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In this paper, nonlinear vibrational behaviors of doubly-curved functionally graded piezoelectric (FGP) microshells in thermal environments have been studied. The doubly-curved microshell has been modeled by using modified couple stress and thin shell theories. The microshell has two material constituents which are piezoelectric materials and their gradation is described using power-law functions. Temperature fields are considered to be uniform, linear, and nonlinear. A closed-form of nonlinear vibration frequency has been obtained by analytically solving the governing equations using the Harmonic balance method. It will be demonstrated that nonlinear vibrational frequency of doubly-curved microshell relies on couple stress influence, material gradation, curvature radius, center deflection, and electrical field. [ABSTRACT FROM AUTHOR]

Based on modified strain gradient theory, nonlinear vibration analysis of a functionally graded piezoelectric doubly curved microshell in thermal environment has been performed in this research. Three scale parameters have been included in the modeling of thin doubly curved microshell in order to capture micro-size effects. Graded material properties between the top and bottom surfaces of functionally graded piezoelectric doubly curved microshell have been considered via incorporating power-law model. It is also assumed that the microshell is exposed to a temperature field of uniform type and the material properties are temperature-dependent. By analytically solving the governing equations based on the harmonic balance method, the closed form of nonlinear vibration frequency has been achieved. Obtained results indicate the relevance of calculated frequencies to three scale parameters, material gradation, electrical voltage, curvature radius, and temperature changes. [ABSTRACT FROM AUTHOR]

The objective of the present paper is to comprehensively study the nonlinear frequency response of viscoelastic piezoelectric nanoplates exposed to dual harmonic external excitation and thermo-electro-mechanical loads. To achieve this goal, firstly, a piezoelectric nanoplate resting on a viscoelastic foundation is modeled. Secondly, using the nonlocal piezoelectricity theory, Kelvin-Voigt model, von Karman nonlinear relations and Hamilton's principle, the nonlinear governing differential equation of motion is derived. In the next step, employing the Galerkin technique and multiple time scales method, the partial differential equation is transformed to an ordinary one and solved. Finally, the modulation equation of viscoelastic piezoelectric nanoplates for combinational excitation is obtained. Emphasizing the effect of dual harmonic excitation and thermo-electro-mechanical loads on nonlinear frequency response of the system, jump and resonance phenomena are discussed. A detailed parametric study is conducted to examine the effect of nonlinearity, damping coefficient, nonlocal parameter, combinational excitation, electric voltage, initial stress and thermal environment. [ABSTRACT FROM AUTHOR]

Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite is the objective of this study. The nanocomposite is exposed to electric voltage and external parametric excitation. First, a functionally graded porous core nanoplate is modeled and then two piezoelectric layers are glued with core. It is also rested on a visco-Pasternak foundation. Second, to derive governing equation of motion, two theories including Mindlin and Kirchhoff plate theories and Hamilton's principle are utilized. In the next step, to obtain and solve ordinary differential equation, Galerkin technique and multiple time scales method are used, respectively. At the end, modulation equation of piezoelectric/functionally graded porous nanocomposite for both primary and secondary resonances is obtained and discussed. Emphasizing the effect of piezoelectric and flexoelectric, von Karman nonlinear deformation and parametric external excitation are simultaneously taken into account. It is found that electric voltage has no effect on the performance of piezoelectricity and flexoelectricity of the material on vibration behavior. The results of this study can be useful as benchmark for the next investigations in field of energy harvesting systems and piezoelectric structures. [ABSTRACT FROM AUTHOR]

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 deals with the study of the temperature effect on the nonlinear vibration behavior of nanoplate-based nano electromechanical systems (NEMS) subjected to hydrostatic and electrostatic actuations. Using Eringen's nonlocal elasticity and Gurtin–Murdoch theory, the nonlocal plate model is derived through Hamilton's principle. The governing equation which is extremely nonlinear due to the geometrical nonlinearity and electrostatic attraction forces is solved numerically using the differential quadrature method (DQM). The accuracy of the present method is verified by comparing the obtained results with the experimental data and those in the literature and very good agreement is obtained. Finally a comprehensive study is carried out to determine the influence of temperature on the nonlinear vibration characteristics of NEMS made of two different materials including aluminum (Al) and silicon (Si) and some conclusions are drawn. [ABSTRACT FROM AUTHOR]

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]