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ORIGINAL ARTICLE

Wave dispersion characteristics of fluid-conveying magneto-electroelastic nanotubes M. Dehghan1 • F. Ebrahimi1 • M. Vinyas2,3 Received: 8 February 2019 / Accepted: 27 May 2019 Ó Springer-Verlag London Ltd., part of Springer Nature 2019

Abstract In this paper, the wave propagation analysis of fluid-conveying magneto-electro-elastic (MEE) nanotube incorporating fluid effect is investigated. To take into account the small-scale effects, the nonlocal elasticity theory of Eringen is employed. Nonlocal governing equations of MEE-FG nanotube have been derived utilizing Hamilton’s principle. The results of this study have been verified by checking them with antecedent investigations. An analytical solution of governing equations is used to acquire wave frequencies and phase velocities. The Knudsen number is applied to study the effect of slip boundary wall of nanotube and flow. Effect of Knudsen number, different modes, length parameter, nonlocal parameter, fluid velocity, fluid effect and slip boundary condition on wave propagation characteristics of fluid-conveying MEE nanotube is investigated, and the results are presented in detail. Keywords Nanotube  Electro-magneto elastic  Wave propagation  Nonlocal strain gradient elasticity theory  Cylindrical shell theory

1 Introduction Magneto-electro-elastic materials (MEEMs) for their special capability and many kinds of energy conversions have received a lot of attention in last researches. These novel types of materials are blend of two phases (piezoelectric phase and piezomagnetic phase). According such advantages, this type of material can be applied in different engineering devices such as sensors, actuators or controllers. Many researchers applied continuum mechanics in order to investigate nanomaterial’s mechanical behavior, and it is very important to take into regard the small-scale influences in the mechanical analysis Therefore, size-dependent continuum theories, such as nonlocal elasticity & F. Ebrahimi [email protected] 1

Mechanical Engineering Department, Faculty of Engineering, Imam Khomeini International University, P.O.B. 16818-34149, Qazvin, Iran

2

Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India

3

Department of Mechanical Engineering, Nitte Meenakshi Institute of Technology, Bangalore 560064, India

theory [1, 2] and strain gradient theory [3], are expanded to consider the small-scale effect [4–6]. Few prominent kinds of the literature have been reported on assessing the various characteristics of nanoplates and nanobeams. Among them, Tlidji et al. [7] evaluated the free vibration response of FG microbeam. Through refined nonlocal shear deformation beam theory, Zemri et al. [8] investigated the mechanical response of FG nanobeams. Bouafia et al. [9] probed the bending and free flexural vibration behaviors of functionally graded nanobeams using a nonlocal quasi-3D theory. Considering the surface effects, the dynamic behavior of nanobeams