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Geomechanics and Engineering
  Volume 16, Number 2, October10 2018, pages 141-150
DOI: https://doi.org/10.12989/gae.2018.16.2.141
 


Vibration analysis of thick orthotropic plates using quasi 3D sinusoidal shear deformation theory
Mohamed Sadoun, Mohammed Sid Ahmed Houari, Ahmed Bakora, Abdelouahed Tounsi, S.R. Mahmoud and Afaf S. Alwabli

 
Abstract
    In this current work a quasi 3D \"trigonometric shear deformation theory\" is proposed and discussed for the dynamic of thick orthotropic plates. Contrary to the classical \"higher order shear deformation theories\" (HSDT) and the \"first shear deformation theory\" (FSDT), the constructed theory utilizes a new displacement field which includes \"undetermined integral terms\" and presents only three \"variables\". In this model the axial displacement utilizes sinusoidal mathematical function in terms of z coordinate to introduce the shear strain impact. The cosine mathematical function in terms of z coordinate is employed in vertical displacement to introduce the impact of transverse \"normal deformation\". The motion equations of the model are found via the concept of virtual work. Numerical results found for frequency of \"flexural mode\", mode of shear and mode of thickness stretch impact of dynamic of simply supported \"orthotropic\" structures are compared and verified with those of other HSDTs and method of elasticity wherever considered.
 
Key Words
    plate theory; vibration; orthotropic plate
 
Address
Mohamed Sadoun and Mohammed Sid Ahmed Houari: 1.) Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
2.) Department of Civil Engineering, University Mustapha Stambouli of Mascara, Mascara, Algeria

Ahmed Bakora: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria

Abdelouahed Tounsi: 1.) Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
2.) Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia

S.R. Mahmoud: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah Saudi Arabia

Afaf S. Alwabli: Department of Biology, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
 

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