• Steel and Composite Structures
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• 제32권2호
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• pp.157-171
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• 2019

In this research, the dynamic instability region (DIR) of the sandwich nano-beams are investigated based on nonlocal strain gradient elasticity theory (NSGET) and various higher order shear deformation beam theories (HSDBTs). The sandwich piezoelectric nano-beam is including a homogenous core and face-sheets reinforced with functionally graded (FG) carbon nanotubes (CNTs). In present study, three patterns of CNTs are employed in order to reinforce the top and bottom face-sheets of the beam. In addition, different higher-order shear deformation beam theories such as trigonometric shear deformation beam theory (TSDBT), exponential shear deformation beam theory (ESDBT), hyperbolic shear deformation beam theory (HSDBT), and Aydogdu shear deformation beam theory (ASDBT) are considered to extract the governing equations for different boundary conditions. The beam is subjected to thermal and electrical loads while is resting on Visco-Pasternak foundation. Hamilton principle is used to derive the governing equations of motion based on various shear deformation theories. In order to analysis of the dynamic instability behaviors, the linear governing equations of motion are solved using differential quadrature method (DQM). After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various shear deformation theories, nonlocal parameter, strain gradient parameter, the volume fraction of the CNTs, various distributions of the CNTs, different boundary conditions, dimensionless geometric parameters, Visco-Pasternak foundation parameters, applied voltage and temperature change on the dynamic instability characteristics of sandwich piezoelectric nano-beam.

• Steel and Composite Structures
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• 제27권2호
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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.

• Advances in aircraft and spacecraft science
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• 제7권2호
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• pp.169-186
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• 2020

Based upon differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT), mechanical-hygro-thermal vibrational analyzes of shear deformable porous functionally graded (FG) nanoplate on visco-elastic medium has been performed. The presented formulation incorporates two scale factors for examining vibrational behaviors of nano-dimension plates more accurately. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. It is supposed that the nano-size plate is exposed to hygro-thermal and variable compressive mechanical loadings. The governing equations achieved by Hamilton's principle are solved implementing DQM. Presented results indicate the prominence of moisture/temperature variation, damping factor, material gradient index, nonlocal coefficient, strain gradient coefficient and porosities on vibrational frequencies of FG nano-size plate.

• Coupled systems mechanics
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• 제7권4호
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• pp.373-393
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• 2018

This paper is concerned with the wave propagation behavior of rotating functionally graded temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field. Uniform, linear and nonlinear temperature distributions across the thickness are investigated. Thermo-elastic properties of FG beam change gradually according to the Mori-Tanaka distribution model in the spatial coordinate. The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function. The governing equations are derived by Hamilton's principle as a function of axial force due to centrifugal stiffening and displacement. By applying an analytical solution and solving an eigenvalue problem, the dispersion relations of rotating FG nanobeam are obtained. Numerical results illustrate that various parameters including temperature change, angular velocity, nonlocality parameter, wave number and gradient index have significant effect on the wave dispersion characteristics of the understudy nanobeam. The outcome of this study can provide beneficial information for the next generation researches and exact design of nano-machines including nanoscale molecular bearings and nanogears, etc.

• Advances in nano research
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• 제9권4호
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• pp.277-294
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• 2020

In current paper, nonlocal (NLT), nonlocal strain gradient (NSGT) and Gurtin-Murdoch surface/interface (GMSIT) theories with classical theory (CT) are utilized to investigate vibration and stability analysis of Double Walled Piezoelectric Nanosensor (DWPENS) based on cylindrical nanoshell. DWPENS simultaneously subjected to direct electrostatic voltage DC and harmonic excitations, structural damping, two piezoelectric layers and also nonlinear van der Waals force. For this purpose, Hamilton's principle, Galerkin technique, complex averaging and with arc-length continuation methods are used to analyze nonlinear behavior of DWPENS. For this work, three nonclassical theories compared with classical theory CT to investigate Dimensionless Natural Frequency (DNF), pull-in voltage, nonlinear frequency response and stability analysis of the DWPENS considering the nonlocal, material length scale, surface/interface (S/I) effects, electrostatic and harmonic excitation.

