• Structural Engineering and Mechanics
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• v.71 no.1
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• pp.37-43
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• 2019

This paper studies application of modified couple stress theory and first order shear deformation theory to magneto-electro-mechanical vibration analysis of three-layered size-dependent curved beam. The curved beam is resting on Pasternak's foundation and is subjected to mechanical, magnetic and electrical loads. Size dependency is accounted by employing a small scale parameter based on modified couple stress theory. The magneto-electro-mechanical preloads are accounted in governing equations to obtain natural frequencies in terms of initial magneto-electro-mechanical loads. The analytical approach is applied to investigate the effect of some important parameters such as opening angle, initial electric and magnetic potentials, small scale parameter, and some geometric dimensionless parameters and direct and shear parameters of elastic foundation on the magneto-electro-elastic vibration responses.

• Structural Engineering and Mechanics
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• v.69 no.2
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• pp.145-153
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• 2019

Modified couple stress formulation and first order shear deformation theory are used for magneto-electro-elastic bending analysis of three-layered curved size-dependent beam subjected to mechanical, magnetic and electrical loads. The governing equations are derived using a displacement field including radial and transverse displacements of middle surface and a rotation component. Size dependency is accounted based on modified couple stress theory by employing a small scale parameter. The numerical results are presented to study the influence of small scale parameter, initial electric and magnetic potentials and opening angle on the magneto-electro-elastic bending results of curved micro beam.

• Structural Engineering and Mechanics
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• v.23 no.5
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• pp.525-542
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• 2006

On the basis of equilibrium equations for static electric and magnetic fields, two unknown functions related to electric and magnetic fields were firstly introduced to rewrite the governing equations, boundary conditions and initial conditions for mechanical field. Then by introducing a dependent variable and a special function satisfying the inhomogeneous mechanical boundary conditions, the governing equation for a new variable with homogeneous mechanical boundary conditions is obtained. By using the separation of variables technique as well as the electric and magnetic boundary conditions, the dynamic problem of a functionally graded magneto-electro-elastic hollow sphere under spherically symmetric deformation is transformed to two Volterra integral equations of the second kind about two unknown functions of time. Cubic Hermite polynomials are adopted to approximate the two undetermined functions at each time subinterval and the recursive formula for solving the integral equations is derived. Transient responses of displacements, stresses, electric and magnetic potentials are completely determined at the end. Numerical results are presented and discussed.

• Steel and Composite Structures
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• v.31 no.5
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• pp.469-488
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• 2019

We in this paper study nonlinear bending of a functionally graded porous nanobeam subjected to multiple physical load based on the nonlocal strain gradient theory. For more reasonable analysis of nanobeams made of porous functionally graded magneto-thermo-electro-elastic materials (PFGMTEEMs), both constituent materials and the porosity appear gradient distribution in the present expression of effective material properties, which is much more suitable to the actual compared with the conventional expression of effective material properties. Besides the displacement function regarding physical neutral surface is introduced to analyze mechanical behaviors of beams made of FGMs. Then we derive nonlinear governing equations of PFGMTEEMs beams using the principle of Hamilton. To obtain analytical solutions, a two-step perturbation method is developed in nonuniform electric field and magnetic field, and then we use it to solve nonlinear equations. Finally, the analytical solutions are utilized to perform a parametric analysis, where the effect of various physical parameters on static bending deformation of nanobeams are studied in detail, such as the nonlocal parameter, strain gradient parameter, the ratio of nonlocal parameter to strain gradient parameter, porosity volume fraction, material volume fraction index, temperature, initial magnetic potentials and external electric potentials.

• Structural Engineering and Mechanics
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• v.88 no.1
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• pp.1-12
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• 2023

In this study, forced vibration behavior of a piezo magneto electric sandwich Timoshenko beam is investigated. It is assumed a sandwich beam with porous core and graphene platelet reinforced composite (GPLRC) in facesheets subjected to magneto-electro-elastic and temperature-dependent material properties. The magneto electro platelets are under linear function along with the thickness that includes a cosine function and magnetic and electric constant potentials. The governing equations of motion are derived using modified strain gradient theory for microstructures. The effects of material length scale parameters, temperature change, different distributions of porous, various patterns of graphene platelets, and the core to face sheets thickness ratio on the natural frequency and excited frequency of a sandwich Timoshenko beam are scrutinized. Various size-dependent methods effects such as MSGT, MCST, and CT on the natural frequency is considered. Moreover, the final results affirm that the increase in porosity coefficient and volume fractions lead to an increase in the amount of natural frequency; while vice versa for the increment in the aspect ratio. From forced vibration analysis, it is understood that by increasing the values of volume fraction and the length thickness of GPL, the maximum deflection of a sandwich beam decreases. Also, it is concluded that increasing the temperature, the thickness of GPL, and the initial force leads to a decrease in the maximum deflection of GPL. It is also shown that resonance phenomenon occurs when the natural and excitation frequencies become equal to each other. Outcomes also reveal that the third natural frequency owns the minimum value of both deflection and frequency ratio and the first natural frequency has the maximum.