Abstract
In this paper, a modified harmonic balance method is presented to solve nonlinear forced vibration problems. A set of nonlinear algebraic equations appears among the unknown coefficients of harmonic terms and the frequency of the forcing term. Usually a numerical method is used to solve them. In this article, a set of linear algebraic equations is solved together with a nonlinear one. The solution obtained by the proposed method has been compared to those obtained by variational and numerical methods. The results show good agreement with the results obtained by both methods mentioned above.
Highlights
Nonlinear vibration is an important issue in science and engineering
A comparison among the results obtained by the proposed method, numerical method, and a variational approach has been presented and graphically presented in Figure 1(a) to (d) and Figure 2(a) and (b)
It is observed that our result agrees reasonably well with those obtained by the variational approach and numerical method
Summary
Nonlinear vibration is an important issue in science and engineering. Most of the differential equations involving physical phenomena are nonlinear. Keywords Harmonic balance, variational method, nonlinear oscillations, forced vibration In the classical HBM, a set of nonlinear algebraic equations is solved by a numerical method to determine the unknown coefficients.
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