Nonlinear Vibrations of Rectangular Laminated Composite Plates With Different Boundary Conditions

Amabili, Marco; Karazis, Kostas; Khorshidi, Korosh

doi:10.1142/s0219455411004294

Cited by 38 publications

(8 citation statements)

References 30 publications

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“…The obtained result is shown in Fig. 3 and is almost coincident with the one by Amabili et al [36], where a third-order shear deformation theory with a 24 dof model was used.…”

Section: Numerical Results For Periodic Responsesupporting

confidence: 86%

“…The Al/Al 2 O 3 FGM square plate with h/a = 0.01 is converted to a metallic plate by assuming a very large value for the volume fraction exponent (k → ∞) and the 30 dof model (Table 2) based on FSDT is used. A con- [36] for an aluminum plate centrated harmonic force of dimensionless amplitude f = 0.16 is assumed at the centre; the damping ratio is ς = 0.0325. The obtained result is shown in Fig.…”

Section: Numerical Results For Periodic Responsementioning

confidence: 99%

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Nonlinear vibrations of FGM rectangular plates in thermal environments

2011

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Geometrically nonlinear vibrations of FGM rectangular plates in thermal environments are investigated via multi-modal energy approach. Both nonlinear first-order shear deformation theory and von Karman theory are used to model simply supported FGM plates with movable edges. Using Lagrange equations of motion, the energy functional is reduced to a system of infinite nonlinear ordinary differential equations with quadratic and cubic nonlinearities. A pseudoarclength continuation and collocation scheme is used and it is revealed that, in order to obtain the accurate natural frequency in thermal environments, an analysis based on the full nonlinear model is unavoidable since the plate loses its original flat configuration due to thermal loads. The effect of temperature variations as well as volume fraction exponent is discussed and it is illustrated that thermally deformed FGM plates have stronger hardening behaviour; on the other hand, the effect of volume fraction exponent is not significant, but modal interactions may rise in thermally deformed FGM plates that could not be seen in their undeformed isotropic counterparts. Moreover, a bifurcation analysis is carried out using Gear's backward differentiation formula (BDF); bifurcation diagrams of Poincaré maps and maximum Lyapunov exponents are obtained in order to detect and classify bifurcations and complex nonlinear dynamics.

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“…The obtained result is shown in Fig. 3 and is almost coincident with the one by Amabili et al [36], where a third-order shear deformation theory with a 24 dof model was used.…”

Section: Numerical Results For Periodic Responsesupporting

confidence: 86%

Section: Numerical Results For Periodic Responsementioning

confidence: 99%

Nonlinear vibrations of FGM rectangular plates in thermal environments

2011

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“…The use of composites and nanocomposites has been developed in the past decades due to their positive effects on the mechanical, thermal and electrical properties. Vibration analysis, 1,2 residual stresses, 3 creep, 4 fracture and fatigue 5 have been investigated by researchers. Reinforcement of metal with laminated composites and adding nanoparticles to polymer are more attention in these years.…”

Section: Introductionmentioning

confidence: 99%

Modeling creep behavior of carbon nanotube/fiber/polymer composite cylinders

Ghasemi

Hosseinpour

Mohandes

2018

Proceedings of the Institution of Mechanical Engineers, Part N:

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In this research, the effects of multi-walled carbon nanotubes on the distribution of long-term creep strains in thickwalled multi-walled carbon nanotube/fiber/polymer three-phase laminated composites are studied. In the first step, micromechanical models are developed to calculate the elastic properties of multi-walled carbon nanotube/vinylester and multi-walled carbon nanotube/E-glass fiber/vinylester composites. Using classical lamination plate theory, equilibrium and compatibility equations and strain-displacement relations, the distribution of effective stresses is considered. Moreover, utilizing Schapery single-integral model for nonlinear viscoelastic materials, Prandtl-Reuss relations and Mendelson's approximation method, not only the distribution of circumferential and radial strains is investigated but also the effects of fiber orientation and weight fraction (wt.%) of the multi-walled carbon nanotubes on the way of distribution are studied. The results demonstrated that the addition of the multi-walled carbon nanotube to the vinylester can reduce absolute values of the radial and circumferential creep strains and dimensionless effective stresses. Moreover, most reduction occurred in the inner wall of the cylindrical shell when fiber orientation was a = 90°. Keywords Long-term creep strain, micromechanical model, multi-walled carbon nanotube/glass fiber/vinylester, Schapery single integral, three-phase composite cylinder Date

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“…Wang et al 20 investigated the stability and dynamics of an axially moving unidirectional plate partially immersed in a liquid and subjected to a nonlinear aerodynamic excitation. Amabili et al 21 numerically analyzed the nonlinear responses of composite laminated rectangular plates based on the third-order shear deformation theory. Thinh and Ngoc 22 used the methods of multiple scales and nite di®erence to study the nonlinear vibrations and stability of an isotropic cantilever plate with viscoelastic laminate.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Flutter and Nonlinear Dynamics of a Composite Laminated Plate

Chen

2016

Int. J. Str. Stab. Dyn.

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This paper presents the analysis of°utter and nonlinear dynamics of an orthotropic composite laminated rectangular plate subjected to aerodynamic pressures and transverse excitation. Thē rst-order linear piston theory is employed to model the air pressures. Based on Reddy's thirdorder shear deformation plate theory and von Karman-type equation for the geometric nonlinearity, the nonlinear governing equations of motion are derived for the composite laminated rectangular plate by applying the Hamilton's principle. The Galerkin method is utilized to discretize the partial di®erential governing equations to a set of nonlinear ordinary di®erential equations. The critical Mach number for occurrence of the°utter of the composite laminated plate is investigated by solving the eigenvalues problem. The relationship between the limit cycle oscillation and the critical Mach number is analyzed based on the nonlinear equations. The numerical simulation is conducted to study the in°uences of the transverse excitation on the nonlinear dynamics of the composited laminated plate. The numerical results, which include bifurcation diagram, phase plots and waveforms, demonstrate that there exist the bifurcation and chaotic motions of the composited laminated plate subjected to the aerodynamic pressures and the transverse excitation.

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Nonlinear Vibrations of Rectangular Laminated Composite Plates With Different Boundary Conditions

Cited by 38 publications

References 30 publications

Nonlinear vibrations of FGM rectangular plates in thermal environments

Nonlinear vibrations of FGM rectangular plates in thermal environments

Modeling creep behavior of carbon nanotube/fiber/polymer composite cylinders

Analysis of Flutter and Nonlinear Dynamics of a Composite Laminated Plate

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