Steady-State Motions of Machines with Finite Degree of Freedom Influenced by Position and Velocity Depending Forces

International Journal of Mechanical Engineering
© 2018 by SSRG - IJME Journal
Volume 5 Issue 1
Year of Publication : 2018
Authors : V. S. Jivkov
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How to Cite?

V. S. Jivkov, "Steady-State Motions of Machines with Finite Degree of Freedom Influenced by Position and Velocity Depending Forces," SSRG International Journal of Mechanical Engineering, vol. 5,  no. 1, pp. 26-30, 2018. Crossref, https://doi.org/10.14445/23488360/IJME-V5I1P105

Abstract:

An algorithm for the solution of non-linear differential equations describing the steady-state motion (T-periodical) of the mechanical systems with one of the finite numbers of degrees of freedom is presented. The initial approximation of the solution is obtained in a poly-harmonic form, one of the most significant merits of the proposed approach. Criteria for estimating the number of harmonics in the stationary solution minimizes the approximation's iterations.
A first-order linear differential equation solves the problem defined in the paper with one degree of freedom. For the systems with a finite number of degrees of freedom, the method's application leads to an extreme task with many variables.

Keywords:

The steady-state motion of machine's units; solution in harmonics; non-linear equations.

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