Thermo magnetic response of nonlocal propagation of waves in rotating graphene tubules
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Thermo magnetic response of nonlocal propagation of waves in rotating graphene tubules A. Amuthalakshmi1 · S. Selvi Celin Prabha1 Received: 10 May 2020 / Accepted: 17 August 2020 © Springer Nature Switzerland AG 2020
Abstract Thermo magnetic response of propagation of waves in rotating graphene tubules is studied with the aid of nonlocal Euler–Bernoulli beam theory within the framework of spectral analysis. The governing dynamic equation of nonlocal rotating graphene tubules under thermo magnetic response is formulated with the help of equation of thermal force, centrifugal force and electromagnetic force. The dispersion equation of nonlocal rotating graphene tubules under thermo magnetic field is derived. The numerical value of non-dimensional wave number is computed and is represented in terms of scattered curves. The scattered curves of graphene tubules at different rotating speed, nonlocal parameter, temperature and magnetic field strength are also drawn. The results give useful information in the study and design of rotary nano-devices such as nano motors, nanoturbines, nano robots etc. The dispersion curves of non-rotating graphene tubules in the absence of thermal and magnetic field are drawn and are compared with the existing literature. Keywords Graphene tubule · Rotational speed · Temperature · Nonlocal parameter · Magnetic field strength Mathematics Subject Classification 74JXX · 74SXX
1 Introduction Graphene tubules are advanced remarkably as a result of numerous applications in science and engineering and it is due to its thermal, mechanical, physical, chemical and magnetic properties. Ebrahimi et al. [1] employed the nonlocal elasticity theory and analyzed the vibration characteristics of rotating non-homogeneous nanobeam using power-law model, Hamilton’s principle and Euler Bernoulli beam theory. Later Ebrahimi and Haghi [2] investigated the dispersion characteristics of rotating nanotube under the thermal environment within the framework of the Galerkin approach. Chan and Zhao [3] developed an inexpensive model to examine the dispersal features of spinning single walled carbon nanotube (SWCNT). Narendar [4] modelled a rotating nanotube utilizing the Euler
Bernoulli beam theory predicated on continuum mechanics. Later the same author [5] developed the nonlocal flap wise wave propagation of rotating nanotube. Narendar et al. [6] deliberate the dispersion features of magnetic response of SWCNTs. Wang et al. [7] examined the outcome of thermal and magnetic response on tera hertz wave conception in fluid conveying SWCNT. Kiani [8] examined the magnetic response of nonlocal flexural wave conception of SWCNTs using Timoshenko, nonlocal Rayleigh and higher-order beams. Wang et al. [9] proposed the magnetic response of propagation of waves fixed in stretchy medium. Guven [10] dispensed the magnetic response of the flexural wave propagation of SWCNT. Ponnusamy and Amuthalakshmi [11] studied the response of thermo magnetic force on fluctuation in double walled carbon nanotubes utilizing nonlocal Timosh
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