Nonlinear energy sink with inerter

Abstract A novel archetype of nonlinear energy sink (NES) enhanced by an inerter is proposed for vibration reduction of vibrating systems. The proposed NES-inerter suppressed vibration more effectively than a convenient NES measured by both energy dissipation and amplitude frequency responses. Complexification-averaging technique is applied to analyze a coupled system to find steady-state periodic solutions, and the analytical results are confirmed by numerical simulations. The analytical solutions are used to bifurcation analysis, and the results show that the saddle node and the Hopf bifurcations occur under a series of parameters in the steady-state responses. The effects of parameters, such as inertance, cubic stiffness, viscous damping, and amplitude of the external excitation, on the performance of the proposed NES are examined based on the analytical solutions. The investigation reveals that the optimal value of the inerter exists in a certain range.

[1]  Alexander F. Vakakis,et al.  Shock Mitigation by Means of Low- to High-Frequency Nonlinear Targeted Energy Transfers in a Large-Scale Structure , 2016 .

[2]  Oleg Gendelman,et al.  Targeted energy transfer in systems with external and self-excitation , 2011 .

[3]  Guilhem Michon,et al.  Experimental Investigation and Design Optimization of Targeted Energy Transfer Under Periodic Forcing , 2014 .

[4]  P. Brzeski,et al.  Novel type of tuned mass damper with inerter which enables changes of inertance , 2015 .

[5]  Fengming Li,et al.  Impact transient response in lattice sandwich panels under various boundaries using reverberation ray matrix method , 2015 .

[6]  Yinlong Hu,et al.  Influence of inerter on natural frequencies of vibration systems , 2014 .

[7]  Tianzhi Yang,et al.  Nonlinear Energy Sink for Whole-Spacecraft Vibration Reduction , 2017 .

[8]  Guilhem Michon,et al.  Targeted Energy Transfer Under Harmonic Forcing With a Vibro-Impact Nonlinear Energy Sink: Analytical and Experimental Developments , 2015 .

[9]  Mohammad A Al-Shudeifat.  Analytical formulas for the energy, velocity and displacement decays of purely nonlinear damped oscillators , 2015 .

[10]  Roman Starosta,et al.  Parametric and External resonances in kinematically and Externally excited nonlinear Spring Pendulum , 2011, Int. J. Bifurc. Chaos.

[11]  Fu-Cheng Wang,et al.  Performance Benefits in Passive Vehicle Suspensions Employing Inerters , 2004 .

[12]  Jean W. Zu,et al.  Steady-State Responses of Pulley-Belt Systems With a One-Way Clutch and Belt Bending Stiffness , 2014 .

[13]  Xingjian Jing,et al.  Vibration isolation using a hybrid lever-type isolation system with an X-shape supporting structure , 2015 .

[14]  Xingjian Jing,et al.  Vibration energy harvesting with a nonlinear structure , 2016 .

[15]  P. Brzeski,et al.  Experimental study of the novel tuned mass damper with inerter which enables changes of inertance , 2017 .

[16]  G. Kopidakis,et al.  Targeted energy transfer through discrete breathers in nonlinear systems. , 2001, Physical review letters.

[17]  Oleg Gendelman,et al.  ApJ, in press , 1999 .

[19]  Alexander F. Vakakis,et al.  A study on torsional vibration attenuation in automotive drivetrains using absorbers with smooth and non-smooth nonlinearities , 2017 .

[20]  Mohammad A. AL-Shudeifat,et al.  Amplitudes Decay in Different Kinds of Nonlinear Oscillators , 2015 .

[21]  M.C. Smith,et al.  The missing mechanical circuit element , 2009, IEEE Circuits and Systems Magazine.

[22]  M. H. Yao,et al.  Vibration suppression for truss core sandwich beam based on principle of nonlinear targeted energy transfer , 2017 .

[23]  Alexander F. Vakakis,et al.  Steady State Passive Nonlinear Energy Pumping in Coupled Oscillators: Theoretical and Experimental Results , 2003 .

[24]  Oleg Gendelman,et al.  Energy pumping in nonlinear mechanical oscillators : Part I : Dynamics of the underlying Hamiltonian systems , 2001 .

