• Steel and Composite Structures
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• 제29권1호
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• pp.53-66
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• 2018

A high-order nonlocal strain gradient model is developed for wave propagation analysis of porous FG nanoplates resting on a gradient hybrid foundation in thermal environment, for the first time. Material properties are assumed to be temperature-dependent and graded in the nanoplate thickness direction. To consider the thermal effects, uniform, linear, nonlinear, exponential, and sinusoidal temperature distributions are considered for temperature-dependent FG material properties. On the basis of the refined-higher order shear deformation plate theory (R-HSDT) in conjunction with the bi-Helmholtz nonlocal strain gradient theory (B-H NSGT), Hamilton's principle is used to derive the equations of wave motion. Then the dispersion relation between frequency and wave number is solved analytically. The influences of various parameters (such as temperature rise, volume fraction index, porosity volume fraction, lower and higher order nonlocal parameters, material characteristic parameter, foundations components, and wave number) on the wave propagation behaviors of porous FG nanoplates are investigated in detail.

• Structural Engineering and Mechanics
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• 제66권2호
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• pp.237-248
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• 2018

This study presents the investigation of wave dispersion characteristics of a magneto-electro-elastic functionally graded (MEE-FG) nanosize beam utilizing nonlocal strain gradient theory (NSGT). In this theory, a material length scale parameter is propounded to show the influence of strain gradient stress field, and likewise, a nonlocal parameter is nominated to emphasize on the importance of elastic stress field effects. The material properties of heterogeneous nanobeam are supposed to vary smoothly through the thickness direction based on power-law form. Applying Hamilton's principle, the nonlocal governing equations of MEE-FG nanobeam are derived. Furthermore, to derive the wave frequency, phase velocity and escape frequency of MEE-FG nanobeam, an analytical solution is employed. The validation procedure is performed by comparing the results of present model with results exhibited by previous papers. Results are rendered in the framework of an exact parametric study by changing various parameters such as wave number, nonlocal parameter, length scale parameter, gradient index, magnetic potential and electric voltage to show their influence on the wave frequency, phase velocity and escape frequency of MEE-FG nanobeams.

• Structural Engineering and Mechanics
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• 제72권3호
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• pp.329-338
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• 2019

In this paper, the magnetic field influence on the wave propagation characteristics of graphene nanosheets is examined within the frame work of a two-variable plate theory. The small-scale effect is taken into consideration based on the nonlocal strain gradient theory. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. A derivation of the differential equation is conducted, employing extended principle of Hamilton and solved my means of analytical solution. A refined trigonometric two-variable plate theory is employed in Kinematic relations. The scattering relation of wave propagation in solid bodies which captures the relation of wave number and the resultant frequency is also investigated. According to the numerical results, it is revealed that the proposed modeling can provide accurate wave dispersion results of the graphene nanosheets as compared to some cases in the literature. It is shown that the wave dispersion characteristics of graphene sheets are influenced by magnetic field, elastic foundation and nonlocal parameters. Numerical results are presented to serve as benchmarks for future analyses of graphene nanosheets.

• Advances in nano research
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• 제10권2호
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• pp.175-189
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• 2021

In this article, frequency characteristics, and sensitivity analysis of a size-dependent laminated composite cylindrical nanoshell under bi-directional thermal loading using Nonlocal Strain-stress Gradient Theory (NSGT) are presented. The governing equations of the laminated composite cylindrical nanoshell in thermal environment are developed using Hamilton's principle. The thermodynamic equations of the laminated cylindrical nanoshell are obtained using First-order Shear Deformation Theory (FSDT) and Fourier-expansion based Generalized Differential Quadrature element Method (FGDQM) is implemented to solve these equations and obtain natural frequency and critical temperature of the presented model. The novelty of the current study is to consider the effects of bi-directional temperature loading and sensitivity parameter on the critical temperature and frequency characteristics of the laminated composite nanostructure. Apart from semi-numerical solution, a finite element model was presented using the finite element package to simulate the response of the laminated cylindrical shell. The results created from finite element simulation illustrates a close agreement with the semi-numerical method results. Finally, the influences of temperature difference, ply angle, length scale and nonlocal parameters on the critical temperature, sensitivity, and frequency of the laminated composite nanostructure are investigated, in details.

• Advances in nano research
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• 제12권3호
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• pp.231-251
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• 2022

Dynamic behavior of temperature-dependent Reddy functionally graded (RFG) nanobeam subjected to thermomagnetic effects under the action of moving point load is carried out in the present work. Both symmetric and sigmoid functionally graded material distributions throughout the beam thickness are considered. To consider the significance of strain-stress gradient field, a material length scale parameter (LSP) is introduced while the significance of nonlocal elastic stress field is considered by introducing a nonlocal parameter (NP). In the framework of the nonlocal strain gradient theory (NSGT), the dynamic equations of motion are derived through Hamilton's principle. Navier approach is employed to solve the resulting equations of motion of the functionally graded (FG) nanoscale beam. The developed model is verified and compared with the available previous results and good agreement is observed. Effects of through-thickness variation of FG material distribution, beam aspect ratio, temperature variation, and magnetic field as well as the size-dependent parameters on the dynamic behavior are investigated. Introduction of the magnetic effect creates a hardening effect; therefore, higher values of natural frequencies are obtained while smaller values of the transverse deflections are produced. The obtained results can be useful as reference solutions for future dynamic and control analysis of FG nanobeams reinforced nanocomposites under thermomagnetic effects.

• Advances in nano research
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• 제14권5호
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• pp.475-493
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• 2023

In the context of nonclassical nonlocal strain gradient elasticity, this article studies the free and forced responses of functionally graded material (FGM) porous nanoplates exposed to thermal and magnetic fields under a moving load. The developed mathematical model includes shear deformation, size-scale, miscorstructure influences in the framework of higher order shear deformation theory (HSDT) and nonlocal strain gradient theory (NSGT), respectively. To explore the porosity effect, the study considers four different porosity models across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The system of quations of motion of the FGM porous nanoplate, including the effects of thermal load, Lorentz force, due to the magnetic field and moving load, are derived using the Hamilton's principle, and then solved analytically by employing the Navier method. For the free and forced responses of the nanoplate, the effects of nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. It is found that the forced vibrations of FGM porous nanoplates under thermal and live loads can be damped by applying a directed magnetic field.

• Steel and Composite Structures
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• 제50권1호
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• pp.15-24
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• 2024

This research presents dynamical reaction investigation of pore-dependent and nano-thickness beams having functional gradation (FG) constituents exposed to a movable particle. The nano-thickness beam formulation has been appointed with the benefits of refined high orders beam paradigm and nonlocal strain gradient theory (NSGT) comprising two scale moduli entitled nonlocality and strains gradient modulus. The graded pore-dependent constituents have been designed through pore factor based power-law relations comprising pore volumes pursuant to even or uneven pore scattering. Therewith, variable scale modulus has been thought-out until process a more accurate designing of scale effects on graded nano-thickness beams. The motion equations have been appointed to be solved via Ritz method with the benefits of Chebyshev polynomials in cosine form. Also, Laplace transform techniques help Ritz-Chebyshev method to obtain the dynamical response in time domain. All factors such as particle speed, pores and variable scale modulus affect the dynamical response.