• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.1
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• pp.85-92
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• 2015

This article presents the dynamic instability response of sigmoid functionally graded material plates on elastic foundation using the higher-order shear deformation theory. The higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The governing equations are then written in the form of Mathieu-Hill equations and then Bolotin's method is employed to determine the instability regions. The boundaries of the instability regions are represented in the dynamic load and excitation frequency plane. The results of dynamic instability analysis of sigmoid functionally graded material plate are presented using the Navier's procedure to illustrate the effect of elastic foundation parameter on dynamic response. The relations between Winkler and Pasternak elastic foundation parameter are discussed by numerical results. Also, the effects of static load factor, power-law index and side-to-thickness ratio on dynamic instability analysis are investigated and discussed. In order to validate the present solutions, the reference solutions are used and discussed. The theoretical development as well as numerical solutions presented herein should serve as reference for the dynamic instability study of S-FGM plates.

• Steel and Composite Structures
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• v.36 no.6
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• pp.711-727
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• 2020

In the present research, the free vibration analysis of functionally graded (FG) nanocomposite deep spherical shells reinforced by graphene platelets (GPLs) on elastic foundation is performed. The elastic foundation is assumed to be Winkler-Past ernak-type. It is also assumed that graphaene platelets are randomly oriented and uniformly dispersed in each layer of the nanocomposite shell. Volume fraction of the graphene platelets as nanofillers may be different in the layers. The modified HalpinTsai model is used to approximate the effective mechanical properties of the multilayer nanocomposite. With the aid of the first order shear deformation shell theory and implementing Hamilton's principle, motion equations are derived. Afterwards, the generalized differential quadrature method (GDQM) is utilized to study the free vibration characteristics of FG-GPLRC spherical shell. To assess the validity and accuracy of the presented method, the results are compared with the available researches. Finally, the natural frequencies and corresponding mode shapes are provided for different boundary conditions, GPLs volume fraction, types of functionally graded, elastic foundation coefficients, opening angles of shell, and thickness-to-radius ratio.

• Advances in nano research
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• v.9 no.3
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• pp.183-191
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• 2020

The content of this study focuses on bending of flexoelectric Magneto-Electro-Elastic (MEE) nanobeams inserted within the foundation of Winkler-Pasternak according to nonlocal elasticity theory. Applying Hamilton's principle, the nonlocal nanobeams' governing equations in the framework higher order refined beam theory are attained and resolved through adapting an analytical solution. A parametric research is demonstrated for studying the effects that magneto-electro-mechanical loadings, the nonlocal parameter, flexoelectric, as well as the aspect ratio all have on the deflection properties of nanobeams. A discovery lead to beam geometrical parameters, the boundary conditions, flexoelectricity and nonlocal parameter partake substantial effects on nanoscale beams' dimensionless deflection.

• Advances in nano research
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• v.8 no.3
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• pp.203-214
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• 2020

This paper investigated bending of magneto-electro-elastic (MEE) nanobeams under hygro-thermal loading embedded in Winkler-Pasternak foundation based on nonlocal elasticity theory. The governing equations of nonlocal nanobeams in the framework parabolic third order beam theory are obtained using Hamilton's principle and solved implementing an analytical solution. A parametric study is presented to examine the effect of the nonlocal parameter, hygro-thermal-loadings, magneto-electro-mechanical loadings and aspect ratio on the deflection characteristics of nanobeams. It is found that boundary conditions, nonlocal parameter and beam geometrical parameters have significant effects on dimensionless deflection of nanoscale beams.

• Advances in nano research
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• v.13 no.1
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• pp.63-75
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• 2022

The nonlinear dynamic behavior of a nonuniform small-scale nonlocal beam is investigated in this work. The nanobeam is theoretically modeled using the nonlocal Eringen theory, as well as a few of Von-nonlinear Kármán's theories and the classical beam theory. The Hamilton principle extracts partial differential equations (PDE) of an axially functionally graded (AFG) nano-scale beam consisting of SUS304 and Si₃N₄ throughout its length, and an elastic Winkler-Pasternak substrate supports the tapered AFG nanobeam. The beam thickness is a function of beam length, and it constantly varies throughout the length of the beam. The numerical solution strategy employs an iteration methodology connected with the generalized differential quadratic method (GDQM) to calculate the nonlinear outcomes. The nonlinear numerical results are presented in detail to examine the impact of various parameters such as nonlinear amplitude, nonlocal parameter, the component of the elastic foundation, rate of cross-section change, and volume fraction parameter on the linear and nonlinear free vibration characteristics of AFG nanobeam.

