The fastest insight into the large amplitude vibration of a string

  • Na Qie School of Science, Xi'an University of Architecture and Technology, Xi’an, China
  • Wei-Fan Houa School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, China
  • Ji-Huan He National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-Ai Road, Suzhou, China
Keywords: He’s frequency formulation; nonlinear oscillator; Duffing equation; least square method.

Abstract

This paper recommends a simple and excusive approach to a strongly nonlinear oscillator. Its frequency property can be immediately obtained by the simplest calculation. The results show that the method leads to an approximate solution with relatively high accuracy. Considering the simplest solution process, this paper provides a highly efficient tool for fast determination of the amplitude-frequency relationship of a nonlinear oscillator. The large amplitude vibration of a string is used as an example to illustrate the solution process.

References

Anjum, N., & He, J. H. (2020c). Nonlinear dynamic analysis of vibratory behavior of a graphene nano/microelectromechanical system. Mathematical Methods in the Applied Sciences, DOI: 10.1002/mma.6699.

Anjum, N., & He, J.H. (2020a). Homotopy perturbation method for N/MEMS oscillators. Mathematical Methods in the Applied Sciences, 2020, DOI: 10.1002/mma.6583.

Anjum, N., & He, J.H. (2020b). Analysis of nonlinear vibration of nano/microelectromechanical system switch induced by electromagnetic force under zero initial conditions. Alexandria Engineering Journal, DOI: 10.1016/j.aej.2020.07.039.

He, C.H., Wang, J.H., & Yao, S.W. (2019). A complement to period/frequency estimation of a nonlinear oscillator, Journal of Low Frequency Noise, Vibration and Active Control, 38(3-4), 992-995.

He, J.H. (2019a). The simplest approach to nonlinear oscillators, Results in Physics, 15, 102546.

He, J.H. (2019b). The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators, Journal of Low Frequency Noise, Vibration and Active Control, 38(3-4), 1252-1260.

He, J.H. (2020a). A short review on analytical methods for a fully fourth-order nonlinear integral boundary value problem with fractal derivatives. International Journal of Numerical Methods for Heat & Fluid Flow. DOI: 10.1108/HFF-01-2020-0060.

He, J.H. (2020b). A simple approach to Volterra-Fredholm integral equations, Journal of Applied and Computational Mechanics. 6(SI), 1184-1186.

He, J.H., & El-Dib, Y.O. (2020). The reducing rank method to solve third-order Duffing equation with the homotopy perturbation, Numerical Methods for Partial Differential Equations, DOI: 10.1002/num.22609.

He, J.H., & Jin, X. (2020). A short review on analytical methods for the capillary oscillator in a nanoscale deformable tube, Mathematical Methods in the Applied Sciences, DOI: 10.1002/mma.6321.

He, J.H., & Latifizadeh, H. (2020). A general numerical algorithm for nonlinear differential equations by the variational iteration method, International Journal of Numerical Methods for Heat and Fluid Flow, DOI: 10.1108/HFF-01-2020-0029.

He, J.H., Nurakhmetov, D., & Skrzypacz, P. (2019). Dynamic pull-in for micro-electromechanical device with a current-carrying conductor. Journal of Low Frequency Noise, Vibration and Active Control, article number: 1461348419847298.

He, J.H. (2006). Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B, 20, 1141–1199.

Lai, S.K., Xiang, Y., & Lim, C.W. (2008). Higher-order approximate solutions for nonlinear vibration of a constant-tension string, Journal of Sound and Vibration, 317, 440–448.

Mahabadi, R.K., & Pazhooh, M.D. (2018). Approximate solutions of large amplitude vibration of a string, Latin American Journal of Solids and Structures, 15(4), e31.

Ren, Z.F., & Hu, G.F. (2019a). He's frequency-amplitude formulation with average residuals for nonlinear oscillators, Journal of Low Frequency Noise, Vibration and Active Control, 38(3-4), 1050-1059.

Ren, Z.F., & Hu, G.F. (2019b). Discussion on the accuracies of He's frequency-amplitude formulation and its modification with average residuals , Journal of Low Frequency Noise, Vibration and Active Control, 38(3-4), 1713-1715.

Skrzypacz, P., Kadyrov, S., & Nurakhmetov, D. (2019). Analysis of dynamic pull-in voltage of a graphene MEMS model. Nonlinear Analysis: Real World Applications, 45, 581-589.

Wang, Q.L., Shi, X.Y., & Li, Z.B. (2019). A short remark on Ren-Hu's modification of He's frequency-amplitude formulation and the temperature oscillation in a polar bear hair, Journal of Low Frequency Noise, Vibration and Active Control, 38(3-4): 1374-1377.

Wang, Y., & An, J.Y. (2019). Amplitude-frequency relationship to a fractional Duffing oscillator arising in microphysics and tsunami motion, Journal of Low Frequency Noise, Vibration and Active Control, 38(3-4), 1008-1012.

Published
2021-01-01
How to Cite
Qie, N., Houa, W.-F., & He, J.-H. (2021). The fastest insight into the large amplitude vibration of a string. Reports in Mechanical Engineering, 2(1), 1-5. Retrieved from https://frontpres.rabek.org/index.php/asd/article/view/28