A unified nonlocal strain gradient model for nanobeams and the importance of higher order terms

In this paper, size-dependent effect of an embedded magneto-electro-elastic (MEE) nanoshell subjected to thermo-electro-magnetic loadings on free vibration behavior is investigated. Also, the surrounding elastic medium has been considered as the model of Winkler characterized by the spring. The size-dependent MEE nanoshell is investigated on the basis of the modified couple stress theory. Taking attention to the first-order shear deformation theory (FSDT), the modeled nanoshell and its equations of motion are derived using principle of minimum potential energy. The accuracy of the presented model is validated with some cases in the literature. Finally, using the Navier-type method, an analytical solution of governing equations for vibration behavior of simply supported MEE cylindrical nanoshell under combined loadings is presented and the effects of material length scale parameter, temperature changes, external electric potential, external magnetic potential, circumferential wave numbers, constant of spring, shear correction factor and length-to-radius ratio of the nanoshell on natural frequency are identified. Since there has been no research about size-dependent analysis MEE cylindrical nanoshell under combined loadings based on FSDT, numerical results are presented to be served as benchmarks for future analysis of MEE nanoshells using the modified couple stress theory.

Free vibration analysis of embedded magneto-electro-thermo-elastic cylindrical nanoshell based on the modified couple stress theory

The present study deals with the size-dependent nonlinear buckling and postbuckling characteristics of magneto-electro-elastic cylindrical composite nanoshells incorporating simultaneously the both of hardening-stiffness and softening-stiffness size effects. To accomplish this purpose, the nonlocal strain gradient elasticity theory is applied to the classical shell theory. Via the virtual work's principle, the size-dependent governing differential equations are constructed including the coupling terms between the axial mechanical compressive load, external magnetic potential and external electrical potential. The nonlinear prebuckling deformations and the large postbuckling deflections are taken into consideration based upon the boundary layer theory of shell buckling. Finally, an improved perturbation technique is employed to achieve explicit analytical expressions for nonlocal strain gradient stability curves of magneto-electro-elastic nanoshells under various surface electric and magnetic voltages. It is seen that a positive electric potential and a negative magnetic potential cause to increase both of the nonlocality and strain gradient size dependencies in the nonlinear instability behavior of axially loaded magneto-electro-elastic composite nanoshells, while a negative electric potential and a positive magnetic potential play an opposite role.

Nonlocal strain gradient shell model for axial buckling and postbuckling analysis of magneto-electro-elastic composite nanoshells

This article aims to study the buckling and free vibrational behavior of axially functionally graded (AFG) nanobeam under thermal effect for the first time. The temperature is considered to be constant and variable along thickness and different boundary conditions. The governing equation is developed using the Hamilton’s principle considering the axial force. The Euler–Bernoulli beam theory is used to model the nanobeam, and Eringen’s nonlocal elasticity theory is utilized to consider the nano-size effect. The generalized differential quadrature method (GDQM) is used to solve the equations. The small-scale parameter, AFG power index, thermal distribution, different functions of temperature increase for different boundary conditions are given in detail.

On size-dependent free vibration and thermal buckling of axially functionally graded nanobeams in thermal environment

Magneto-electro-elastic (MEE) materials have been receiving a special attention from the research community owing to their specialized performance and coupled behavior under thermal, electric, magnetic and mechanical loads. The possibility of prospective energy conversion means, have additionally been added to the cause of researching about these materials. Therefore, the review presented here may be considered as a topical discussion on MEE materials and structures. Through this paper, all critical concepts revolving around MEE materials are discussed in separate sections ranging from the very definition of MEE materials, their material phenomenon, types and properties, to certain fundamental theories and micromechanical models, structural analyses of MEE structures and their nano-sized counterparts, effects of various external and internal parameters and prospective applications of these materials. The present study is in no ways exhaustive to the methods and results observed, but it may be considered as a guide to researchers and scholars about the behavior of MEE materials, wherein critical observations and analyses’ techniques are discussed.

Computational Analysis of Smart Magneto-Electro-Elastic Materials and Structures: Review and Classification

In this work, bending, buckling, and free vibration of magnetoelectroelastic nanobeam are investigated based on nonlocal theory and Timoshenko beam theory. According to Maxwell equation and magneto...

http://journals.sagepub.com/doi/pdf/10.1177/1045389X15585899

Bending, buckling, and free vibration of magnetoelectroelastic nanobeam based on nonlocal theory:

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Bending, buckling, and free vibration of magnetoelectroelastic nanobeam based on nonlocal theory: