|
Advances in Aircraft and Spacecraft Science Volume 3, Number 4, October 2016 , pages 379-397 DOI: https://doi.org/10.12989/aas.2016.3.4.379 |
||
|
The effect of finite strain on the nonlinear free vibration of a unidirectional composite Timoshenko beam using GDQM |
||
Ahmad Reza Ghasemi and Masood Mohandes
|
||
| Abstract | ||
| In this manuscript, free vibrations of a unidirectional composite orthotropic Timoshenko beam based on finite strain have been studied. Using Green-Lagrange strain tensor and comprising all of the nonlinear terms of the tensor and also applying Hamilton\'s principle, equations of motion and boundary conditions of the beam are obtained. Using separation method in single-harmonic state, time and locative variables are separated from each other and finally, the equations of motion and boundary conditions are gained according to locative variable. To solve the equations, generalized differential quadrature method (GDQM) is applied and then, deflection and cross-section rotation of the beam in linear and nonlinear states are drawn and compared with each other. Also, frequencies of carbon/epoxy and glass/epoxy composite beams for different boundary conditions on the basis of the finite strain are calculated. The calculated frequencies of the nonlinear free vibration of the beam utilizing finite strain assumption for various geometries have been compared to von Karman one. | ||
| Key Words | ||
| finite strain; composite beam; Timoshenko model; nonlinear free vibration; GDQM | ||
| Address | ||
| Ahmad Reza Ghasemi and Masood Mohandes: Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran | ||
