Size-Dependent Geometrically Nonlinear Free Vibration of First-Order Shear Deformable Piezoelectric-Piezomagnetic Nanobeams Using the Nonlocal Theory
Year: 2018
Author: Raheb Gholami, Reza Ansari
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 1 : pp. 184–208
Abstract
This article investigates the geometrically nonlinear free vibration of piezoelectric-piezomagnetic nanobeams subjected to magneto-electro-thermal loading taking into account size effect using the nonlocal elasticity theory. To this end, the size-dependent nonlinear governing equations of motion and corresponding boundary conditions are derived according to the nonlocal elasticity theory and the first-order shear deformation theory with von Kármán-type of kinematic nonlinearity. The effects of size-dependence, shear deformations, rotary inertia, piezoelectric-piezomagnetic coupling, thermal environment and geometrical nonlinearity are taken into account. The generalized differential quadrature (GDQ) method in conjunction with the numerical Galerkin method, periodic time differential operators and pseudo arc-length continuation method is utilized to compute the nonlinear frequency response of piezoelectric-piezomagnetic nanobeams. The influences of various parameters such as non-dimensional nonlocal parameter, temperature change, initial applied electric voltage, initial applied magnetic potential, length-to-thickness ratio and different boundary conditions on the geometrically nonlinear free vibration characteristics of piezoelectric-piezomagnetic nanobeams are demonstrated by numerical examples. It is illustrated that the hardening spring effect increases with increasing the non-dimensional nonlocal parameter, positive initial applied voltage, negative initial applied magnetic potential, temperature rise and decreases with increasing the negative initial applied voltage, positive initial applied magnetic potential and length-to-thickness ratio.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2015.m1298
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 1 : pp. 184–208
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Piezoelectric-piezomagnetic nanobeams geometrically nonlinear free vibration nonlocal elasticity theory size effect magneto-electro-thermal loading.
Author Details
-
Analysis of resonant/nonresonant vibrations of simply-supported Kirchhoff nanoplates under in–plane magnetic field based on a strongly coupled two-mode model
Sypniewska-Kamińska, G. | Awrejcewicz, J. | Mazur, O.Thin-Walled Structures, Vol. 199 (2024), Iss. P.111832
https://doi.org/10.1016/j.tws.2024.111832 [Citations: 0] -
Vibration control of an axially loaded composite beam bonded with Piezoelectric actuator and sensor layers on a Winkler–Pasternak foundation and under transverse excitation force based on first-order shear deformation theory
Mamandi, Ahmad
Sādhanā, Vol. 48 (2023), Iss. 4
https://doi.org/10.1007/s12046-023-02239-4 [Citations: 0] -
Size-dependent vibration of functionally graded rotating nanobeams with different boundary conditions based on nonlocal elasticity theory
Fang, Jianshi | Yin, Bo | Zhang, Xiaopeng | Yang, BinProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 236 (2022), Iss. 6 P.2756
https://doi.org/10.1177/09544062211038029 [Citations: 18] -
Nonlinear vibration of magnetoelectroelastic nanoscale shells embedded in elastic media in thermoelectromagnetic fields
Wang, Yan Qing | Liu, Yun Fei | Zu, Jean WJournal of Intelligent Material Systems and Structures, Vol. 30 (2019), Iss. 15 P.2331
https://doi.org/10.1177/1045389X19862382 [Citations: 6] -
Hygro-thermo-mechanical vibration of two vertically aligned single-walled boron nitride nanotubes conveying fluid
Zarabimanesh, Yalda | Roodgar Saffari, Pouyan | Roudgar Saffari, Peyman | Refahati, NimaJournal of Vibration and Control, Vol. 28 (2022), Iss. 15-16 P.2101
https://doi.org/10.1177/10775463211006512 [Citations: 28] -
Free vibration problem of fluid-conveying double-walled boron nitride nanotubes via nonlocal strain gradient theory in thermal environment
Roodgar Saffari, Pouyan | Fakhraie, Mehran | Roudbari, Mir AbbasMechanics Based Design of Structures and Machines, Vol. 50 (2022), Iss. 10 P.3665
https://doi.org/10.1080/15397734.2020.1819310 [Citations: 23] -
Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory
Malikan, Mohammad | Nguyen, Van BacPhysica E: Low-dimensional Systems and Nanostructures, Vol. 102 (2018), Iss. P.8
https://doi.org/10.1016/j.physe.2018.04.018 [Citations: 79] -
Elastic Buckling and Free Vibration of Functionally Graded Piezoelectric Nanobeams Using Nonlocal Integral Models
Ren, Yanming | Qing, HaiInternational Journal of Structural Stability and Dynamics, Vol. 22 (2022), Iss. 05
https://doi.org/10.1142/S021945542250047X [Citations: 19] -
Nonlinear dynamics and vibration of reinforced piezoelectric scale-dependent plates as a class of nonlinear Mathieu–Hill systems: parametric excitation analysis
Shariati, Ali | Hosseini, S. Hamed S. | Ebrahimi, Farzad | Toghroli, AliEngineering with Computers, Vol. 37 (2021), Iss. 3 P.2285
https://doi.org/10.1007/s00366-020-00942-y [Citations: 17]