In reality, the behavior and nature of nonlinear dynamical systems are ubiquitous in many practical engineering problems. The mathematical models of such problems are often governed by a set of coupled second-order differential equations to form multi-degree-of-freedom (MDOF) nonlinear dynamical systems. It is extremely difficult to find the exact and analytical solutions in general. In this paper, the homotopy analysis method is presented to derive the analytical approximation solutions for MDOF dynamical systems. Four illustrative examples are used to show the validity and accuracy of the homotopy analysis and modified homotopy analysis methods in solving MDOF dynamical systems. Comparisons are conducted between the analytical approximation and exact solutions. The results demonstrate that the HAM is an effective and robust technique for linear and nonlinear MDOF dynamical systems. The proof of convergence theorems for the present method is elucidated as well.
- Design Engineering Division and Computers in Engineering Division
Homotopy Analysis Method for Multi-Degree-of-Freedom Nonlinear Dynamical Systems
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Zhang, W, Qian, YH, Yao, MH, & Lai, SK. "Homotopy Analysis Method for Multi-Degree-of-Freedom Nonlinear Dynamical Systems." Proceedings of the ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 3: 30th Computers and Information in Engineering Conference, Parts A and B. Montreal, Quebec, Canada. August 15–18, 2010. pp. 19-28. ASME. https://doi.org/10.1115/DETC2010-28089
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