Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM

Mehar, Kulmani; Panda, Sidhartha; Bui, Tinh Quoc; Mahapatra, Trupti Ranjan

doi:10.1080/01495739.2017.1318689

Cited by 81 publications

(19 citation statements)

References 39 publications

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“…It is noticed that both the power spectrum and the Poincaré map can distinguish the periodic motions and the chaotic motions. When the l 2 is in the range of [21,27], the periodic motions and chaotic motions alternately occur, the system experiences periodic motion, multiperiodic motion, quasi-periodic motion, and chaotic motion. It is obvious that the nonlinear vibration characteristics of the system are complicated under the influence of external excitation.…”

Section: Numerical Simulationmentioning

confidence: 99%

“…A third-order theory which accounted for a cubic variation of the in-plane displacements through the plate thickness was derived by Librescu and Reddy [17]. Great progress has also been achieved in the study of the nonlinear thermoelastic frequency analysis [18][19][20][21][22]. Zhang [23] studied the global bifurcations and chaotic dynamics of simply supported rectangular thin plates under parametrical excitation by introducing von Karman's geometric nonlinearity plate theory.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Vibrations of Laminated Cross-Ply Composite Cantilever Plate in Subsonic Air Flow

Liu

Zhang

2020

Mathematical Problems in Engineering

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The nonlinear vibrations and responses of a laminated composite cantilever plate under the subsonic air flow are investigated in this paper. The subsonic air flow around the three-dimensional cantilever rectangle laminated composite plate is considered to be decreasing from the wing root to the wing tip. According to the ideal incompressible fluid flow condition and the Kutta–Joukowski lift theorem, the subsonic aerodynamic lift on the three-dimensional finite length flat wing is calculated by using the Vortex Lattice (VL) method. The finite length flat wing is modeled as a laminated composite cantilever plate based on Reddy’s third-order shear deformation plate theory and the von Karman geometry nonlinearity is introduced. The nonlinear partial differential governing equations of motion for the laminated composite cantilever plate subjected to the subsonic aerodynamic force are established via Hamilton’s principle. The Galerkin method is used to separate the partial differential equations into two nonlinear ordinary differential equations, and the four-dimensional nonlinear averaged equations are obtained by the multiple scale method. Through comparing the natural frequencies of the linear system with different material and geometric parameters, the relationship of 1 : 2 internal resonance is considered. Corresponding to several selected parameters, the frequency-response curves are obtained. The hardening-spring-type behaviors and jump phenomena are exhibited. The influence of the force excitation on the bifurcations and chaotic behaviors of the laminated composite cantilever plate is investigated numerically. It is found that the system is sensitive to the exciting force according to the complicate nonlinear behaviors exhibited in this paper.

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Section: Numerical Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibrations of Laminated Cross-Ply Composite Cantilever Plate in Subsonic Air Flow

Liu

Zhang

2020

Mathematical Problems in Engineering

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“…Based on several higher order shear deformation theories and generalized di erential quadrature method, Tornabene and co-workers [43][44][45] analyzed the static and free vibration responses of laminated composite plates and doubly curved shells reinforced by agglomerated CNTs. Using nite element method and a higher order shear deformation theory, nonlinear vibration and exural behaviors of composite single layer and sandwich doubly curved shell panels reinforced by CNTs under mechanical and thermal loads have been investigated by Mehar and co-authors [46][47][48][49][50][51][52]. There is a limited number of investigations on the nonlinear stability of FG-CNTRC doubly curved panels.…”

Section: Introductionmentioning

confidence: 99%

Thermomechanical nonlinear stability of pressure-loaded CNT-reinforced composite doubly curved panels resting on elastic foundations

Trang

Tung

2019

Nonlinear Engineering

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Nonlinear stability of nanocomposite spherical and cylindrical panels reinforced by carbon nanotubes (CNTs), resting on elastic foundations and subjected to uniform external pressure in thermal environments is investigated in this paper. CNTs are embedded into matrix phase through uniform distribution (UD) or functionally graded (FG) distribution, and effective properties of CNT-reinforced composite are estimated through an extended rule of mixture. Governing equations are based on classical shell theory taking geometrical nonlinearity, initial geometrical imperfection and panel-foundation interaction into consideration. Approximate solutions of deflection and stress functions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain nonlinear load-deflection relation. Numerical examples show the effects of volume fraction and distribution type of CNTs, in-plane condition of edges, curvature of panel, thermal environments, elastic foundations and imperfection size on the nonlinear response and snap-through instability of the curved panels. The present study reveals that efficiency of CNT distribution type depends on curvature of panel and in-plane behavior of boundary edges, and bifurcation type buckling response of pressure-loaded panels may occur at elevated temperature.

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“…Also, Thu and Duc considered the problem of nonlinear stability response of imperfect three‐phase sandwich laminated polymer nanocomposite panels resting on elastic foundations in thermal environments. Mehar et al . used the rule of mixture for nonlinear thermoelastic frequency analysis of FG CNT reinforced single/doubly curved shallow shell panels by finite element method.…”

Section: Introductionmentioning

confidence: 99%

Size‐dependent free vibration of sandwich micro beam with porous core subjected to thermal load based on SSDBT

2019

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In this study, free vibration of the sandwich microbeam with porous core and FG carbon nanotubes reinforced composite face sheets which is rested on Winkler‐Pasternak substrate is investigated. It is assumed the beam is in thermal environment and is subjected to thermal load and the displacement components are described based on sinusoidal shear deformation beam theory. The small scale effects are taken into account according to the modified couple stress theory. The core and face sheets properties are diffused through the thickness. The motion equations are derived and solved using Hamilton's principle and Navier's method, respectively. Effect of different parameters such as porosity coefficient and distributions, different types of CNTs distribution, small scale and geometrical size of the beam is considered. The results show by enhancing the porosity, the frequency decreased. The findings of the current study can be used to design prominent role in modern engineering applications.

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Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM

Cited by 81 publications

References 39 publications

Nonlinear Vibrations of Laminated Cross-Ply Composite Cantilever Plate in Subsonic Air Flow

Nonlinear Vibrations of Laminated Cross-Ply Composite Cantilever Plate in Subsonic Air Flow

Thermomechanical nonlinear stability of pressure-loaded CNT-reinforced composite doubly curved panels resting on elastic foundations

Size‐dependent free vibration of sandwich micro beam with porous core subjected to thermal load based on SSDBT

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