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

Abstract

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.

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

“…The vast majority of those recent contributions are devoted to the analysis of free vibrations and parametric analyses of the dependence of dynamic characteristics in systems on various details of the model, see e.g., . The second large group of papers concerns the harmonic forced vibrations, both linear [155,[214][215][216] and geometrically nonlinear [217][218][219][220][221][222][223][224][225][226][227][228][229]. The other group of contributions focuses on the vibrations forced by a moving load or a moving mass, e.g., [193,[230][231][232].…”

“…A large variety of types of structural elements is considered, including beams [187,194,195,206,213,228,232], plates [193,202,203,214,218,220,227], shells [204], composite beams [186,198,201,207,211,215,224,225], composite plates [155,185,191,199,200,210,212,222,223,226], composite shells [190,216,219,221], nanobeams [184,189,196], FG nanoplates [192,197,208,[229][230][231], and FG nanoshells/nanopanels [188,209,217].…”

Flexoelectricity and surface effects on coupled electromechanical responses of graphene reinforced functionally graded nanocomposites: A unified size-dependent semi-analytical framework

“…Yan and Jiang (2012a) and Yan and Jiang (2012b) investigated the influences of surface parameters on the static bending, vibration, and buckling behavior of a non-FGM nanoplate where they mentioned two cases, traction free boundary condition and without in-plane movement of plate's mid-plane, and reported that the residual surface stress becomes more noticeable in the latter case. By using Mindlin and Kirchhoff plate theories, Ebrahimi and Hosseini (2020) studied the effect of flexoelectricity on nonlinear forced vibration of piezoelectric FG porous composite nanoplate subjected to electric voltage and external parametric excitation without considering surface effect. They also reported that electric voltage has no influence on the performance of piezoelectric and flexoelectric properties of the material on vibrational response.…”

Universal converse flexoelectricity in dielectric materials via varying electric field direction

“…For this purpose, cantilever-shaped energy harvesters and sensors, due to the presence of nonuniform strain in bending, have been vastly investigated in the past [22][23][24][25][26][27][28][29][30][31][32][33] Variable mechanical characteristics can result in varying strain distribution within the domain. A few studies have suggested the use of special composite materials to achieve variation in mechanical properties and thereby a strain gradient [34][35][36][37][38][39]. This method eliminates the need for special designs and dimensions of the devices to be employed, however, it requires an additional effort at manufacturing stage for compositional variation.…”