• Advances in nano research
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• 제7권6호
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• pp.391-403
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• 2019

In this article the frequency response analysis of curved magneto-electro-viscoelastic functionally graded (CMEV-FG) nanobeams resting on viscoelastic foundation has been carried out. To this end, the study incorporates the Euler-Bernoulli beam model in association with Eringen's nonlocal theory to incorporate the size effects. The viscoelastic foundation in the current investigation is assumed to be the combination of Winkler-Pasternak layer and viscous layer of infinite parallel dashpots. The equations of motion are derived with the aid of Hamilton's principle and the solution to vibration problem of CMEV-FG nanobeams are obtained analytically. The material gradation is considered to follow Power-law rule. This study thoroughly investigates the influence of prominent parameters such as linear, shear and viscous layers of foundation, structural damping coefficient, opening angle, magneto-electrical field, nonlocal parameter, power-law exponent and slenderness ratio on the frequencies of FG nanobeams.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.813-823
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• 2021

In this work, we present the classical formulation for the antiplane problem of a eletro-viscoelastic materialswith total sliprate dependent friction and write the corresponding variational formulation. In the second step, we prove that the solution converges to the solution of the corresponding electro-elastic problem as the viscosity converges to zero.

• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.305-320
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• 2024

We consider a mathematical model which describes the quasistatic contact of electro-viscoelastic rod with an obstacle. We use a modified Kelvin-Voigt viscoelastic constitutive law in which the elasticity operator is nonlinear and locally Lipschitz continuous, taking into account the piezoelectric effect of the material. We model the contact with a general damped response condition. We establish a local existence and uniqueness result of the solution by using arguments of time-dependent nonlinear equations and Schauder's fixed-point theorem and obtain a global existence for small enough data.

• 대한수학회지
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• 제53권1호
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• pp.161-185
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• 2016

We consider a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and an electrically conductive obstacle, the so-called foundation. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with Signorini's conditions and a version of Coulomb's law of dry friction in which the adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation for the model, in the form of a system for the displacements, the electric potential and the adhesion. Under a smallness assumption which involves only the electrical data of the problem, we prove the existence of a unique weak solution of the model. The proof is based on arguments of time-dependent quasi-variational inequalities, differential equations and Banach's fixed point theorem.

• Structural Engineering and Mechanics
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• 제71권5호
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• pp.485-502
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• 2019

In this research, the nonlinear static, buckling and vibration analysis of viscoelastic micro-composite beam reinforced by various distributions of boron nitrid nanotube (BNNT) with initial geometrical imperfection by modified strain gradient theory (MSGT) using finite element method (FEM) are presented. The various distributions of BNNT are considered as UD, FG-V and FG-X and also, the extended rule of mixture is used to estimate the properties of micro-composite beam. The components of stress are dependent to mechanical, electrical and thermal terms and calculated using piezoelasticity theory. Then, the kinematic equations of micro-composite beam using the displacement fields are obtained. The governing equations of motion are derived using energy method and Hamilton's principle based on MSGT. Then, using FEM, these equations are solved. Finally the effects of different parameters such as initial geometrical imperfection, various distributions of nanotube, damping coefficient, piezoelectric constant, slenderness ratio, Winkler spring constant, Pasternak shear constant, various boundary conditions and three material length scale parameters on the behavior of nonlinear static, buckling and vibration of micro-composite beam are investigated. The results indicate that with an increase in the geometrical imperfection parameter, the stiffness of micro-composite beam increases and thus the non-dimensional nonlinear frequency of the micro structure reduces gradually.

• Structural Engineering and Mechanics
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• 제78권5호
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• pp.557-572
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• 2021

The current study considers free vibration of the spherical panel with magnetorheological (MR) fluids core and magneto-electro-elastic face sheets. The panel is subjected to electro-magnetic loads and also is located on an orthotropic visco-Pasternak elastic foundation. To describe the displacement components of the structure, the first-order shear deformation theory (FSDT) is used and the motion equations are extracted by employing Hamilton's principle. To solve the motion differential equations, Navier's method is selected as an exact analytical solution for simply supported boundary conditions. Effect of the most important parameters such as magnetic field intensity, loss factor, multi-physical loads, types of an elastic medium, geometrical properties of the panel, and also different material types for the face sheets on the results is considered and discussed in details. The outcomes of the present work may be used to design more efficient smart structures such as sensors and actuators.

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.487-510
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• 2023

We propose a mathematical model which describes the frictional contact between a piezoelectric body and an electrically conductive foundation. The behavior of the material is described with a linearly electro-viscoelastic constitutive law with long term memory. The mechanical process is dynamic and the electrical conductivity coefficient depends on the total slip rate, the friction is modeled with Tresca's law which the friction bound depends on the total slip rate with taking into account the electrical conductivity of the foundation both. The main results of this paper concern the existence and uniqueness of the weak solution of the model; the proof is based on results for second order evolution variational inequalities with a time-dependent hemivariational inequality in Banach spaces.

• Smart Structures and Systems
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• 제4권1호
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• pp.35-46
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• 2008

In this paper the authors address the problem of comparing two different smart damping techniques using the numerical modelling of the electro-mechanical impedance for plate structures partially treated with active constrained layer damping treatments. The paper summarizes the modelling procedures including a finite element formulation capable of accounting for the observed behaviour. The example used is a smart cantilever plate structure containing a viscoelastic material (VEM) layer sandwiched between a piezoelectric constrained layer and the host vibrating plate. Comparisons are made between active constrained layer and active damping only and based on the resonance frequency amplitudes of the electrical admittance numerically evaluated at the surface of the piezoelectric model of the vibrating structure.

• Steel and Composite Structures
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• 제33권6호
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• pp.891-906
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• 2019

This study considers the instability behavior of sandwich plates considering magnetorheological (MR) fluid core and piezoelectric reinforced facesheets. As facesheets at the top and bottom of structure have piezoelectric properties they are subjected to 3D electric field therefore they can be used as actuator and sensor, respectively and in order to control the vibration responses and loss factor of the structure a proportional-derivative (PD) controller is applied. Furthermore, Halpin-Tsai model is used to determine the material properties of facesheets which are reinforced by graphene platelets (GPLs). Moreover, because the core has magnetic property, it is exposed to magnetic field. In addition, Kelvin-Voigt theory is applied to calculate the structural damping of the piezoelectric layers. In order to consider environmental forces applied to structure, the visco-Pasternak model is assumed. In order to consider the mechanical behavior of structure, sinusoidal shear deformation theory (SSDT) is assumed and Hamilton's principle according to piezoelasticity theory is employed to calculate motion equations and these equations are solved based on differential cubature method (DCM) to obtain the vibration and modal loss factor of the structure subsequently. The effect of different factors such as GPLs distribution, dimensions of structure, electro-magnetic field, damping of structure, viscoelastic environment and boundary conditions of the structure on the vibration and loss factor of the system are considered. In order to indicate the accuracy of the obtained results, the results are validated with other published work. It is concluded from results that exposing magnetic field to the MR fluid core has positive effect on the behavior of the system.