Free vibration analysis of a structural system with a pair of irrational nonlinearities |
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| Institution: | 1. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, PR China;2. School of Electro-Mechanical Engineering, Guangdong University of Technology, Guangzhou 510006, PR China;3. Department of Architecture and Civil Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, PR China |
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| Abstract: | An alternative method of deriving accurate and simple analytical approximate solutions to a structural dynamical system governed by a pair of strong irrational restoring forces is presented. This system can be used to represent mathematical models in various engineering problems. Prior to solving the problem, a rational approximation of the nonlinear restoring force function is applied to achieve a convergent truncation. Analytical solutions are then obtained using the combination of the harmonic balance method and Newton's method. This approach shows that lower-order analytical procedures can yield highly accurate and exact solutions that are difficult to obtain with an analytical expression. |
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