An exact solution for the nonlinear forced vibration of functionally graded nanobeams in thermal environment based on surface elasticity theory

A size-dependent shell model which accounts for geometrical imperfection sensitivity of the axial postbuckling characteristics of a cylindrical nanoshell made of functionally graded material (FGM) is proposed within the framework of the surface elasticity theory. In accordance with a power law, the material properties of the FGM nanoshell are supposed to vary through the shell thickness. In order to eliminate the stretching-bending coupling terms, the change in the position of physical neutral plane corresponding to different volume fractions is taken into account. Based upon the virtual work’s principle, the non-classical governing differential equations are derived and then deduced to boundary layer-type ones. After that, a perturbation-based solution methodology is employed to predict the size dependency in the nonlinear instability of perfect and imperfect axially loaded FGM nanoshells with various values of shell thickness, material property gradient index and different uniform temperature changes. It was seen that for thicker FGM nanoshells in which the surface free energy effects diminish, the influence of the initial geometric imperfection on the critical buckling load is higher than its influence on the minimum load of the postbuckling domain. It is also found that through reduction of the surface free energy effects, the influence of material property gradient index on the critical end-shortening of FGM nanoshell decreases.

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Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite resting on viscoelastic foundation

The Journal of Strain Analysis for Engineering Design ◽

10.1177/0309324719890868 ◽

2019 ◽

Vol 55 (1-2) ◽

pp. 53-68

Author(s):

Farzad Ebrahimi ◽

S Hamed S Hosseini

Keyword(s):

Forced Vibration ◽

Functionally Graded ◽

Multiple Time Scales ◽

Multiple Time ◽

Electric Voltage ◽

Modulation Equation ◽

Flexoelectric Effect ◽

Nonlinear Forced Vibration ◽

Piezoelectric Structures ◽

Porous Nanocomposite

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.

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