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In this paper, the nonlinear forced vibration of single layered graphene sheet including the pre-Stressed effect is studied based on nonlocal elasticity theory. The graphene sheet is located on a viscoelastic foundation based on Kelvin-Voigt model and exposed to thermo-magnetic-mechanical loads. A particle with constant velocity and concentrated load moves on the graphene sheet and applies mechanical shock to it. At first, using nonlinear strain-displacement relations, the geometrical nonlinearity is modeled. Besides, nonlocal plate theory and Hamilton's principle are utilized for deriving the governing equation. In the second step, using Galerkin method, the partial differential equation is transformed to the ordinary differential equation. Then, governing equation is solved based on multiple time scales method. Finally, frequency-response equations under sub-harmonic and super-harmonic stimulation are studied. Emphasizing the effect of nonlinearity, the results for the nondimensional nonlinear frequency versus nondimensional amplitude, the nondimensional phase angle and nondimensional velocity for single layered graphene sheet are plotted. At the end, numerical results are compared with results in the other researches. The results emphasize that the velocity of the nano particle and force amplitude are responsible to make resonance in the system based on a SLGS. Besides, force amplitude can be effective to intensify the effect of the mechanical shock in behavior of SLGS. [ABSTRACT FROM AUTHOR]

This paper proposes a four-variable shear deformation refined plate theory for free vibration analysis of embedded smart plates made of porous magneto-electro-elastic functionally graded (MEE-FG) materials. Magneto-electro-elastic properties of FG plate are supposed to vary through the thickness direction and are estimated through the modified power-law rule in which the porosities with even and uneven type are approximated. The governing differential equations and boundary conditions of embedded porous FG plate under magneto-electrical field are derived through Hamilton's principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factors. An analytical solution procedure is used to achieve the natural frequencies of embedded porous FG plate supposed to magneto-electrical field with various boundary condition. Influences of several important parameters such as material graduation exponent, porosity volume fraction, magnetic potential, electric voltage, various boundary conditions, elastic foundation parameters and plate side-to-thickness ratio on natural frequencies of embedded porous MEE-FG plate are investigated and discussed in detail. It is concluded that these parameters play significant roles on the dynamic behavior of porous MEE-FG plates resting on elastic foundation. Presented numerical results can serve as benchmarks for future analyses of MEE-FG plates with porosity phases. [ABSTRACT FROM AUTHOR]

Abstract: Analytical investigation of the free vibration behavior of thin circular functionally graded (FG) plates integrated with two uniformly distributed actuator layers made of piezoelectric (PZT4) material based on the classical plate theory (CPT) is presented in this paper. The material properties of the FG substrate plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents and the distribution of electric potential field along the thickness direction of piezoelectric layers is simulated by a quadratic function. The differential equations of motion are solved analytically for clamped edge boundary condition of the plate. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. The results are verified by those obtained from three-dimensional finite element analyses. [Copyright &y& Elsevier]

This article investigates the nonlinear vibration behavior of multiscale nanocomposites nanoshell subjected to hygrothermal environment and resting on elastic foundations. The novelty and contribution of this article is considering a multiscale doubly curved sandwich nanoshell. Three-phase composite nanoshell composes of polymer-Carbon nanotube-fiber (PCF) and polymer-Graphene platelet-fiber (PGF) according to Halpin-Tsai model. Various distributions patterns such as U (uniform), X, A and O are considered. The classical shell theory and nonlocal strain gradient theory including von Kármán strain–displacement relationships are employed to build the size-dependent governing equations. The governing equations of multiscale nanoshell have been implemented by Hamilton's principle and solved by homotopy perturbation method. For investigating correctness and accuracy, this paper is validated by other previous researches. Finally, the effects of different parameters such as temperature rise, various distributions patterns and curvature ratio have been investigated. • Nonlinear vibration behavior of multiscale nanocomposites nanoshell is investigated in hygrothermal environment. • The influence of different parameters such as temperature rise, various distributions patterns, curvature ratio are investigated in detail. • Various distributions patterns such as U (uniform), X, A and O are considered. • Via the classical shell theory and the von Kármán type hypothesis the displacements are expressed. • Nonlocal strain gradient governing equations of multiscale nanoshell have been implemented by employing the Hamilton's principle. • Using the homotopy perturbation method, the equations of motions are solved. • The governing equations of multiscale shell have been derived by implementing Hamilton's principle. [ABSTRACT FROM AUTHOR]

