Nonlinear dynamic characteristics of nonlocal multi-phase magneto-electro-elastic nano-tubes with different piezoelectri
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Nonlinear dynamic characteristics of nonlocal multi‑phase magneto‑electro‑elastic nano‑tubes with different piezoelectric constituents Seyed Sajad Mirjavadi1 · Masoud Forsat1 · Salman Badnava2 · Mohammad Reza Barati3 · A. M. S. Hamouda1 Received: 10 September 2019 / Accepted: 19 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Analysis of exact nonlinear dynamic behavior of multi-phase magneto-electro-elastic (MEE) nanoshells has been presented in this paper using Jacobi elliptic functions. Multi-phase MEE material is constructed form piezoelectric and piezo-magnetic constituents for which the material properties can be controlled based on the percentages of the constituents. Nonlinear governing equations are established for MEE nanoshell based on nonlocal elasticity theory and an exact solution is provided using Jacobi elliptic function method. This method gives an exact value of vibration frequency in nonlinear regime and overcomes the shortcomings of several approximate solutions applied in the studies on nanostructures. It will be shown that nonlinear vibration behavior of MEE nanoshell in electro-magnetic field depends on the constituent’s percentages. Influences of nonlocal scale factor, piezoelectric reinforcement, magnetic field intensity, and electrical voltage on vibration frequencies of the nanoshell are also investigated. Keywords Nonlinear vibration · Classical shell theory · Jacobi elliptic function · Magneto-electro-elastic material · Nonlocal theory
1 Introduction Giving topmost mechanical efficiency under electrical and magnetic fields, a magneto-electro-elastic (MEE) material may be defined as a species of smart material having different application in sensing apparatus, smart systems, and structural components [1]. Exposing to an exterior mechanical loading, a MEE material is capable to render electrical–magnetic field * Masoud Forsat [email protected] Seyed Sajad Mirjavadi [email protected] Mohammad Reza Barati [email protected] A. M. S. Hamouda [email protected] 1
Department of Mechanical and Industrial Engineering, Qatar University, P.O. Box 2713, Doha, Qatar
2
Department of Electrical Engineering, Qatar University, Doha, Qatar
3
Fidar Project Qaem Company, Darvazeh Dolat, 15875‑4413 Tehran, Iran
sensing [2]. Furthermore, under electro-magnetic fields, such material experiences elastic deformations [3]. For example, BaTiO3 and C oFe2O4 may be composed to each other for creating a composite of MEE materials. According to the percentages of the two constituents, it is feasible to define material properties of the composite such as elastic moduli and piezomagnetic constants [4]. It is shown by other authors that vibration frequency of MEE structures is sensitive to the percentage of piezoelectric phase and hence vibration behavior of MEE can be controlled by varying the material composition [5]. MEE materials and structures have found their application in nano-technologies due to possessing extraordinary character in ele
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