Piezomagnetic Face-sheets Research Articles

Investigating forced vibration of an intelligent sandwich plate consisting of a metal foam core, stiff nanocomposite layers and active piezomagnetic face-sheets exposed to electro-magnetic potentials

The main purpose of the present article is to present a forced vibrational analysis for a new intelligent sandwich plate made up of various layers. The proposed intelligent structure contains a porous metal foam core, super stiff double-FG nanocomposite layers, and piezomagnetic actuators which will be actuated magnetically and electrically. For the metal foam core of the structure, three kinds of porosity patterns are considered and, in the double-FG nanocomposite layers, Carbon Nanotubes (CNTS) are dispersed through various FG patterns in an FG metal-ceramic matrix. The power-law function is used to form the FG metal-ceramic matrix of the nanocomposite layers. Then, first-order shear deformation theory (FSDT) is utilized to derive the governing equations, and the resonance and natural frequencies of the proposed sandwich structure with simply-supported boundary conditions are obtained employing Navier’s analytical solution method. Finally, the effects of various parameters such as the CNTs’ volume fraction, magnetic and electric potentials, porosity patterns, core-to-nanocomposite layers thickness ratio, power-law index, etc on the resonance behavior of the structure will be discussed based on tabular and graphical results. The results demonstrate that the occurrence of the resonance phenomenon in such a multi-layered structure remarkably depends on the mentioned parameters and can be somehow controlled by applying magnetic and electric potentials to the piezomagnetic actuators connected to the top and bottom of the structure.

Size-dependent vibration of laminated composite nanoplate with piezo-magnetic face sheets

Laminated composites are extensively employed in many aerospace structures due to their excellent mechanical properties. In this paper, a size-dependent model on the basis of the nonlocal strain gradient theory is adopted to reveal the vibration behavior of laminated nanoplate with piezo-magnetic face sheets in its upper and lower surfaces. The governing equations are derived by employing the Hamilton’s principle and Mindlin plate theory. The validation of the present study is carried out by comparison with two previous works and good agreements are achieved. By comparing the vibrational frequencies of composite laminated core sandwich nanoplate with and without the piezo-magnetic face sheets, it is demonstrated that the upper and lower piezo-magnetic face sheets will extensively enhance the vibrational frequencies of laminated core sandwich nanoplates. Furthermore, a comprehensive numerical investigation is performed to examine the influence of the cross-ply laminated type, external electric and magnetic potentials, thickness ratio, size scale parameters, as well as aspect and width-to-thickness ratios on the vibration of the laminated core piezo-magnetic sandwich nanoplate. It is expected that the current work can provide some helpful guidelines for employing the piezo-magnetic surfaces as sensors and actuators to control their vibration behaviors of composite laminated nanostructures.

Two-dimensional bending behavior of the three-layered shear deformable nanoshells: Electro-elastic size-dependent

First-order shear deformation theory and nonlocal piezoelasticity relations are employed in this work for size-dependent electro-elastic bending analysis of three-layered piezoelectric nanoshells. The three-layered nanoshell includes a nano core and two piezo-magnetic face-sheets as sensor and actuator. A two-dimensional formulation along the axial and radial directions is presented based on first-order shear deformation theory to account shear strains and stresses especially at boundaries. Principle of virtual work is used to derive the governing equations of electro-elastic bending for a size-dependent piezoelectric nanoshell. The numerical results are presented based on analytical approach to investigate the influence of significant parameters such as nonlocal parameter, two parameters of Pasternak’s foundation and initial electric potential on the electro-elastic bending results.

3-D magneto-electro-thermal analysis of layered nanoplate including porous core nanoplate and piezomagnetic face-sheets

In the present article, three-dimensional size dependent thermal analysis of three-layered nanoplate with porous graded core and two piezomagnetic face-sheets is studied based on nonlocal strain gradient theory considering thickness stretching effect. The sandwich nanoplate standing on an elastic foundation and face layers are exposed to electric/magnetic potentials. Porosity is evenly and unevenly repartitioned thorough thickness of the core. To predict both reduction and enhancement of stiffness in small scales, a nonlocal parameter and a strain gradient parameter is used for analysis. The governing equations are derived using the principle of virtual works based on sinusoidal shear and normal deformation theory. The small size effect is obtained exploiting Eringen’s nonlocal elasticity theory. The influences of the porosity coefficient, temperature parameters, electric/magnetic potential, boundary conditions (simply supported and clamped) and parameters of foundation on bending, electrical, and magnetic behaviors of the sandwich nanoplate are presented and discussed.

Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets

The present research is devoted to examine nonlinear forced vibration behavior of sandwich nanobeams with piezo-magnetic face sheets and rested on a hardening elastic substrate based on ordinary differential nonlocal elasticity. A uniform harmonic load is applied to the sandwich nanobeam leading to forced oscillations. The face sheets are constructed from two phases called piezoelectric and magnetic phases. In the face sheets, different percentages of the piezoelectric phase is considered for the first time. It will be shown that vibration behavior of the nanobeam is affected by the amount of piezoelectric phase in the face sheets. Via an analytical procedure, the ordinary nonlinear governing equation is solved to express the amplitude-frequency relationship. It is also shown that the effect of electric and magnetic fields on forced vibrations of sandwich nanobeam rely on the amount of piezoelectric content. Also, forced vibration characteristics of the nanobeam are prominently affected by the nonlocality, hardening foundation and applied harmonic load.

Application of nonlocal strain gradient theory to size dependent bending analysis of a sandwich porous nanoplate integrated with piezomagnetic face-sheets

Bending analysis of a sandwich plate is studied in this paper based on first order shear deformation theory and nonlocal strain gradient theory. The sandwich nanoplate is including a porous core and two piezomagnetic facesheets. It is assumed that nanoplate is resting on Pasternak's foundation. Power law function is used to describe change of porosity along the thickness direction. To account size dependency, nonlocal strain gradient theory is employed to predict this behavior. The principle of virtual work is used to derive governing equations in terms of primary functions. A nonlocal parameter and a strain gradient parameter are employed to describe both stiffness reduction and stiffness enhancement of nanoplates. The analytical solution is presented to solve seven governing equation using Navier’s solution. The numerical results are presented to evaluate the effect of various distribution of porosities, porosity volume fraction, nonlocal and strain gradient parameter, electric and magnetic potentials, geometrical characteristics, and parameters of foundation on the results of problem.

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

The free vibration analysis of a nonlocal strain gradient elastic sandwich nanoplate with porous graded core and piezomagnetic face sheets is presented in this paper. The rectangular elastic sandwich nanoplate is resting on Pasternak's foundation. Porosities are distributed evenly and unevenly through the thickness of the core. The gradation of material properties having porosities is described using a modified power-law function. A nonlocal parameter and a strain gradient parameter are employed to describe both stiffness reduction and stiffness enhancement of nanoplates. The governing equations of the motion are derived from Hamilton’s principle based on the first order shear deformation theory. In addition, Eringen’s nonlocal strain gradient piezo-magneto-elasticity theory is used to consider nanoscale effects. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually, the natural frequency is surveyed for different side length ratios, nonlocal coefficient, porosity volume fraction, and parameters of foundation numerically with even and uneven porosity distributions.

Magneto-electro-mechanical bending analysis of three-layered exponentially graded microplate with piezomagnetic face-sheets resting on Pasternak's foundation via MCST

ABSTRACTThe present work is devoted to the bending behavior of elastic three-layered microplate with exponentially graded core and piezomagnetic face-sheets using the modified couple stress theory (MCST). The micro piezomagnetic layers are subjected to electric and magnetic potentials and the model is resting on Pasternak's foundation. To capture size-dependency for a micro sized rectangular microplate, the MCST is used. Numerical investigation of this problem is surveyed for effect of significant parameters of microplate such as micro length scale parameter, in-homogenous index, electric and magnetic potentials, geometrical characteristics and parameters of foundation on results of problem.

Smart electrical and magnetic stability analysis of exponentially graded shear deformable three-layered nanoplate based on nonlocal piezo-magneto-elasticity theory

The present research deals with magnetic and electric buckling loads of three-layered elastic nanoplate with exponentially graded core and piezomagnetic face-sheets. Material properties of the nano-graphene core obey the exponential function along the thickness direction. The governing equations based on first-order shear deformation theory are deduced using variational method. The influence of nanoscale is considered by employing nonlocal piezo-magneto-elasticity theory. The governing equations of nanostructure are solved analytically. Eventually the effect of significant parameters such as length-scale parameter, in-homogenous index, geometrical characteristics and parameters of foundation on the magneto-electro responses of problem is numerically investigated.

Size-dependent vibration and electro-magneto-elastic bending responses of sandwich piezomagnetic curved nanobeams

Size-dependent free vibration responses and magneto-electro-elastic bending results of a three layers piezomagnetic curved beam rest on Pasternak's foundation are presented in this paper. The governing equations of motion are derived based on first-order shear deformation theory and nonlocal piezo-elasticity theory. The curved beam is containing a nanocore and two piezomagnetic face-sheets. The piezomagnetic layers are imposed to applied electric and magnetic potentials and transverse uniform loadings. The analytical results are presented for simply-supported curved beam to study influence of some parameters on vibration and bending results. The important parameters are spring and shear parameters of foundation, applied electric and magnetic potentials, nonlocal parameter and radius of curvature of curved beam. It is concluded that the increase in radius of curvature tends to an increase in the stiffness of curved beam and consequently natural frequencies increase and bending results decrease. In addition, it is concluded that with increase of nonlocal parameter of curved beam, the stiffness of structure is decreased that leads to decrease of natural frequency and increase of bending results.

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 present work is devoted to the free vibration analysis of elastic three-layered nano-/micro-plate with exponentially graded core and piezomagnetic face-sheets using the modified couple stress theory. To capture size-dependency for a nano-/micro-sized rectangular plate, the couple stress theory is used as a non-classical continuum theory. The rectangular elastic three-layered nano-/micro-plate is resting on Pasternak’s foundation. The present model contains one material length scale parameter and can capture the size effect. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on the modified couple stress theory and first-order shear deformation theory. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually the natural frequency is scrutinized for different side length ratio, thickness ratio, inhomogeneity parameter, material length scale, and parameters of foundation numerically.

Influence of magneto-electric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory

In this work, an analytical solution for bending analysis of the three-layer curved nanobeams is presented. The nanobeams are including a nanocore and two piezomagnetic face-sheets. The structure is subjected to applied electric and magnetic potentials while is resting on Pasternak's foundation. To reach more accurate results, sinusoidal shear deformation theory is employed to derive displacement field of the curved nanobeams. In addition, nonlocal electro-magneto-elasticity relations are employed to derive governing equations of bending based on the principle of virtual work. The analytical results are presented for simply supported curved nanobeam to discuss the influence of important parameters on the vibration and bending results. The important parameters are included spring and shear parameters of the foundation, applied electric and magnetic potentials, nonlocal parameter, and radius of curvature of curved nanobeam.

Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak’s foundation

This work is devoted to the free vibration nonlocal analysis of an elastic three-layered nanoplate with exponentially graded graphene sheet core and piezomagnetic face-sheets. The rectangular elastic three-layered nanoplate is resting on Pasternak’s foundation. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on first-order shear deformation theory. In addition, Eringen’s nonlocal piezo-magneto-elasticity theory is used to consider size effects. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually, the natural frequency is scrutinized for different side length ratio, nonlocal parameter, inhomogeneity parameter, and parameters of foundation numerically. The comparison with various references is performed for validation of our analytical results.

Vibration and bending analyses of magneto–electro–thermo-elastic sandwich microplates resting on viscoelastic foundation

Magneto–electro–thermo-mechanical bending and free vibration analysis of a sandwich microplate using strain gradient theory is expressed in this paper. The sandwich plate is made of a core and two integrated piezo-magnetic face sheets. The structure is subjected to electric and magnetic potentials, thermal loadings, and resting on Pasternak’s foundation. Electro-magnetic equations are developed by considering the variation form of Hamilton’s principle. The effects of important parameters of this problem such as applied electric and magnetic potentials, direct and shear parameter of foundation, three microlength-scale parameters, and two parameters of temperature rising are investigated on the vibration and bending results of problem.

Thermo-electro-magneto-mechanical bending behavior of size-dependent sandwich piezomagnetic nanoplates

Thermo-electro-magneto-mechanical bending analysis of a sandwich nanoplate is presented in this paper based on Kirchhoff’s plate theory and nonlocal theory. The sandwich nanoplate includes an elastic nano-core and two piezomagnetic face-sheets actuated by applied electric and magnetic potentials. The governing equations for the electro-magneto-mechanical bending are derived in terms of the displacement components and electric and magnetic potentials. Then, the problem is solved analytically by using Navier’s method. A parametric study is presented to show the effects of the nonlocal parameter, temperature rise, applied electric and magnetic potentials on the bending behaviors of sandwich nanoplates for simply-supported boundary conditions. As a main result of study, it is concluded that the deflection decreases as applied electric potential increases and applied magnetic potential decreases. In addition, the increase of nonlocal parameter leads to increase of deflection and maximum electric potential through the thickness direction.