This is the first research on the nonlinear vibration of smart viscoelastic composite doubly curved sandwich shell with flexible core and MR layers with different distribution patterns. By using Reddy's third order shear deformation theory (TSDT), the strains and stresses are obtained. This smart model including multiscale composite layers, flexible core and magnetorheological layer (MR). According to the Halpin-Tsai model three-phase composites layers have been considered. The governing equations of the multiscale doubly curved shell have been derived by implementing the Hamilton's principle. For investigating correctness and accuracy, this paper is validated by other previous studies. The results of this work are validated through the comparison with the results available researches. Finally, the influence of different parameters such as temperature rise, various distributions pattern, magnetic fields, and curvature ratios on nonlinear frequency response are investigated in the details. The results presented that the multiscale doubly curved sandwich shell with flexible core show a complex behavior. [ABSTRACT FROM AUTHOR]

This is the first research on the nonlinear vibration analysis of composite sandwich doubly curved shell with a flexible core integrated with a piezoelectric layer. By using the higher order shear deformable theory (HSDT) for the face sheets and the third-order polynomial theory for the flexible core, the strains and stresses are obtained. It is assumed a smart model including multiscale composite layers shell with a flexible core and magnetorheological layer (MR) that leading up by the nonlinearity of the in-plane and the vertical displacements of the core. Three-phase composites shells with polymer/Carbon nanotube/fiber (PCF) and polymer/Graphene platelet/fiber (PGF) and Shape Memory Alloy (SMA)/matrix either according to Halpin-Tsai model have been considered. The governing equations of multiscale shell have been derived by implementing Hamilton's principle and solved by multiple scale method. For investigating the correctness and accuracy, this paper is validated by other previous researches. Finally, the effect of different parameters such as temperature rise, various distributions pattern, magnetic fields and curvature ratio are explored in detail. [ABSTRACT FROM AUTHOR]

Present manuscript is mainly arranged to take into consider the influences of nanofillers' aggregation, beam's shear deformation and various boundary conditions on the vibration frequency of multi-scale hybrid nanocomposites in the framework of finite element based Rayleigh-Ritz method. The constituent material is made from three phases, namely polymer matrix, macro-scale carbon fibers and nano-scale carbon nanotubes. Homogenization procedure is procured based on Eshelby-Mori-Tanaka approach incorporated with a micromechanical scheme to obtain the effective material properties via a two-step method. In addition, a new refined higher-order beam theory is introduced to govern shear stress and strain through the thickness direction. Furthermore, influences of different boundary conditions are included, too. The accuracy of the presented finite element formulations is examined by setting a comparison between the dimensionless frequency of multi-scale hybrid nanocomposite beams via both analytical and finite element solutions. Afterwards, parametric studies are adopted to put emphasize on the influence of various terms on the vibrational behaviors of nanocomposite beams. It is reported that influence of different parameters deeply depends on the magnitude of volume fraction of nanofillers inside the inclusions. • Vibration frequency of multi-scale hybrid nanocomposites in the framework of finite element based Rayleigh-Ritz method is investigated. • A new refined higher-order beam theory is introduced to govern shear stress and strain through the thickness direction. • The influences of nanofillers' aggregation, beam's shear deformation and various boundary conditions are considered. • Homogenization procedure is procured based on Eshelby-Mori-Tanaka approach incorporated with a micromechanical scheme. • Comparison of the finite element responses with those achieved from the analytical solution guarantees the accuracy of the presented model. [ABSTRACT FROM AUTHOR]

This is the first research on the free vibration analysis of functionally graded graphene platelets reinforced composite (FG-GPLRC) viscoelastic annular plate resting on the visco-Pasternak foundation and subjected to the nonlinear temperature gradient and mechanical loading within the framework of higher-order shear deformation theory (HSDT). Hamilton's principle is employed to establish governing equations within the framework of HSDT. In this paper, viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. Generalized differential quadrature method (GDQM) is applied to obtain a numerical solution. Numerical results are compared with those published in the literature to examine the accuracy and validity of the applied approach. A comprehensive parametric study is accomplished to reveal the influence of the stiffness of the substrate, patterns of temperature rise, axial load, damper and viscoelasticity coefficient, weight fraction and distribution patterns of GPLs and geometric dimensions of GPLs on the frequency response of the structure. The results revealed that applying sinusoidal temperature rise and locating more square-shaped GPLs in the vicinity of the top and bottom surfaces have important effect of the highest natural frequency and buckling load of the FG-GPLRC viscoelastic structure. • Free vibration analysis of FG-GPLRC viscoelastic annular plate is investigated. • The effects of the nonlinear temperature gradient and mechanical load is considered. • Hamilton's principle is employed to establish governing equations of motion within the framework of HSDT. • Viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. • The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. [ABSTRACT FROM AUTHOR]