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Smart Structures and Systems Volume 20, Number 4, October 2017 , pages 509-524 DOI: https://doi.org/10.12989/sss.2017.20.4.509 |
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Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory |
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Fatima Zohra Zaoui, Abdelouahed Tounsi and Djamel Ouinas
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| Abstract | ||
| In this article, a free vibration analysis of functionally graded (FG) plates resting on elastic foundations is presented using a quasi-3D hybrid-type higher order shear deformation theory. Undetermined integral terms are employed in the proposed displacement field and modeled based on a hybrid-type (sinusoidal and parabolic) quasi-3D HSDT with five unknowns in which the stretching effect is taken into account. Thus, it can be said that the significant feature of this theory is that it deals with only 5 unknowns as the first order shear deformation theory (FSDT). The elastic foundation parameters are introduced in the present formulation by following the Pasternak (two-parameter) mathematical model. Equations of motion are obtained via the Hamilton\'s principles and solved using Navier\'s method. Accuracy of the proposed theory is confirmed by comparing the results of numerical examples with the ones available in literature. | ||
| Key Words | ||
| vibration; functionally graded plate; elastic foundation; shear deformation theory; stretching effect | ||
| Address | ||
| Fatima Zohra Zaoui and Djamel Ouinas: Laboratoire de Modélisation Numérique et Expérimentale des Phénomènes Mécaniques, Faculté des Sciences et Technologie, Département de Génie Mécanique, Université Abdelhamid Ibn Badis of Mostaganem, 27000, Algeria Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes,Faculté de Technologie, Département de génie civil, Algeria; Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria | ||