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Structural Engineering and Mechanics Volume 50, Number 4, May25 2014 , pages 487-500 DOI: https://doi.org/10.12989/sem.2014.50.4.487 |
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Nonlinear in-plane free oscillations of suspended cable investigated by homotopy analysis method |
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Yaobing Zhao, Ceshi Sun, Zhiqian Wang and Jian Peng
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| Abstract | ||
| An analytical solution for the nonlinear in-plane free oscillations of the suspended cable which contains the quadratic and cubic nonlinearities is investigated via the homotopy analysis method (HAM). Different from the existing analytical technique, the HAM is indeed independent of the small parameter assumption in the nonlinear vibration equation. The nonlinear equation is established by using the extended Hamilton\'s principle, which takes into account the effects of the geometric nonlinearity and quasi-static stretching. A non-zero equilibrium position term is introduced due to the quadratic nonlinearity in order to guarantee the rule of the solution expression. Therefore, the mth-order analytic solutions of the corresponding equation are explicitly obtained via the HAM. Numerical results show that the approximate solutions obtained by using the HAM are in good agreement with the numerical integrations (i.e., Runge-Kutta method). Moreover, the HAM provides a simple way to adjust and control the convergent regions of the series solutions by means of an auxiliary parameter. Finally, the effects of initial conditions on the linear and nonlinear frequency ratio are investigated. | ||
| Key Words | ||
| suspended cable; nonlinear free oscillation; homotopy analysis method; Runge-Kutta method | ||
| Address | ||
| Yaobing Zhao, Ceshi Sun : College of Civil Engineering, Hunan University, Changsha, Hunan, China Zhiqian Wang : College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan, China Jian Peng: School of Civil Engineering, Hunan University of Science and Technology, Xiangtan, Hunan, China | ||