摘要
振动共振现象在弱信号检测和能量采集等领域具有重要应用价值,然而现有工作多集中于对称双稳系统或线性耗散情形.为此,本文研究了双频信号驱动下具有非线性耗散项的非对称双稳系统中的振动共振现象.运用快慢变量分离法得出系统在低频处的响应幅值.根据响应幅值的解析表达式,研究了双频周期信号的参数、非线性耗散参数和非对称参数对振动共振现象的影响.结果表明:非线性耗散系数的增大会使系统发生更弱的振动共振现象;在含有非线性耗散项的系统中,非对称参数的变化可以改变振动共振的形态,对称的双稳系统会发生双共振,而非对称的双稳系统发生单共振;非对称参数不影响共振发生的位置,但是能够减弱响应幅值;理论预测与数值模拟结果吻合较好,验证了理论分析的有效性.
The phenomenon of vibrational resonance holds significant application value in weak signal detection and energy harvesting.However,existing studies predominantly focus on symmetric bistable systems or linear dissipation scenarios.To address this gap,this paper investigates vibrational resonance(VR)in an asymmetric bistable system with nonlinear dissipation,driven by biharmonic forces at two different frequencies.The fast and slow variable separation method is applied to derive the response amplitude of the system at low frequencies.Moreover,based on the analytical expression of the response amplitude,the effects of the dual-frequency periodic signal,the nonlinear dissipation and the asymmetric parameter on the VR are investigated.The results indicate that,first,the larger the nonlinear dissipation factor,the weaker the VR of the system occurs.Second,for the systems with nonlinear dissipative term,tuning the asymmetric parameter can change the shape of the VR,that is,the symmetric bistable systems emerge the double resonance,and the asymmetric bistable systems have the single resonance.Third,the asymmetric parameter does not influence the location of the VR,but it can weaken the response amplitude.Finally,the theoretical predictions are in good agreement with the numerical simulation results,verifying the validity of the theoretical analysis.
作者
肖玉柱
李佳明
孙中奎
赵楠楠
Xiao Yuzhu;Li Jiaming;Sun Zhongkui;Zhao Nannan(School of Science,Chang’an University,Xi’an 710064,China;School of Mathematics and Statistics,Northwestern Polytechnical University,Xi’an 710129,China)
出处
《动力学与控制学报》
2025年第2期64-71,共8页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(12302033)
陕西省自然科学基础研究计划资助项目(2023-JC-QN-0009)。
关键词
振动共振
双稳系统
非线性耗散项
非对称参数
vibrational resonance
bistable system
nonlinear dissipation
asymmetric parameter
作者简介
通信作者:赵楠楠,E-mail:nzhao@chd.edu.cn。