• Steel and Composite Structures
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• 재36권6호
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• pp.643-656
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• 2020

This article presents a comprehensive static analysis of simply supported cross-ply carbon nanotubes reinforced composite (CNTRC) laminated nanobeams under various loading profiles. The nonlocal strain gradient constitutive relation is exploited to present the size-dependence of nano-scale. New higher shear deformation beam theory with hyperbolic function is proposed to satisfy the zero-shear effect at boundaries and parabolic variation through the thickness. Carbon nanotubes (CNTs), as the reinforced elements, are distributed through the beam thickness with different distribution functions, which are, uniform distribution (UD-CNTRC), V- distribution (FG-V CNTRC), O- distribution (FG-O CNTRC) and X- distribution (FG-X CNTRC). The equilibrium equations are derived, and Fourier series function are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear or sinusoidal mechanical loadings. Numerical results are obtained to present influences of CNTs reinforcement patterns, composite laminate structure, nonlocal parameter, length scale parameter, geometric parameters on center deflection ad stresses of CNTRC laminated nanobeams. The proposed model is effective in analysis and design of composite structure ranging from macro-scale to nano-scale.

• Advances in nano research
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• 제14권2호
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• pp.141-154
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• 2023

Effects of viscoelastic foundation on vibration of curved-beam structure with clamped and simply-supported boundary conditions is investigated in this study. In doing so, a micro-scale laminate composite beam with two piezoelectric face layer with a carbon nanotube reinforces composite core is considered. The whole beam structure is laid on a viscoelastic substrate which normally occurred in actual conditions. Due to small scale of the structure non-classical elasticity theory provided more accurate results. Therefore, nonlocal strain gradient theory is employed here to capture both nano-scale effects on carbon nanotubes and microscale effects because of overall scale of the structure. Equivalent homogenous properties of the composite core is obtained using Halpin-Tsai equation. The equations of motion is derived considering energy terms of the beam and variational principle in minimizing total energy. The boundary condition is assumed to be clamped at one end and simply supported at the other end. Due to nonlinear terms in the equations of motion, semi-analytical method of general differential quadrature method is engaged to solve the equations. In addition, due to complexity in developing and solving equations of motion of arches, an artificial neural network is design and implemented to capture effects of different parameters on the inplane vibration of sandwich arches. At the end, effects of several parameters including nonlocal and gradient parameters, geometrical aspect ratios and substrate constants of the structure on the natural frequency and amplitude is derived. It is observed that increasing nonlocal and gradient parameters have contradictory effects of the amplitude and frequency of vibration of the laminate beam.

• Advances in nano research
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• 제15권4호
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• pp.339-353
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• 2023

This work aims to present a solution for the buckling behavior of perforated nano/microbeams with deformable boundary conditions using nonlocal strain gradient theory (NLSGT). For the first time, a solution that can provide buckling loads based on the non-local and strain gradient effects of perforated nanostructures on an elastic foundation, while taking into account both deformable and rigid boundary conditions. Stokes' transformation and Fourier series are used to realize this aim and determine the buckling loads under various boundary conditions. We employ the NLSGT to account for size-dependent effects and utilize the Winkler model to formulate the elastic foundation. The buckling behavior of the perforated nano/microbeams restrained with lateral springs at both ends is studied for various parameters such as the number of holes, the length and filling ratio of the perforated beam, the internal length, the nonlocal parameter and the dimensionless foundation parameter. Our results indicate that the number of holes and filling ratio significantly affect the buckling response of perforated nano/microbeams. Increasing the filling ratio increases buckling loads, while increasing the number of holes decreases buckling loads. The effects of the non-local and internal length parameters on the buckling behavior of the perforated nano/microbeams are also discussed. These material length parameters have opposite effects on the variation of buckling loads. This study presents an effective eigenvalue solution based on Stokes' transformation and Fourier series of the restrained nano/microbeams under the effects of elastic medium, perforation parameters, deformable boundaries and nonlocal strain gradient elasticity for the first time.

• Steel and Composite Structures
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• 제25권3호
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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.

• Advances in nano research
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• 제9권1호
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• pp.33-45
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• 2020

Geometrically nonlinear buckling of functionally graded magneto-electro-elastic (FG-MEE) nanoshells with the use of classical shell theory and nonlocal strain gradient theory (NSGT) has been analyzed in present research. Mathematical formulation based on NSGT gives two scale coefficients for simultaneous description of structural stiffness reduction and increment. Functional gradation of material properties is described based on power-law formulation. The nanoshell is under a multi-physical field related to applied voltage, magnetic potential, and mechanical load. Exerting a strong electric voltage, magnetic potential or mechanical load may lead to buckling of nanoshell. Taking into account geometric nonlinearity effects after buckling, the behavior of nanoshell in post-buckling regime can be analyzed. Nonlinear governing equations are reduced to ordinary equations utilizing Galerkin's approach and post-buckling curves are obtained based on an analytical procedure. It will be shown that post-buckling curves are dependent on nonlocal/strain gradient parameters, electric voltage magnitude and sign, magnetic potential magnitude and sign and material gradation exponent.