Transient analysis of a three-layer microbeam subjected to electric potential

Abstract

In this paper, free vibration, wave propagation, and bending analyses of a sandwich microbeam integrated with piezoelectric face-sheets resting on Pasternak foundation under electric potential are presented based on the strain gradient theory and Euler-Bernoulli beam theory. The material properties of core are assumed variable along the thickness direction and piezoelectric face-sheets are assumed homogeneous piezoelectric materials. A two-dimensional electric potential distribution along the axial and transverse direction is applied on the face-sheets of microbeam. Hamilton principal is used to derive governing differential equations of motion. Three behaviors of sandwich microbeam including free vibration, wave propagation, and bending analyses are studied in this paper. Some numerical results are presented to capture the effect of important parameters of the problem such as in-homogeneous index, applied voltage, parameters of foundation, and material length scales. The numerical results indicate that the effect of electric potential along the axial direction is very small rather than one along the transverse direction where initial voltage is applied. ARTICLE HISTORY

Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak’s foundation via MCST

“…The governing equations of motion of the Mindlin’s plate models are derived using Hamilton’s principle as [37, 38] where δKe and δUs are the variational kinetic and strain energies, and δWl is the variational work done by the external forces applied on the nano-/micro-plate. The strain energy U s is already appeared in equation (1) and its variation in equation (7) while the kinetic energy of the system is defined as [23, 29, 30] and for this type of foundation, the external work is defined as follows [22–29, 31] where F f is transverse loadings that can be calculated as where k W and k G are Pasternak's foundation parameters related to Winkler’s and shear constants, respectively.…”

“…Furthermore, the effect of different distributions of electric potential on the phase velocity of the nanorod was evaluated. The influence of electrical and magnetic fields on the responses of micro and nano beams and plates was studied by Arefi and Zenkour [30–34].…”

Nonlinear Parametric Dynamics of Bidirectional Functionally Graded Beams

“…With the rapid development of engineering construction, various composite materials have been increasingly used such as the classic laminated composite and sandwich structures [1][2][3][4][5][6][7] which have advantages of high stiffness and strength-to-weight ratios and long fatigue life. However, classic laminated composites and sandwich structure may produce great interlaminar stresses between layers, when it is deformed.…”

Nonlocal strain gradient theory for the magneto-electro-elastic vibration response of a porous FG-core sandwich nanoplate with piezomagnetic face sheets resting on an elastic foundation

“…Arefi and Khoshgoftar [25] studied the influence of the in-homogeneous index of the piezoelectric material and mechanical and electrical boundary conditions on the electro-elastic results of functionally graded piezoelectric spherical shell. The influence of electric and magnetic fields on the responses of micro- and nanobeams and plates was studied by Arefi and Zenkour [26–30]. Barati [31] studied the vibration of porous FG nanoshells with even and uneven porosity distributions using the nonlocal strain gradient elasticity.…”