摘要
研究受简谐激励含分数阶阻尼的SD振子系统的幅频响应特性,并与含整数阶阻尼的SD振子系统对比。提出求解系统运动微分方程刚度非线性的傅里叶等效模型,解决了系统运动微分方程刚度非线性不可积问题。使用平均法求解等效系统运动微分方程,得到幅频响应解析表达式,基于Lyapunov稳定性理论与Routh判据建立周期解稳定性判断条件,通过与数值方法结果对比,验证了幅频响应解析方法的正确性。研究表明,SD振子系统非线性刚度项的傅里叶等效模型可以应用于系统大振幅运动的研究,大大提高了计算精度。阻尼系数相同时,分数阶阻尼系统的幅频响应与整数阶阻尼系统相比其共振频率及振幅发生了很大的变化;改变分数阶系数,会改变分数阶阻尼系统幅频响应骨架曲线,整数阶阻尼系统幅频响应骨架曲线不受影响;改变分数阶阶次时,分数阶阻尼系统振幅在分界点两侧变化相反。
The amplitude-frequency response characteristic of SD oscillator with fractional damping under harmonic excitation is studied,compared with the SD oscillator with integral damping.The Fourier equivalent model is proposed to solve the nonlinear stiffness of the differential equation of system motion,the problem of the nonlinear stiffness non-integrability of the differential mo‐tion equation of the system is solved.The expression of amplitude-frequency response is obtained by solving the differential equa‐tion of system motion using the average method.The stability of periodic solution is determined based on the Lyapunov stability theory and the Routh criterion.The correctness of the analytical method for amplitude-frequency response is verified by comparing with the numerical results.The result shows that the Fourier transform equivalent model of the nonlinear stiffness term of the SD oscillator can be applied to the motion characteristic of the system with large amplitude,which greatly improves the calculation ac‐curacy.With the same damping coefficient,the amplitude-frequency response of the fractional damping system is different from that of the integral damping system,the resonance frequency and amplitude of the fractional damping system vary greatly.Chang‐ing the fractional coefficient will change the amplitude-frequency response backbone curve of the fractional damping system,but the integral damping system is not affected.When the fractional order is changed,the amplitude of the fractional damping system changes oppositely on both sides of the cut-off point.
作者
陈恩利
王明昊
王美琪
常宇健
CHEN En-li;WANG Ming-hao;WANG Mei-qi;CHANG Yu-jian(State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao Uni‐versity,Shijiazhuang 050043,China;School of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;School of Electrical and Electronic Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)
出处
《振动工程学报》
EI
CSCD
北大核心
2022年第5期1068-1075,共8页
Journal of Vibration Engineering
基金
国家自然科学基金资助项目(12072205)
石家庄铁道大学研究生创新项目(YC2021045)。
关键词
非线性振动
SD振子
分数阶
骨架曲线
nonlinear vibration
SD oscillator
fractional order
backbone curve
