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Periodic Solution of the Differential Equations of Machine Units

International Journal of Mechanical Engineering
© 2019 by SSRG - IJME Journal
Volume 6 Issue 9
Year of Publication : 2019
Authors : Venelin Jivkov
10.14445/23488360/IJME-V6I9P101
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How to Cite?

Venelin Jivkov, "Periodic Solution of the Differential Equations of Machine Units," SSRG International Journal of Mechanical Engineering, vol. 6,  no. 9, pp. 1-3, 2019. Crossref, https://doi.org/10.14445/23488360/IJME-V6I9P101

Abstract:

The paper proposes a new matrix algorithm and an iterative procedure for searching a periodic solution of the differential equation of machine units with one degree of freedom subjected to forces that depend on speed and position. To search the solution, an approach for calculating the Fourier series's coefficients for each iteration of a variant of Lyapunov's equation is proposed. For illustration, an example of a machine unit with one degree of freedom is presented. The periodic solution is in excellent agreement with similar examples in the scientific literature.

Keywords:

matrix form, periodic solution in harmonics, steady-state motion, nonlinear equation.

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