Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT

Sabrina Boutaleb , Kouider Halim Benrahou , Ahmed Bakora , Ali Algarni , Abdelmoumen Anis Bousahla , Abdelouahed Tounsi , Abdeldjebbar Tounsi , S.R. Mahmoud

Abstract

In the present work the dynamic analysis of the functionally graded rectangular nanoplates is studied. The theory of nonlocal elasticity based on the quasi 3D high shear deformation theory (quasi 3D HSDT) has been employed to determine the natural frequencies of the nanosize FG plate. In HSDT a cubic function is employed in terms of thickness coordinate to introduce the influence of transverse shear deformation and stretching thickness. The theory of nonlocal elasticity is utilized to examine the impact of the small scale on the natural frequency of the FG rectangular nanoplate. The equations of motion are deduced by implementing Hamilton\'s principle. To demonstrate the accuracy of the proposed method, the calculated results in specific cases are compared and examined with available results in the literature and a good agreement is observed. Finally, the influence of the various parameters such as the nonlocal coefficient, the material indexes, the aspect ratio, and the thickness to length ratio on the dynamic properties of the FG nanoplates is illustrated and discussed in detail.

Key Words

nonlocal elasticity theory; FG nanoplate; free vibration; refined theory; elastic foundation

Address

(1) Sabrina Boutaleb, Kouider Halim Benrahou, Ahmed Bakora, Abdelouahed Tounsi, Abdeldjebbar Tounsi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
(2) Ahmed Bakora — Département de Génie Civil, Faculté d\'Architecture et de Génie Civil, Université des Sciences et de la Technologie d\'Oran, BP 1505 El M\'naouer, USTO, Oran, Algeria
(3) Ali Algarni — Statistics Department, Faculty of Science, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia
(4) Abdelmoumen Anis Bousahla — Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria
(5) Abdelmoumen Anis Bousahla — Centre Universitaire Ahmed Zabana de Relizane, Algeria
(6) Abdelouahed Tounsi — Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia
(7) S.R. Mahmoud — Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.

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