Vibration analysis of different material distributions of functionally graded microbeam

Youcef Tlidji , Mohamed Zidour , Kadda Draiche , Abdelkader Safa , Mohamed Bourada , Abdelouahed Tounsi , Abdelmoumen Anis Bousahla , S.R. Mahmoud

Abstract

In the current research paper, a quasi-3D beam theory is developed for free vibration analysis of functionally graded microbeams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by three functions, power function, symmetric power function and sigmoid law distribution. The modified coupled stress theory is used to incorporate size dependency of micobeam. The equation of motion is derived by using Hamilton\'s principle, however, Navier type solution method is used to obtain frequencies. Numerical results show the effects of the function distribution, power index and material scale parameter on fundamental frequencies of microbeams. This model provides designers with guidance to select the proper distributions and functions.

Key Words

vibration; microbeam; law distribution; quasi-3D theory; functionally graded material

Address

Youcef Tlidji and Kadda Draiche — 1) Laboratory of Materials et Hydrology, University of Sidi Bel Abbes, BP 89 Cite Ben M\'hidi, 22000 Sidi Bel Abbes, Algeria 2) Department of Civil Engineering, Ibn Khaldoun University, BP 78 Zaaroura, 14000 Tiaret, Algeria
Mohamed Zidour — 1) Department of Civil Engineering, Ibn Khaldoun University, BP 78 Zaaroura, 14000 Tiaret, Algeria 2) Laboratory of Geomatics and Sustainable Development, Ibn Khaldoun University of Tiaret, Algeria
Abdelkader Safa and Abdelmoumen Anis Bousahla — 1) Laboratory of Materials et Hydrology, University of Sidi Bel Abbes, BP 89 Cite Ben M\'hidi, 22000 Sidi Bel Abbes, Algeria 2) Department of Civil Engineering, Ahmed Zabana University, 48000 Relizane, Algeria
Mohamed Bourada — Laboratory of Materials et Hydrology, University of Sidi Bel Abbes, BP 89 Cite Ben M\'hidi, 22000 Sidi Bel Abbes, Algeria
Abdelouahed Tounsi — 1) Laboratory of Materials et Hydrology, University of Sidi Bel Abbes, BP 89 Cite Ben M\'hidi, 22000 Sidi Bel Abbes, Algeria 2) Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia
S.R. Mahmoud — Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

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