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.

KEYWORDS:

• Nonlinear fractional damping
• Volterra series
• output frequency response function
• force transmissibility

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors are most grateful to the National Natural Science Foundation of China [grant number 91216106], [grant number 11472089] for financial supports in this investigation.

Notes on contributors

Jingfei Jiang

Jingfei Jiang received her B.S. degree in Applied Mathematics from Shangqiu Normal University, P.R. China, in 2010 and her M.S. degree in Applied Mathematics from Xiangtan University, China in 2013. Now She is pursuing Ph.D. degree in Dynamics and Control from Harbin Institute of Technology, P.R. China. Her research covers a wide range of fields including qualitative and stability theory of fractional order differential equation, fractional order functional differential equations, theory of causal differential equations, control of fractional order finite/infinite dimensional system, control of variable order fractional order systems and the frequency domain analysis of nonlinear isolator with fractional order damping.

Dengqing Cao

Dengqing Cao received his Ph.D. degree in Dynamics and Control from Southwest Jiaotong University in May 1993. Since 2006 he was with the School of Astronautics, Harbin Institute of Technology, China, where he currently serves as a full time Professor. He held visiting positions at Hong Kong Polytechnic University in 1996 and 1999 and Lancaster University, England from 2000 to 2006. He is the author of more than 260 journal and conference proceedings papers. His research interests are in the fields of nonlinear dynamics of slender structures, robust stability of dynamical systems, rotor dynamics, dynamic modeling and vibration control of spacecraft.

Huatao Chen

Huatao Chen received his B.S. degree in Applied Mathematics from Dezhou University, P.R. China, in 2007 and his M.S. degree in Applied Mathematics from Southwest Jiaotong University, China in 2011. Now he is pursuing Ph.D. degree in Dynamics and Control from Harbin Institute of Technology, P.R. China. His current research interests include long-time behavior and Control for Infinite dynamical systems and simulations of global dynamics for modal equations associated with Infinite dynamical systems.

Kun Zhao

Kun Zhao received his B.S. degree in Flight Vehicle Propulsion Engineering from Changchun University, P. R. China, in 2012 and his M.S. degree in Dynamics and Control from Harbin Institute of Technology, China in 2014. Now he is pursuing Ph.D. degree in Dynamics and Control from Harbin Institute of Technology, P.R. China. His current research interests include mechanism and control of stone-skipping and the applications in dynamics and control of spacecraft.