On propagation of elastic waves in an embedded sigmoid functionally graded curved beam

Linyun Zhou , Zohre Moradi , Haneen M. Al-Tamimi , H. Elhosiny Ali

Abstract

This investigation studies the characteristics of wave dispersion in sigmoid functionally graded (SFG) curved beams lying on an elastic substrate for the first time. Homogenization process was performed with the help of sigmoid function and two power laws. Moreover, various materials such as Zirconia, Alumina, Monel and Nickel steel were explored as curved beams materials. In addition, curved beams were rested on an elastic substrate which was modelled based on Winkler–Pasternak foundation. The SFG curved beams'governing equations were derived according to Euler-Bernoulli curved beam theory which is known as classic beam theory and Hamilton's principle. The resulted governing equations were solved via an analytical method. In order to validate the utilized method, the obtained outcomes were compared with other researches. Finally, the influences of various parameters, including wave number, opening angle, gradient index, Winkler coefficient and Pasternak coefficient were evaluated and indicated in the form of diagrams.

Key Words

elastic substrate; Euler-Bernoulli curved beam theory; sigmoid functionally graded; wave dispersion analysis

Address

Linyun Zhou — School of Transportation, Southeast University, Nanjing 210096, Jiangsu, China
Zohre Moradi — 1) Faculty of Engineering and Technology, Department of Electrical Engineering, Imam Khomeini International University, 34149-16818 Qazvin, Iran 2) Department of Biomaterials, Saveetha Dental College and Hospital, Saveetha Institute of Medical and Technical Sciences, Chennai 600 077, India
Haneen M. Al-Tamimi — Air Conditioning and Refrigeration Techniques Engineering Department, Al-Mustaqbal University College, Babylon, Iraq
H. Elhosiny Ali — 1) Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia 2) Research Center for Advanced Materials Science (RCAMS), King Khalid University, Abha 61413, P.O. Box 9004, Saudi Arabia 3) Physics Department, Faculty of Science, Zagazig University, 44519 Zagazig, Egypt

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