• Advances in nano research
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• v.16 no.5
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• pp.489-500
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• 2024

This paper studies the free vibration analysis of the piezo-magneto-thermo-elastic FG nanobeam submerged in a fluid environment. The problem governed by the partial differential equations is determined by refined higher-order State Space Strain Gradient Theory (SSSGT). Hamilton's principle is applied to discretize the differential equation and transform it into a coupled Euler-Lagrange equation. Furthermore, the equations are solved analytically using Navier's solution technique to form stiffness, damping, and mass matrices. Also, the effects of nonlocal ceramic and metal parts over various parameters such as temperature, Magnetic potential and electric voltage on the free vibration are interpreted graphically. A comparison with existing published findings is performed to showcase the precision of the results.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.18 no.9
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• pp.52-60
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• 2017

This study examined the structural stability of nonlocal magneto-electro-elastic nano plates on elastic foundations using first-order shear deformation theory. Navier's method has been used to solve the buckling loads for all edges simply supported boundary conditions. On the other hand, biaxial buckling analysis of nano-plates has beenrarely studied. According to the Maxwell equation and the magneto-electro boundary condition, the change inthe magnetic and electric potential along the thickness direction of the magneto-electro-elastic nano plate wasdetermined. To reformulate the elasticity theory of the magneto- electro-elastic nano plate, the differential constitutive equation of Eringen was used and the governing equation of the nonlocal elasticity theory was studied using variational theory. The effects of the elastic foundation arebased on Pasternak's assumption. The relationship between nonlocal theory and local theory was analyzed through calculation results. In addition, structural stability problems were investigated according to the electric and magnetic potentials, nonlocal parameters, elastic foundation parameters, and side-to-thickness ratio. The results of the analysis revealedthe effects of the magnetic and electric potential. These calculations can be used to compare future research on new material structures made of magneto-electro-elastic materials.

• Steel and Composite Structures
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• v.33 no.1
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• pp.123-131
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• 2019

The present investigation is concerned with two dimensional deformation in a homogeneous nonlocal thermoelastic solid with two temperature. The nonlocal thermoelastic solid is subjected to inclined load. Laplace and Fourier transforms are used to solve the problem. The bounding surface is subjected to concentrated and distributed sources. The analytical expressions of displacement, stress components, temperature change are obtained in the transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerical simulated results are depicted graphically to show the effect of angle of inclination and nonlocal parameter on the components of displacements, stresses and conductive temperature. Some special cases are also deduced from the present investigation.

• Advances in nano research
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• v.12 no.4
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• pp.345-352
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• 2022

In this paper, natural frequency curves are presented for three specific end supports considering distinct values of nonlocal parameter. The vibrational behavior of zigzag double walled carbon nanotubes is investigated using wave propagation with nonlocal effect. Frequency spectra of zigzag (12, 0) double walled carbon nanotubes have been analyzed with proposed model. Effects of nonlocal parameters have been fully investigated on the natural frequency against against variation of Poisson's ratio. A slow increase in frequencies against variation of Poisson's ratio also indicates insensitivity of it for suggested nonlocal model. Moreover, decrease in frequencies with increase in nonlocal parameter authenticates the applicability of nonlocal Love shell model. Also the frequency curves for C-F are lower throughout the computation than that of C-C curves.

• Steel and Composite Structures
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• v.25 no.3
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• pp.361-374
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• 2017

In this study, the influences of triaxial magnetic field on the wave propagation behavior of anisotropic nanoplates are studied. In order to include small scale effects, nonlocal strain gradient theory has been implemented. To study the nanoplate as a continuum model, the three-dimensional elasticity theory is adopted in Cartesian coordinate. In our study, all the elastic constants are considered and assumed to be the functions of (x, y, z), so all kind of anisotropic structures such as hexagonal and trigonal materials can be modeled, too. Moreover, all types of functionally graded structures can be investigated. eigenvalue method is employed and analytical solutions for the wave propagation are obtained. To justify our methodology, our results for the wave propagation of isotropic nanoplates are compared with the results available in the literature and great agreement is achieved. Five different types of anisotropic structures are investigated in present paper and then the influences of wave number, material properties, nonlocal and gradient parameter and uniaxial, biaxial and triaxial magnetic field on the wave propagation analysis of anisotropic nanoplates are presented. From the best knowledge of authors, it is the first time that three-dimensional elasticity theory and nonlocal strain gradient theory are used together with no approximation to derive the governing equations. Moreover, up to now, the effects of triaxial magnetic field have not been studied with considering size effects in nanoplates. According to the lack of any common approximations in the displacement field or in elastic constant, present theory has the potential to be used as a bench mark for future works.

