Primary Resonance of a Nonlinear Fractional Model for Cerebral Aneurysm at the Circle of Willis
Zhoujin Cui, Zaihua Wang
Abstract: This paper studies the primary response of a fractional model proposed in Cui et al. (Int J Bifurcat Chaos 31:2150135, 2021) for cerebral aneurysm at the circle of Willis, which is described by a damped fractional Duffing oscillator with both quadratic and cubic nonlinearities under an external harmonic excitation. By using the multiple scale method, the amplitude-frequency equation of primary resonance is obtained. When the parameter values are fixed, typical hardening or softening characteristics of the oscillator are observed as the excitation frequency changes. The newly introduced number K, a combination of the nonlinear stiffness coefficients and the natural frequency, plays an important role in creating typical hardening or softening characteristics. When the excitation frequency is fixed, characteristics similar to hardening or softening spring as well as other kinds of characteristics are also observed as a parameter changes. The flexibility of using the amplitude-frequency equation to estimate the amplitude of the resonant solutions is verified numerically when the excitation frequency is close to the natural frequency of the oscillator, and the implication of the obtained results is suggested.
文章链接：https://link.springer.com/article/10.1007/s11071-022-07445-z