Electro-magneto-elastic analysis of a three-layer curved beam

In this paper, based on first-order shear deformation theory, the governing equations of motion for a sandwich curved beam including an elastic core and two piezo-magnetic face-sheets are presented. The curved beam model is resting on Pasternak\'s foundation and subjected to applied electric and magnetic potentials on the piezo-magnetic face-sheets and transverse loading. The five equations of motion are analytically solved and the bending and vibration results are obtained. The influence of important parameters of the model such as direct and shear parameters of foundation and applied electric and magnetic potentials are studied on the electro-mechanical responses of the problem. A comparison with literatures was performed to validate our formulation and results.

Effect of thermo-magneto-electro-mechanical fields on the bending behaviors of a three-layered nanoplate based on sinusoidal shear-deformation plate theory

The nonlocal thermo-magneto-electro-mechanical bending behaviors of a three-layered nanoplate are presented in this study. The three-layered nanoplate includes a nano-sheet and two piezo-magnetic face-sheets at the top and the bottom. Temperature distribution is assumed linear along the thickness of the plate. The piezo-magnetic face-sheets are subjected to three-dimensional electric and magnetic potentials. The applied electric and magnetic potentials are applied at top of the face-sheets. The constitutive thermo-electro-magneto relations are derived based on the sinusoidal shear-deformation plate theory and nonlocal electro-magneto-elasticity. Using the principle of virtual work seven equations of the equilibrium are derived. The numerical results of this research indicate that some parameters have considerable effect on the bending behavior of three-layered nanoplate. Nonlocal parameter, applied electric and magnetic potentials, and temperature distribution are important parameters in this analysis.

Size-dependent vibration and bending analyses of the piezomagnetic three-layer nanobeams

Vibration and electro-magneto-elastic bending analysis of a three-layer nanobeam with a nanocore and two piezomagnetic face sheets are studied in this paper. Timoshenko model of beam as well as nonlocal magneto-electro-elastic relations are used for analysis of this problem. The nanoface sheets are subjected to applied electric and magnetic potentials. The nanobeam rests on Winkler–Pasternak foundation. Electric and magnetic potentials are assumed as combination of linear function along the thickness direction that reflects applied electric and magnetic potentials and a cosine function that satisfies boundary conditions. Numerical results of this problem investigate the effect of some important parameters of nanobeam, such as nonlocal parameter, applied electric and magnetic potentials, and parameters of foundation on the vibration and magneto-electro-mechanical bending behaviors of the problem.

Theoretical investigation on vibration frequency of sandwich plate with PFRC core and piezomagnetic face sheets under variable in-plane load

This research investigated the vibration frequency of sandwich plate made of piezoelectric fiber reinforced composite core (PFRC) and face sheets of piezomagnetic materials. The effective electroelastic constants for PFRC materials are obtained by the micromechanical approach. The resting medium of sandwich plate is modeled by Pasternak foundation including normal and shear modulus. Besides, sandwich plate is subjected to linearly varying normal stresses that change by load factor. The coupled equations of motion are derived using first order shear deformation theory (FSDT) and energy method. These equations are solved by differential quadrature method (DQM) for simply supported boundary condition. A detailed numerical study is carried out based on piezoelectricity theory to indicate the significant effect of load factor, volume fraction of fibers, modulus of elastic foundation, core-to-face sheet thickness ratio and composite materials on dimensionless frequency of sandwich plate. These findings can be used to aerospace, building and automotive industries.

Size-dependent analysis of a sandwich curved nanobeam integrated with piezomagnetic face-sheets

The aim of this research is to develop nonlocal transient magneto-electro-elastic formulation of a sandwich curved nanobeam including a nano-core and two piezo-magnetic face-sheets subjected to transverse mechanical loads and applied electric and magnetic potentials rest on Pasternak’s foundation. Nonlocal magneto-electro-elastic relations and Hamilton’s principle are used for derivation of the governing equations of motion. The analytical solution based on Fourier solution is presented for a simply-supported sandwich curved nanobeam. The numerical results are presented to investigate influence of significant parameters such as nonlocal parameter, radius of curvature, applied electric and magnetic potentials and two parameters of Pasternak's foundation on the dynamic responses of sandwich curved nanobeam.