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...

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Detalles Bibliográficos
Autores: Librado Arturo Sarmiento Reyes, ALEJANDRO DIAZ SANCHEZ
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
Descripción
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.