Analysis of the Coupled Nonlinear Vibration of a Two-Mass System

Document Type : Research Paper

Authors

Department of Mechanical Engineering, Faculty of Engineering, University of Port Harcourt, Port Harcourt, Rivers State, Nigeria

Abstract

This paper presents a fixed-end two-mass system (TMS) with end constraints that permits uncoupled solutions for different masses. The coupled nonlinear models for the present fixed-end TMS were solved using the continuous piecewise linearization method (CPLM) and detailed investigation on the effect of mass-ratio on the TMS response was conducted. The investigations showed that increased mass-ratio leads to decreased oscillation frequency and an asymptotic response was obtained at very large mass-ratios. Theoretical solutions to determine the asymptotic response were derived. Also, it was observed that distinct responses can be obtained for the same mass-ratio depending on the mass combination in the TMS. The present fixed-end TMS and the analyses presented give a broader understanding of fixed-end TMS.

Keywords

Main Subjects

[1] Cveticanin, L., Vibrations of a coupled two-degree-of-freedom system, Journal of Sound and Vibration, 247(2), 2001, 279-292.
[2] Cveticanin, L., The motion of a two-mass system with non-linear connection, Journal of Sound and Vibration, 252(2), 2002, 361-369.
[3] Lai, S.K., Lim, C.W., Nonlinear vibration of a two-mass system with nonlinear stiffnesses, Nonlinear Dynamics, 44, 2007, 233-249.
[4] Hashemi Kachapi SHA., Dukkipati, R.V., Hashemi, K.S.Gh., Hashemi, K.S.Mey., Hashemi, K.S.Meh., Hashemi, K.SK., Analysis of the nonlinear vibration of a two-mass-spring system with linear and nonlinear stiffness, Nonlinear Analysis: Real World Applications, 11, 2010, 1431-1441.
[5] Bayat, M., Shahidi, M., Barari, A., Ganji D., Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems, Z. Naturforsch., 66a, 2011, 67-74.
[6] Ganji, S.S., Barari, A., Ganji, D.D., Approximate analysis of two-mass–spring systems and buckling of a column, Computers and Mathematics with Applications, 61, 2011, 1088-1095.
[7] Cveticanin, L., KalamiYazdi, M., Saadatnia, Z., Vibration of a two-mass system with non-integer order nonlinear connection, Mechanics Research Communications, 43, 2012, 22-28.
[8] Cveticanin, L., Vibrations of a free two-mass system with quadratic non-linearity and a constant excitation force, Journal of Sound and Vibration, 270, 2004, 441-449.
[9] Cveticanin, L., A solution procedure based on the Ateb function for a two-degree-of-freedom oscillator, Journal of Sound and Vibration, 346, 2015, 298-313.
[10] Big-Alabo, A., Periodic solutions of Duffing-type oscillators using continuous piecewise linearization method, Mechanical Engineering Research, 8(1), 2018, 41-52.
[11] Big-Alabo, A., Harrison P., & Cartmell, M.P., Algorithm for the solution of elastoplastic half-space impact. Force-Indentation Linearization Method, Journal of Mechanical Engineering Sciences, 229(5), 2015, 850-858.
[12] Big-Alabo, A., Cartmell, M.P., & Harrison P., On the solution of asymptotic impact problems with significant localised indentation, Journal of Mechanical Engineering Sciences, 231(5), 2017, 807-822.
[13] Big-Alabo, A., Rigid body motions and local compliance response during impact of two deformable spheres, Mechanical Engineering Research, 8(1), 2018, 1-15.
[14] Big-Alabo, A., Equivalent impact system approach for elastoplastic impact analysis of two dissimilar spheres, International Journal of Impact Engineering, 113, 2018, 168-179.
[15] Sanchez, N.E., A view to the new perturbation technique valid for large parameters, Journal of Sound and Vibration, 282, 2005, 1309-1316.
[16] Nayfeh, A.H. and Mook, D.T., Nonlinear oscillations, John Wiley & Sons, New York, 1995.
[17] Jordan, D.W. and Smith, P., Nonlinear ordinary differential equations: Problems and solutions, Oxford University Press, Oxford, 2007.