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Structural Engineering and Mechanics Volume 59, Number 1, July10 2016 , pages 1-14 DOI: https://doi.org/10.12989/sem.2016.59.1.001 |
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Nonlinear vibration analysis of a type of tapered cantilever beams by using an analytical approximate method |
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Weipeng Sun, Youhong Sun, Yongping Yu and Shaopeng Zheng
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| Abstract | ||
| In this paper, an alternative analytical method is presented to evaluate the nonlinear vibration behavior of single and double tapered cantilever beams. The admissible lateral displacement function satisfying the geometric boundary conditions of a single or double tapered cantilever beam is derived by using Rayleigh-Ritz method. Based on the Lagrange method and the Newton Harmonic Balance (NHB) method, analytical approximate solutions in closed and explicit form are obtained. These approximate solutions show excellent agreement with those of numeric method for small as well as large amplitude. Moreover, due to brevity of expressions, the present analytical approximate solutions are convenient to investigate effects of various parameters on the large amplitude vibration response of tapered beams. | ||
| Key Words | ||
| Newton Harmonic Balance method; analytical approximation; nonlinear vibration; tapered beam | ||
| Address | ||
| Weipeng Sun: Department of Mechanics and Engineering Science, School of Mathematics, Jilin University, Changchun 130012, PR China Youhong Sun, Yongping Yu and Shaopeng Zheng: College of Construction Engineering, Jilin University, Changchun 130026, P.R. China | ||