https://doi.org/10.1140/epjp/s13360-021-01591-w
Regular Article
Elasto-dynamics of doubly mislocated stocky beam-like nanostructures immersed in inclined magnetic fields using nonlocal continuum mechanics
1
School of Civil Engineering and Architecture, Nanchang Institute of Technology, 330099, Nanchang, China
2
Department of Civil Engineering, K.N. Toosi University of Technology, P.O. Box: 15875-4416, Valiasr Ave., Tehran, Iran
b k_kiani@kntu.ac.ir, keivankiani@yahoo.com
Received:
22
December
2020
Accepted:
19
May
2021
Published online:
4
June
2021
Transverse vibration of double-parallel nanobeams with a mislocation under action of an inclined magnetic field is of high interest. From mechanics point of view, the mislocation substantially influences on the rigorous inter-structure van der Waals forces, while the inclination of the magnetic field is incorporated into the transverse Lorentzian forces as well as the lateral stiffness of the nanosystem. By utilizing the principle of Hamilton, dynamical governing equations of the nanosystem are constructed by employing nonlocal continuum-based Euler–Bernoulli, Timoshenko, and Reddy–Bickford beams. These are, respectively, two, four, and four coupled partial differential equations. To solve them for nonlocal frequencies, reproducing kernel particle method (RKPM) is exploited. To validate the carried out calculations, a Galerkin-based admissible modes approach (AMA) is also developed. For simply supported nanosystem, the results of the RKPM are successfully checked with those of the AMA. In continuing, the effects of magnetic field strength, its inclination, nonlocality, mislocation, and shear effect on the dominant frequencies are explained methodically. Additionally, the roles of crucial geometry parameters, including slenderness ratio, length ratio, and radii of nanobeams on the vibrations of the magnetically affected-mislocated nanosystem, under various boundary conditions on the basis of the above-mentioned theories are displayed.
K. Kiani: Dedicated to the honorable memory of my beloved mother, Kobra Ahmadi (1950–July 21, 2020).
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
