An analytic solution of transversal oscillation of quintic non-linear beam with homotopy analysis method
- 作者：Hamid M. Sedighi ; h-msedighi@phdstu.scu.ac.ir ; hmsedighi@gmail.com ; Kourosh H. Shirazi ; Jamal Zare
- 关键词：Homotopy analysis method ; Non-linear transversal vibration ; Quintic nonlinearity ; Hamilton&rsquo ; s principle ; Bubnov&ndash ; Galerkin
- 刊名：International Journal of Non-Linear Mechanics
- 出版年：2012
- 期刊代码：87_00207462
- 类别：et
- 出版时间：September, 2012
- 卷：47
- 期：7
- 页码：777-784
- 文件大小：1002 K
摘要
non-linear vibration analysis of beam used in steel structures is of particular importance in mechanical and industrial applications. To achieve a proper design of the beam structures, it is essential to realize how the beam vibrates in its transverse mode which in turn yields the natural frequency of the system. Equation of transversal vibration of hinged-hinged flexible beam subjected to constant excitation at its free end is identified as a non-linear differential equation. The quintic non-linear equation of motion is derived based on Hamilton鈥檚 principle and solved by means of an analytical technique, namely the Homotopy analysis method. To verify the soundness of the results, a comparison between analytical and numerical solutions is developed. Finally, to express the impact of the quintic nonlinearity, the non-linear responses obtained by HAM are compared with the results from usual beam theory.