1. SID AHMED REFFAS - Laboratoire Mécanique et Physique Des Matériaux, Département Génie Mécanique, Faculté de
Technologie, Université de Sidi Bel Abbes, BP 89 Cité Ben M’hidi, Sidi Bel Abbes, Algeria.
2. BENOUMRANE SALLAI - Département de Génie Civil et Des Travaux Publics, Faculté de Technologie, Université de Sidi Bel Abbes,
BP 89 Cité Ben M’hidi, Sidi Bel Abbes, Algeria.
3. YASSINE KHALFI - Laboratoire de Génie des Procédés, Matériaux et Environnement, Département Denseignements de Base
en Sciences et de la Technologie, Faculté de Technologie, Université de Sidi Bel Abbes, BP 89 Cité Ben
M’hidi, Sidi Bel Abbes, Algeria.
4. BACHIR BOUIADJRA BACHIR - LMPM, Institute of Maintenance and Industrial Safety, University of Oran 2 Mohamed Ben Ahmed, P.B 05
El M naouer Oran Algeria.
This study introduces an efficient shear strain theory for analyzing the vibration of functionally graded plates. The theory incorporates the parabolic distribution of transverse shear strains using a new hyperbolic warping function and meets zero-tension boundary conditions on the plate surfaces without employing shear correction factors. The mechanical properties of functionally graded plates are assumed to vary following a power-law distribution of the constituent volume fractions. The equations of motion are derived using the principle of variational energy and virtual work. Analytical solutions for the natural frequency are obtained for simply supported plates. The accuracy of these solutions is validated by comparing the results with those predicted by classical theory, first-order shear deformation theory, and higher-order shear deformation theory. It can be concluded that the proposed theory is both accurate and straightforward for predicting the natural frequencies of functionally graded plates.
Vibration; Functionally Graded Material; New Hyperbolic Warping Function; Volume Fraction; Power Law Index; Natural Frequency.