Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory

Hakima Matouk , Abdelmoumen Anis Bousahla , Houari Heireche , Fouad Bourada , E.A. Adda Bedia , Abdeldjebbar Tounsi , K.H. Benrahou

Abstract

In the current research, the free vibrational behavior of the FG nano-beams integrated in the hygro-thermal environment and reposed on the elastic foundation is investigated using a novel integral Timoshenko beam theory (ITBT). The current model has only three variables unknown and requires the introduction of the shear correction factor because her uniformed variation of the shear stress through the thickness. The effective properties of the nano-beam vary according to power-law and symmetric sigmoid distributions. Three models of the hygro-thermal loading are employed. The effect of the small scale effect is considered by using the nonlocal theory of Eringen. The equations of motion of the present model are determined and resolved via Hamilton principle and Navier method, respectively. Several numerical results are presented thereafter to illustrate the accuracy and efficiency of the actual integral Timoshenko beam theory. The effects of the various parameters influencing the vibrational responses of the P-FG and SS-FG nano-beam are also examined and discussed in detail.

Key Words

FG nano-beam; vibrational behavior; Integral Timoshenko beam theory; hygro-thermal effect

Address

(1) Hakima Matouk, Abdelmoumen Anis Bousahla, Houari Heireche, Abdelouahed Tounsi, S.R. Mahmoud
, Abdeldjebbar Tounsi — Laboratoire de Modélisation et Simulation Multi-échelle, Départment de Physique, Faculté des Sciences Exactes, Université de Sidi Bel Abbés, Algeria
(2) Abdelmoumen Anis Bousahla — Centre Universitaire de Relizane, Algérie; (3) Abdelmoumen Anis Bousahla, E.A. Adda Bedia, Abdelouahed Tounsi: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia; (4) Fouad Bourada, Abdelouahed Tounsi
, K.H. Benrahou — Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
(5) Fouad Bourada — Département des Sciences et de la Technologie, centre universitaire de Tissemsilt, BP 38004 Ben Hamouda, Algeria; (6) S.R. Mahmoud: GRC Department, Jeddah Community College, King Abdulaziz University, Jeddah, Saudi Arabia.

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