Approximations for Large Deflection of a Cantilever Beam under a Terminal Follower Force and Nonlinear Pendulum
In theoretical mechanics field, solution methods for nonlinear differential equations are very important because many problems are modelled using such equations. In particular, large deflection of a cantilever beam under a terminal follower force and nonlinear pendulum problem can be described by th...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2013 |
| País: | México |
| Institución: | Instituto Nacional de Astrofísica, Óptica y Electrónica |
| Repositorio: | Repositorio Institucional del INAOE |
| Idioma: | inglés |
| OAI Identifier: | oai:inaoe.repositorioinstitucional.mx:1009/2359 |
| Acceso en línea: | http://inaoe.repositorioinstitucional.mx/jspui/handle/1009/2359 |
| Access Level: | acceso abierto |
| Palabra clave: | info:eu-repo/classification/Inspec/Theoretical mechanics field info:eu-repo/classification/Inspec/Nonlinear differential equations info:eu-repo/classification/Inspec/Large deflection info:eu-repo/classification/Inspec/Homotopy perturbation method info:eu-repo/classification/cti/1 info:eu-repo/classification/cti/22 info:eu-repo/classification/cti/2203 |
| Sumario: | In theoretical mechanics field, solution methods for nonlinear differential equations are very important because many problems are modelled using such equations. In particular, large deflection of a cantilever beam under a terminal follower force and nonlinear pendulum problem can be described by the same nonlinear differential equation. Therefore, in this work, we propose some approximate solutions for both problems using nonlinearities distribution homotopy perturbation method, homotopy perturbation method, and combinations with Laplace-Padé posttreatment. We will show the high accuracy of the proposed cantilever solutions, which are in good agreement with other reported solutions. Finally, for the pendulum case, the proposed approximation was useful to predict, accurately, the period for an angle up to 179.99999999º yielding a relative error of 0.01222747. |
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