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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