[25]  G. Kerschen,et al.  Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems , 2008 .

[26]  Oleg Gendelman,et al.  Isolated Resonance Captures and Resonance Capture Cascades Leading to Single- or Multi-Mode Passive Energy Pumping in Damped Coupled Oscillators , 2004 .

[27]  Stephane Pernot,et al.  Design criteria for optimally tuned nonlinear energy sinks—part 1: transient regime , 2012 .

[28]  E. Dowell,et al.  Natural frequencies of a super-critical transporting Timoshenko beam , 2017 .

[29]  Claude-Henri Lamarque,et al.  Targeted energy transfer with parallel nonlinear energy sinks. Part I: Design theory and numerical results , 2011 .

[30]  Roman Starosta,et al.  Internal motion of the complex oscillators near main resonance , 2012 .

[31]  Alexander F. Vakakis,et al.  Non-linear dynamics of a system of coupled oscillators with essential stiffness non-linearities , 2004 .

[32]  Xingjian Jing,et al.  Nonlinear vibration energy harvesting with adjustable stiffness, damping and inertia , 2017 .

[33]  S. Theodossiades,et al.  Targeted energy transfer and modal energy redistribution in automotive drivetrains , 2016, Nonlinear dynamics.

[34]  Claude-Henri Lamarque,et al.  Targeted energy transfer with parallel nonlinear energy sinks, part II: theory and experiments , 2012 .

[35]  Li-Qun Chen,et al.  Complexification-averaging analysis on a giant magnetostrictive harvester integrated with a nonlinear energy sink , 2018 .

[36]  Mohammad A. AL-Shudeifat,et al.  Asymmetric Magnet-Based Nonlinear Energy Sink , 2015 .

[37]  Hu Ding,et al.  Chaotic Dynamics of an Axially Accelerating Viscoelastic Beam in the Supercritical Regime , 2014, Int. J. Bifurc. Chaos.

[38]  Hu Ding.  Steady-state responses of a belt-drive dynamical system under dual excitations , 2016 .

[39]  Oleg Gendelman,et al.  Energy Pumping in Nonlinear Mechanical Oscillators: Part II—Resonance Capture , 2001 .

[40]  D. M. McFarland,et al.  Toward a Fundamental Understanding of the Hilbert-Huang Transform in Nonlinear Structural Dynamics , 2006 .

[41]  Da-Peng Li,et al.  Static and dynamic behaviors of belt-drive dynamic systems with a one-way clutch , 2014 .

[42]  Roman Starosta,et al.  Asymptotic analysis of kinematically excited dynamical systems near resonances , 2012 .

[43]  Leonid I. Manevitch,et al.  The Description of Localized Normal Modes in a Chain of Nonlinear Coupled Oscillators Using Complex Variables , 2001 .

[44]  Alexander F. Vakakis,et al.  Inducing Passive Nonlinear Energy Sinks in Vibrating Systems , 2001 .

[45]  Malcolm C. Smith.  Synthesis of mechanical networks: the inerter , 2002, IEEE Trans. Autom. Control..

[46]  Oleg V. Gendelman,et al.  Transition of Energy to a Nonlinear Localized Mode in a Highly Asymmetric System of Two Oscillators , 2001 .

[47]  Alexander F. Vakakis,et al.  High-frequency vibration energy harvesting from impulsive excitation utilizing intentional dynamic instability caused by strong nonlinearity , 2016 .

[48]  Hu Ding,et al.  Periodic responses of a pulley−belt system with one-way clutch under inertia excitation , 2015 .

[49]  Zhaobo Chen,et al.  Band stop vibration suppression using a passive X-shape structured lever-type isolation system , 2016 .

[50]  Xiang Li,et al.  Integration of a nonlinear energy sink and a giant magnetostrictive energy harvester , 2017 .

[51]  D. M. McFarland,et al.  On the effect of multiple parallel nonlinear absorbers in palliation of torsional response of automotive drivetrain , 2017 .

[52]  Yinlong Hu,et al.  Analysis and optimisation for inerter-based isolators via fixed-point theory and algebraic solution , 2015 .

[53]  Alexander F. Vakakis,et al.  Experimental study of non-linear energy pumping occurring at a single fast frequency , 2005 .