Optimal Homotopy Asymptotic Approach to Self-Excited Vibrations

Abstract:

This paper is concerned with analytical treatment of nonlinear oscillation of a self-excited system. An analytic approximate technique, namely OHAM is employed for this purpose. Our procedure provides us with a convenient way to optimally control the convergence of solutions, such that the accuracy is always guaranteed. An excellent agreement of the approximate solutions with the numerical ones has been demonstrated. Three examples are given and the results reveal that the procedure is very effective and accurate, demonstrating the general validity and the great potential of the OHAM for solving strongly nonlinear problems.

• Periodical: Applied Mechanics and Materials (Volume 430)
• Pages: 27-31
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.430.27
• Online since: September 2013
• Authors: Nicolae Herisanu, Vasile Marinca
• Keywords: Nonlinear Damped Vibration, OHAM, Self-Excited Vibration

References

[1] Gh. Silas, M. Rădoi, L. Brîndeu, M. Klepp, A. Hegedus, Culegere de probleme de vibraţii mecanice (in Romanian), Ed. Tehnică, Bucureşti, (1973).

[2] J. -J. Sinou, Transient non-linear dynamic analysis of automotive disc brake squeal – On the need to consider both stability and non-linear analysis, Mech. Res. Commun. 37 (2010) 96–105.

DOI: 10.1016/j.mechrescom.2009.09.002

[3] Albert C.J. Luo, Jianzhe Huang, Discontinuous dynamics of a non-linear, self-excited, friction-induced, periodically forced oscillator, Nonlinear Anal. Real World Appl. 13 (2012) 241–257.

DOI: 10.1016/j.nonrwa.2011.07.030

[4] M. Siddhpura, R. Paurobally, A review of chatter vibration research in turning, Int. J. Mach. Tools Manufact. 61 (2012) 27–47.

DOI: 10.1016/j.ijmachtools.2012.05.007

[5] J. Awrejcewicz, P. Olejnik, Analysis of dynamic systems with various friction laws, Appl. Mech. Rev. 58 (2005) 389-411.

DOI: 10.1115/1.2048687

[6] C.W. Lim, B.S. Wu, A new analytical approach to the Duffing-harmonic oscillator, A new analytical approach to the Duffing-harmonic oscillator, Phys. Let. A. 311 (2003) 365-373.

DOI: 10.1016/s0375-9601(03)00513-9

[7] B.S. Wu, C.W. Lim, Large amplitude nonlinear oscillations of a general conservative system, Int. J. Non-Linear Mech. 39 (2004) 859-870.

DOI: 10.1016/s0020-7462(03)00071-4

[8] V. Marinca, N. Herisanu, Determination of periodic solutions for the motion of a particle on a rotating parabola by means of Optimal Homotopy Asytmptotic Method, J. Sound Vibr. 329 (2010) 1450-1459.

DOI: 10.1016/j.jsv.2009.11.005

[9] N. Herisanu, V. Marinca, Accurate analytical solutions to nonlinear oscillators with discontinuities and fractional-power restoring force by means of the Optimal Homotopy Asymptotic Method, Comp. Math. Appl. 60 (2010) 1607-1611.

DOI: 10.1016/j.camwa.2010.06.042

[10] V. Marinca, N. Herisanu, Nonlinear Dynamical Systems in Engineering. Some Approximate Approaches, Springer, Berlin, (2011).