• Steel and Composite Structures
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• v.37 no.6
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• pp.695-709
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• 2020

The buckling properties of a single-layered graphene sheet (SLGS) are examined using nonlocal integral first shear deformation theory (FSDT) by incorporating the influence of visco-Pasternak's medium. This model contains only four variables, which is even less than the conventional FSDT. The visco-Pasternak's medium is introduced by considering the damping influence to the conventional foundation model which modeled by the linear Winkler's coefficient and Pasternak's (shear) foundation coefficient. The nanoplate under consideration is subjected to compressive in- plane edge loads per unit length. The impacts of many parameters such as scale parameter, aspect ratio, the visco-Pasternak's coefficients, damping parameter, and mode numbers on the stability investigation of the SLGSs are examined in detail. The obtained results are compared with the corresponding available in the literature.

• Advances in nano research
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• v.15 no.4
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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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• v.37 no.1
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• pp.51-73
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• 2020

The present paper investigates the simultaneous resonance behavior of spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells with internal and external functionally graded stiffeners under the two-term large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness. The cylindrical shell has three layers consist of ceramic, FGM, and metal. The exterior layer of the cylindrical shell is rich ceramic while the interior layer is rich metal and the functionally graded material layer is located between these layers. With regard to classical shells theory, von-Kármán equation, and Hook law, the relations of stress-strain are derived for shell and stiffeners. The spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. According to the Galerkin method, the discretized motion equation is obtained. The simultaneous resonance is obtained using the multiple scales method. Finally, the influences of different material and geometrical parameters on the system resonances are investigated comprehensively.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.764-767
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• 2005

This paper deals with the flexural-torsional free vibrations of circular strip foundations with a variable breadth. The breadth of strip foundation varies with the linear functional fashion, which is symmetric about the mid-arc. Differential equations governing free vibrations of such foundations are derived, in which Winkler foundation is considered as the model of elastic soils. Effects of the rotatory and torsional inertias and shear deformation are included in the governing equations. Differential equations are numerically solved to calculate the natural frequencies. In the numerical examples, the free-free end constraint is considered. Effects of the rotatory and torsional inertias and shear parameter on the natural frequencies are reported. Parametric studies between frequency parameters and various system parameters are investigated.

• Smart Structures and Systems
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• v.20 no.6
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• pp.709-728
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• 2017

This disquisition proposes a nonlocal strain gradient beam theory for thermo-mechanical dynamic characteristics of embedded smart shear deformable curved piezoelectric nanobeams made of porous electro-elastic functionally graded materials by using an analytical method. Electro-elastic properties of embedded curved porous FG nanobeam are assumed to be temperature-dependent and vary through the thickness direction of beam according to the power-law which is modified to approximate material properties for even distributions of porosities. It is perceived that during manufacturing of functionally graded materials (FGMs) porosities and micro-voids can be occurred inside the material. Since variation of pores along the thickness direction influences the mechanical and physical properties, so in this study thermo-mechanical vibration analysis of curve FG piezoelectric nanobeam by considering the effect of these imperfections is performed. Nonlocal strain gradient elasticity theory is utilized to consider the size effects in which the stress for not only the nonlocal stress field but also the strain gradients stress field. The governing equations and related boundary condition of embedded smart curved porous FG nanobeam subjected to thermal and electric field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is utilized to achieve the natural frequencies of porous FG curved piezoelectric nanobeam resting on Winkler and Pasternak foundation. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality parameter, electric voltage, coefficient of porosity, elastic foundation parameters, thermal effect, gradient index, strain gradient, elastic opening angle and slenderness ratio on the natural frequency of embedded curved FG porous piezoelectric nanobeam are successfully discussed. It is concluded that these parameters play important roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.