Natural frequencies of FGM nanoplates embedded in an elastic medium

Halima Bouafia, Abdelbaki Chikh, Abdelmoumen Anis Bousahla, Fouad Bourada, Houari Heireche, Abdeldjebbar Tounsi, Kouider Halim Benrahou, Abdelouahed Tounsi, Mesfer Mohammad Al-Zahrani and Muzamal Hussain

Abstract

The small scale impact on the vibrational properties of "unctionally graded" (FG) nanoplate embedded in an elastic medium is examined. The formulation is based on the four-unknown refined integral plate theory on aggregate with the nonlocal elasticity theory. Contrary to other theories, this one involves only four unknown variables. The solution procedure is obtained by employing the motion differential equations of physical phase that are converted into set of "linear algebraic equations". After, these are solved by a computer code. The influences of aspect ratio, material index, nonlocal parameter and elastic medium stiffness on the different modal vibrations of FG nanoplate are explored. The results demonstrate the significant impact of different physical and geometrical parameters on the vibration behavior of FG nanoplate.

Key Words

elastic medium; FG nanoplate; four-unknown refined integral plate theory; nonlocal theory; vibration

Address

Halima Bouafia, Abdelmoumen Anis Bousahla and Houari Heireche: Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria Abdelbaki Chikh: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria/ Université Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algérie Fouad Bourada: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria/ Département des Sciences et de la Technologie, Université de Tissemsilt, BP 38004 Ben Hamouda, Algérie Abdeldjebbar Tounsi and Kouider Halim Benrahou: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria/ YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea/ Civil and Environmental Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia Mesfer Mohammad Al-Zahrani: Civil and Environmental Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia Muzamal Hussain: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan

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