• Steel and Composite Structures
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• v.27 no.2
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• pp.201-216
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• 2018

In this paper, three-dimensional (3D) elasticity theory in conjunction with nonlocal strain gradient theory (NSGT) is developed for mechanical analysis of anisotropic nanoparticles. The present model incorporates two scale coefficients to examine the mechanical characteristics much accurately. All the elastic constants are considered and assumed to be the functions of (r, ${\theta}$, ${\varphi}$), so all kind of anisotropic structures can be modeled. Moreover, all types of functionally graded spherical structures can be investigated. To justify our model, our results for the radial vibration of spherical nanoparticles are compared with experimental results available in the literature and great agreement is achieved. Next, several examples of the radial vibration and wave propagation in spherical nanoparticles including nonlocal strain gradient parameters are presented for more than 10 different anisotropic nanoparticles. From the best knowledge of authors, it is the first time that 3D elasticity theory and NSGT are used together with no approximation to derive the governing equations in the spherical coordinate. Moreover, up to now, the NSGT has not been used for spherical anisotropic nanoparticles. It is also the first time that all the 36 elastic constants as functions of (r, ${\theta}$, ${\varphi}$) are considered for anisotropic and functionally graded nanostructures including size effects. According to the lack of any common approximations in the displacement field or in elastic constant, present theory can be assumed as a benchmark for future works.

• Structural Engineering and Mechanics
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• v.55 no.5
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• pp.1001-1014
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• 2015

Bending analysis of functionally graded (FG) nano-plates is investigated in the present work based on a new sinusoidal shear deformation theory. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. The material properties of nano-plate are assumed to vary according to power law distribution of the volume fraction of the constituents. The size effects are considered based on Eringen's nonlocal theory. Governing equations are derived using energy method and Hamilton's principle. The closed-form solutions of simply supported nano-plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. The effects of different parameters such as nano-plate length and thickness, elastic foundation, orientation of foundation orthtotropy direction and nonlocal parameters are shown in dimensionless displacement of system. It can be found that with increasing nonlocal parameter, the dimensionless displacement of nano-plate increases.

• Computers and Concrete
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• v.24 no.6
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• pp.579-586
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• 2019

In this research paper, the free vibrational behavior of the simply supported FG nano-plate is studied using the nonlocal two variables integral refined plate theory. The present model takes into account the small scale effect. The effective's properties of the plate change according to the power law variation (P-FGM). The equations of motion of the system are determined and resolved via Hamilton's principle and Navier procedure, respectively. The validity and efficiency of the current model are confirmed by comparing the results with those given in the literature. At the last section, several numerical results are presented to show the various parameters influencing the vibrational behavior such as the small-scale effect, geometry ratio, material index and aspect ratio.

• Coupled systems mechanics
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• v.9 no.3
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• pp.201-217
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• 2020

This paper employs differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT) for studying free vibrational characteristics of porous functionally graded (FG) nanoplates coupled by visco-elastic foundation. A secant function based refined plate theory is used for mathematical modeling of the nano-size plate. Two scale factors are included in the formulation for describing size influences based on NSGT. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. Visco-elastic foundation is presented based on three factors including a viscous layer and two elastic layers.The governing equations achieved by Hamilton's principle are solved implementing DQM. The nanoplate vibration is shown to be affected by porosity, temperature rise,scale factors and viscous damping.

• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.659-674
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• 2020

The present paper employs nonlocal strain gradient theory (NSGT) to study buckling behavior of functionally graded magneto-electro-thermo-elastic (FG-METE) nanoshells under various physical fields. NSGT modeling of the nanoshell contains two size parameters, one related to nonlocal stress field and another related to strain gradients. It is considered that mechanical, thermal, electrical and magnetic loads are exerted to the nanoshell. Temperature field has uniform and linear variation in nanoshell thickness. According to a power-law function, piezo-magnetic, thermal and mechanical properties of the nanoshell are considered to be graded in thickness direction. Five coupled governing equations have been obtained by using Hamilton's principle and then solved implementing Galerkin's method. Influences of temperature field, electric voltage, magnetic potential, nonlocality, strain gradient parameter and FG material exponent on buckling loads of the FG-METE nanoshell have been studied in detail.