Abstract
Nonlinear energy sink (NES) refers to a typical passive vibration device connected to linear or weakly nonlinear structures for vibration absorption and mitigation. This study investigates the dynamics of 1-dof and 2-dof NES with nonlinear damping and combined stiffness connected to a linear oscillator. For the system of 1-dof NES, a truncation damping and failure frequency are revealed through bifurcation analysis using the complex variable averaging method. The frequency detuning interval for the existence of the strongly modulated response (SMR) is also reported. For the system of 2-dof NES, it is reported in a similar bifurcation analysis that the mass distribution between NES affects the maximum value of saddle-node bifurcation. To obtain the periodic solution of the 2-dof NES system with the consideration of frequency detuning, the incremental harmonic balance method (IHB) and Floquet theory are employed. The corresponding response regime is obtained by Poincare mapping, it shows that the responses of the linear oscillator and 2-dof NES are not always consistent, and 2-dof NES can generate extra SMR than 1-dof NES. Finally, the vibration suppression effect of the proposed NES with nonlinear damping, and combined stiffness is analyzed and verified by the energy spectrum, and it also shows that the 2-dof NES system demonstrates better performance.
Highlights
The suppression of unwanted vibration has attracted significant attention in various engineering applications for many years
This study focuses on the analysis of the dynamic behavior of the system with nonlinear damping and combined stiffness nonlinear energy sink (NES) considering frequency detuning under harmonic excitation
The structure of the study is as follows: Section 2 introduces the dynamics of the linear oscillator coupled with 1-dof NES, which mainly analyzes its bifurcation and strongly modulated response (SMR), while considering the influence of frequency detuning
Summary
The suppression of unwanted vibration has attracted significant attention in various engineering applications for many years. It is generally considered that nonlinearity is harmful, but most of the studies show that NES is more effective than linear absorbers in suppressing vibration [11,12,13]. This study focuses on the analysis of the dynamic behavior of the system with nonlinear damping and combined stiffness NES considering frequency detuning under harmonic excitation. By analyzing the bifurcation and SMR of the coupled with 1-dof and 2-dof NES systems, and comparing the energy of different structural systems, the effects of the system frequency detuning, nonlinear damping and combined stiffness are shown. The structure of the study is as follows: Section 2 introduces the dynamics of the linear oscillator coupled with 1-dof NES, which mainly analyzes its bifurcation and SMR, while considering the influence of frequency detuning.
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