Stability Configuration of a Rocking Rigid Rod over a Circular Surface Using the Homotopy Perturbation Method and Laplace Transform

被引：0
作者：
Yusry O. El-Dib
Galal M. Moatimid
机构：
[1] Ain Shams University,Department of Mathematics, Faculty of Education
来源：
Arabian Journal for Science and Engineering | 2019年 / 44卷
关键词：
Homotopy perturbation method; Laplace transform; Frequency analysis; Stability analysis; Rocking rigid rod;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The current paper is concerned with the motion of a rocking uniform rigid rod, without slipping, over a rigid circular surface. The governing equation of motion resulted in a highly nonlinear second-order ordinary differential equation. This nonlinear equation has no natural frequency. A coupling the homotopy perturbation method and Laplace transform is adopted to obtain an approximate solution of the equation of motion. In addition, He’s transformation method is used to obtain a periodic solution. Stability conditions are derived by making use of a nonlinear frequency analysis. Numerical calculations are achieved to investigate the governed perturbed solutions as well as the stability picture. It is found that the radius of the length of the rigid rod as well as the radius of the circular surface has a stabilizing influence. In contrast, the initial angular velocity has a destabilizing effect.
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收藏
页码：6581 / 6591
页数：10
相关论文
共 44 条
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