Effects of viscoelasticity on the stability and bifurcations of nonlinear energy sinks

doi:10.1007/s10483-023-2944-9

摘要/Abstract

摘要： Due to the increasing use of passive absorbers to control unwanted vibrations, many studies have been done on energy absorbers ideally, but the lack of studies of real environmental conditions on these absorbers is felt. The present work investigates the effect of viscoelasticity on the stability and bifurcations of a system attached to a nonlinear energy sink (NES). In this paper, the Burgers model is assumed for the viscoelasticity in an NES, and a linear oscillator system is considered for investigating the instabilities and bifurcations. The equations of motion of the coupled system are solved by using the harmonic balance and pseudo-arc-length continuation methods. The results show that the viscoelasticity affects the frequency intervals of the Hopf and saddle-node branches, and by increasing the stiffness parameters of the viscoelasticity, the conditions of these branches occur in larger ranges of the external force amplitudes, and also reduce the frequency range of the branches. In addition, increasing the viscoelastic damping parameter has the potential to completely eliminate the instability of the system and gradually reduce the amplitude of the jump phenomenon.

关键词: viscoelasticity, Burgers model, nonlinear energy sink (NES), saddle-node bifurcation, Hopf bifurcation

Abstract: Due to the increasing use of passive absorbers to control unwanted vibrations, many studies have been done on energy absorbers ideally, but the lack of studies of real environmental conditions on these absorbers is felt. The present work investigates the effect of viscoelasticity on the stability and bifurcations of a system attached to a nonlinear energy sink (NES). In this paper, the Burgers model is assumed for the viscoelasticity in an NES, and a linear oscillator system is considered for investigating the instabilities and bifurcations. The equations of motion of the coupled system are solved by using the harmonic balance and pseudo-arc-length continuation methods. The results show that the viscoelasticity affects the frequency intervals of the Hopf and saddle-node branches, and by increasing the stiffness parameters of the viscoelasticity, the conditions of these branches occur in larger ranges of the external force amplitudes, and also reduce the frequency range of the branches. In addition, increasing the viscoelastic damping parameter has the potential to completely eliminate the instability of the system and gradually reduce the amplitude of the jump phenomenon.

Key words: viscoelasticity, Burgers model, nonlinear energy sink (NES), saddle-node bifurcation, Hopf bifurcation

中图分类号:

74H45
74H60

A. MOSLEMI, M. R. HOMAEINEZHAD. Effects of viscoelasticity on the stability and bifurcations of nonlinear energy sinks[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(1): 141-158.

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