Dynamic analysis of the nonlinear energy sink with local and global potentials: geometrically nonlinear damping
- PDF / 3,700,411 Bytes
- 24 Pages / 547.087 x 737.008 pts Page_size
- 11 Downloads / 203 Views
(0123456789().,-volV) ( 01234567 89().,-volV)
ORIGINAL PAPER
Dynamic analysis of the nonlinear energy sink with local and global potentials: geometrically nonlinear damping Yang Liu . Guoping Chen . Xiao Tan
Received: 19 January 2020 / Accepted: 3 August 2020 Ó Springer Nature B.V. 2020
Abstract In this paper, the considered two-DOF system consists of a linear oscillator (LO) under external harmonic excitation and an attached lightweight nonlinear energy sink (NES) with local potential and geometrically nonlinear damping. With the application of complex-averaging method, the steadystate dynamical behavior of the system is investigated by the slow invariant manifold, folding singularities and equilibrium points. Different scenarios of strongly modulated responses are presented based on the geometry of SIM, and the numerical simulation results are in consistent with the analytical prediction. The incremental harmonic balance method is applied to detect the frequency response curves of the system around the fundamental resonance, and the accuracy of the theoretical analysis is fully verified by the numerical results obtained by direct integration of equations of motion of the system. It is demonstrated that the increase in external forcing amplitude, global nonlinear stiffness and local nonlinear stiffness can drive the frequency response curves move toward the right and widen the frequency bandwidth of the coexistence of multiple steady-state response regimes, while the increase in nonlinear damping the reverse. The numerical simulation results also show that the
Y. Liu (&) G. Chen X. Tan State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, 29 Yudao St., Nanjing 210016, China e-mail: [email protected]
addition of geometrically nonlinear damping and local potential in the proposed NES can drastically enhance the capacity of the nonlinear vibration absorber to suppress the shock-induced response of the LO, and the proposed NES is effective for a comparatively broad range of applied impulsive energies, particularly for the high impulsive energies. Keywords Geometrically nonlinear damping Slow invariant manifold Incremental harmonic balance method Nonlinear energy sink Asymptotic analysis
1 Introduction In the past decades, the suppression of unwanted vibration has attracted extensive attention from engineers and scientists. Regarding the passive linear vibration mitigation devices, one can mention tuned mass dampers (TMDs) or tuned vibration neutralizers (TVNs) [1–3], and the addition of the simple lighweight mass-spring-damper substructure can effectively suppress oscillations of primary system. However, despite the excellent performance around the natural frequency of linear structure, the main drawback of the classical linear absorber is the limitation of effective frequency range. To effectively dissipate the unwanted vibrationary energy in a broad bandwidth, another alternative design of vibration absorber is to introduce ess
Data Loading...
