Nonlinear vibration characteristics of refined higher-order multi-phase piezo-magnetic nanobeams
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Nonlinear vibration characteristics of refined higher-order multi-phase piezo-magnetic nanobeams Raad M. Fenjan, Ridha A. Ahmed, Nadhim M. Faleha Engineering College, Al-Mustansiriah University, P.O. Box 46049, Bab-Muadum, Baghdad 10001, Iraq Received: 1 January 2020 / Accepted: 13 April 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper studies nonlinear dynamic characteristics of a nonlocal two-phase piezo-magnetic beam based on a refined higher-order beam formulation and piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. Nonlinear governing equations of a smart nanobeam are derived based on refined beam theory, and a numerical trend is provided to obtained nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric phase in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behavior of smart nanobeam is dependent on the magnitude of exerted electric voltage, magnetic potential, hardening elastic foundation and shear deformation.
1 Introduction A sort of composite intelligent material named magneto-electro-elastic (MEE) material owns enormous possible benefits in smart devices and even nanoscale devices and structures owing to representing outstanding electrical, magnetic and mechanical coupling performances [1–3]. Applying electrical or magnetic field to MEE nanobeams yields their elastic deformations and changing of vibrational properties [4–6]. Due to the reason that experimental investigation on the nanobeams is so hard yet, many scholars have represented their mathematical models by taking into account small-scale influences. According to nonlocal theory of elasticity [7], it may be feasible to bring up small-scale influences in mathematical formulation of a nanobeam [8–16]. The theory recommends a size factor called nonlocal parameter to declare the nonlocal character of stress field at nanoscale. There are many published articles on vibrational analysis of piezo-magnetic nanoscale beams based on nonlocal theory of elasticity and different beam theories. Using nonlocal theory, an investigation on small-amplitude vibrational characteristics of MEE nanobeams has been provided by Ke and Wang [17]. Also, Jandaghian and Rahmani [18] reported smallamplitude vibrational study of MEE nano-size beams lied on elastic foundation. In another paper, vibrational behaviors of a functionally graded piezo-magnetic nanobeam based on nonlocal theory have been explored by Ebrahimi and Barati [19]. Furthermore, Ebrahimi and
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Barati [20] investigated the influences of viscoelastic substrate on vibrational behaviors of MEE nanobeams according to nonloca
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