验证。分析了DMF的输入激励、惯量、分段线性刚度和阻尼等参数对系统谐振幅值、谐振频带和等效线性固有频率的影响。结果表明，通过增大初级飞轮惯量、减小次级飞轮惯量，可以明显减小幅频特性曲线随激磁频率和谐振振幅峰值变化的弯曲和跳跃现象。通过分析不同激励频率下的受迫振动响应，得到周期1、准周期、混沌等复杂的非线性动态现象。