Global residue harmonic balance method to periodic solutions of a class of strongly nonlinear oscillators |
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Authors: | Peijun Ju Xin Xue |
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Institution: | 1. School of Control Science and Engineering, Shandong University, Jinan, PR China;2. School of Mathematics and Statistics, Taishan University, Taian 271021, PR China |
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Abstract: | A new approach, namely the global residue harmonic balance method, was advanced to determine the accurate analytical approximate periodic solution of a class of strongly nonlinear oscillators. A class of nonlinear jerk equation containing velocity-cubed and velocity times displacements-squared was taken as a typical example. Unlike other harmonic balance methods, all the former residual errors are introduced in the present approximation to improve the accuracy. Comparison of the result obtained using this approach with the exact one and simplicity and efficiency of the proposed procedure. The method can be easily extended to other strongly nonlinear oscillators. |
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Keywords: | Jerk equation Periodic solution Residual error Global residue harmonic balance |
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