The vibration transmissibility of a single degree of freedom oscillator with nonlinear fractional order damping

ABSTRACT Motivated by the theoretical analysis of the effects of nonlinear viscous damping on vibration isolation using the output frequency response function approach, the output frequency response function approach is employed to investigate the effects of the nonlinear fractional order damping on vibration isolation based on Volterra series in the frequency domain. First, the recursive algorithm which is proposed by Billings et al. is extended to deal with the system with fractional order terms. Then, the analytical relationships are established among the force transmissibility, nonlinear characteristic coefficients and fractional order parameters for the single degree of freedom oscillator. Consequently, the effects of the nonlinear system parameters on the force transmissibility are discussed in detail. The theoretical analysis reveals that the force transmissibility of the oscillator is suppressed due to the existence of the fractional order damping, but presents different effects on suppressing the force transmissibility of the oscillator over the frequency region by varying the fractional order parameters. Moreover, the fractional order parameters, which affect the force transmissibility, the bandwidth of the frequency region and the resonance frequency, can be used as designing parameters for vibration isolation systems. At last, numerical studies are presented to illustrate the theoretical results.

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