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Volume 13, Issue 3
Bifurcation and Chaos of Functionally Graded Carbon Nanotube Reinforced Composite Beam with Piezoelectric Layer

Jinhua Yang, Gaofeng Sun & Jie Yang

Adv. Appl. Math. Mech., 13 (2021), pp. 569-589.

Published online: 2020-12

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  • 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.

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@Article{AAMM-13-569, author = {Yang , JinhuaSun , Gaofeng and Yang , Jie}, title = {Bifurcation and Chaos of Functionally Graded Carbon Nanotube Reinforced Composite Beam with Piezoelectric Layer}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {13}, number = {3}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0081}, url = {http://global-sci.org/intro/article_detail/aamm/18498.html} }
TY - JOUR T1 - Bifurcation and Chaos of Functionally Graded Carbon Nanotube Reinforced Composite Beam with Piezoelectric Layer AU - Yang , Jinhua AU - Sun , Gaofeng AU - Yang , Jie JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 569 EP - 589 PY - 2020 DA - 2020/12 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2020-0081 UR - https://global-sci.org/intro/article_detail/aamm/18498.html KW - FG-CNTRC beam, bifurcation and chaos, piezoelectric, Runge-Kutta method, Galerkin procedure. AB -

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.

Jinhua Yang, Gaofeng Sun & Jie Yang. (1970). Bifurcation and Chaos of Functionally Graded Carbon Nanotube Reinforced Composite Beam with Piezoelectric Layer. Advances in Applied Mathematics and Mechanics. 13 (3). 569-589. doi:10.4208/aamm.OA-2020-0081
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