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Analytical Approximations for Stick-Slip Amplitudes and Frequency of Duffing Oscillator

Publication Type : Journal Article

Publisher : Journal of Computational and Nonlinear Dynamics, American Society of Mechanical Engineers

Source : Journal of Computational and Nonlinear Dynamics, American Society of Mechanical Engineers (ASME), Volume 12, Issue 4, Number 044501 (2017)

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Keywords : Amplitude of oscillation, Analytical approximation, Analytical expressions, Analytical investigations, Approximate analytical expressions, Dynamical characteristics, Frequency of oscillation, Friction, Oscillators (mechanical), Slip forming, Stick-slip, Stick-slip oscillation, Tribology

Campus : Coimbatore

School : School of Engineering

Department : Mechanical Engineering

Year : 2017

Abstract : Linear spring mass systems placed on a moving belt have been subjected to numerous investigations. Dynamical characteristics like amplitude and frequency of oscillations and bifurcations have been well studied along with different control mechanisms for this model. But the corresponding nonlinear system has not received comparable attention. This paper presents an analytical investigation of the behavior of a Duffing oscillator placed on a belt moving with constant velocity and excited by dry friction. A negative gradient friction model is considered to account for the initial decrease and the subsequent increase in the frictional forces with increasing relative velocity. Approximate analytical expressions are obtained for the amplitudes and base frequencies of friction-induced stick-slip and pure-slip phases of oscillations. For the pure-slip phase, an expression for the equilibrium point is obtained, and averaging procedure is used to arrive at approximate analytical expressions of the periodic amplitude of oscillations around this fixed-point. For stick-slip oscillations, analytical expressions for amplitude are arrived at by using perturbation analysis for the finite time interval of the stick phase, which is linked to the subsequent slip phase through conditions of continuity and periodicity. These analytical results are validated by numerical studies and are shown to be in good agreement with them. It is shown that the pure-slip oscillation phase and the critical velocity of the belt remain unaffected by the nonlinear term. It is also shown that the amplitude of the stick-slip phase varies inversely with nonlinearity. The effect of different system parameters on the vibration amplitude is also studied. Copyright © 2017 by ASME

Cite this Research Publication : K. Devarajan and B. Balaram, “Analytical Approximations for Stick-Slip Amplitudes and Frequency of Duffing Oscillator”, Journal of Computational and Nonlinear Dynamics, vol. 12, no. 4, 2017.

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