基于多谐波平衡法的滞回分数阶系统稳态动力响应

Steady-state response determination of a hysteretic system endowed with fractional elements via a multi-harmonic balance method

  • 摘要: 结构隔震和耗能减振装置有时会同时体现出动力特性的频率依赖和滞回关系,分数阶导数模型能以较少的参数模拟力-位移关系的频率依赖性。采用谐波平衡法研究简谐激励下同时具有滞回特性和分数阶阻尼单元的系统稳态响应。利用激励和响应过程的Fourier级数展开并取谐波平衡后,求得滞回响应和位移响应Fourier级数之间的关系;将滞回微分方程写成余量的形式并结合Galerkin方法和Levenberg-Marquardt算法求得响应的Fourier级数;分别对硬化和软化Bouc-Wen滞回系统的数值模拟显示所建议方法的精度。研究结果表明,分数阶数和稳态位移幅值之间的关系依赖于系统和滞回参数以及激励频率。

     

    Abstract: Civil structures and its energy dissipation devices often exhibit hysteretic and frequency-depended behavior.In this regard,the fractional derivative model can be used for frequency-dependent force-displacement relationship with very few parameters.The paper presents a multi harmonic balance method for determining steady-state response of a hysteretic system endowedwith fractional elements.Specifically,the Fourier series expansion both for the excitation and response and utilizing the multi harmonic balancing on both sides of the equation of motion,leads to a relationship between the Fourier coeficients of the excitationand that of the response.Next,recasting the hysteretic differential equation into a residue form and projecting it on the Fourier basisleads an algebraic equation with unknown response Fourier coeficients.The Levenberg-Marquardt algorithm is used to obtain theunknowns.Pertinent numerical examples including a softening and hardening Bouc-Wen system with different fractional order demonstrate the accuracy of the proposed method.

     

/

返回文章
返回