A unified Krylov-Bogoliubov-Mitropolskii method for solving hyperbolic-type nonlinear partial differential systems
A general asymptotic solution is presented for investigating the transient response of non-linear systems modeled by hyperbolic-type partial differential equations with small nonlinearities. The method covers all the cases when eigen-values of the corresponding unperturbed systems are real, complex...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Publishing House for Science and Technology
2008-03-01
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| Series: | Vietnam Journal of Mechanics |
| Online Access: | https://vjs.ac.vn/index.php/vjmech/article/view/5607 |
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| Summary: | A general asymptotic solution is presented for investigating the transient response of non-linear systems modeled by hyperbolic-type partial differential equations with small nonlinearities. The method covers all the cases when eigen-values of the corresponding unperturbed systems are real, complex conjugate, or purely imaginary. It is shown that by suitable substitution for the eigen-values in the general result that the solution corresponding to each of the three cases can be obtained. The method is an extension of the unified Krylov-Bogoliubov-Mitropolskii method, which was initially developed for un-darnped, under-clamped and over-clamped cases of the second order ordinary differential equation. The methods also cover a special condition of the over-damped case in which the general solution is useless. |
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| ISSN: | 0866-7136 2815-5882 |