Bifurcation and Chaos of Functionally Graded Carbon Nanotube Reinforced Composite Beam with Piezoelectric Layer

Bifurcation and Chaos of Functionally Graded Carbon Nanotube Reinforced Composite Beam with Piezoelectric Layer

Year:    2021

Author:    Jinhua Yang, Gaofeng Sun, Jie Yang

Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 3 : pp. 569–589

Abstract

This paper investigates bifurcation and chaos of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) beam containing piezoelectric layer (PL) under combined electro-thermo-mechanical loads. We assumed that FG-CNTRC material properties were graded along thickness direction and determined them using mixtures' law. Governing equations of structures were derived according to the theory of Euler-Bernoulli beam, PL with thermal effects and von Kármán geometric nonlinearity. Next, the governing equations were transformed into second order nonlinear ordinary differential equations (SNODE) with cubic terms through Galerkin procedure and further into first order nonlinear ordinary differential equations (FNODE) through introducing additional state variables. Complex system dynamic behavior was qualitatively examined using fourth order Runge-Kutta method. The effects of different factors including applied voltage, volume fraction, temperature change, and distribution of carbon nanotubes (CNTs) on bifurcation and chaos of FG-CNTRC beams with PL were comprehensively studied.

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.OA-2020-0081

Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 3 : pp. 569–589

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    FG-CNTRC beam bifurcation and chaos piezoelectric Runge-Kutta method Galerkin procedure.

Author Details

Jinhua Yang

Gaofeng Sun

Jie Yang

  1. Investigating the Elastic Response of Smart Cylinders Under Asymmetric Loading

    Eftekhari , Malihe

    International journal of Modern Achievement in Science, Engineering and Technology, Vol. 1 (2023), Iss. 1 P.65

    https://doi.org/10.63053/ijset.5 [Citations: 0]
  2. Thermal coupling model of a traveling flexible printing electronical membrane subjected to nonlinear electrostatical force

    Ying, Shudi | Wu, Jimei | Wang, Yan

    Journal of Low Frequency Noise, Vibration and Active Control, Vol. 42 (2023), Iss. 4 P.1616

    https://doi.org/10.1177/14613484231164547 [Citations: 0]
  3. Exact Solution for Dynamic Deflection of Fluid-Conveying Nanotubes Flexibly Restrained at the Ends by Means of Green’s Function Method

    Hosseini, M. | Makkiabadi, M. | Bahaadini, R.

    Mechanics of Solids, Vol. 57 (2022), Iss. 5 P.1157

    https://doi.org/10.3103/S0025654422050077 [Citations: 3]