• Structural Engineering and Mechanics
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• v.72 no.4
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• pp.525-540
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• 2019

The purpose of the present work was to study the dynamic instability of a three-layered, symmetric sandwich beam subjected to a periodic axial load resting on nonlinear elastic foundation. A higher-order theory was used for analysis of sandwich beams with soft core on elastic foundations. In the higher-order theory, the Reddy's third-order theory was used for the face sheets and quadratic and cubic functions were assumed for transverse and in-plane displacements of the core, respectively. The elastic foundation was modeled as nonlinear's type. The dynamic instability regions and free vibration were investigated for simply supported conditions by Bolotin's method. The results showed that the responses of the dynamic instability of the system were influenced by the excitation frequency, the coefficients of foundation, the core thickness, the dynamic and static load factor. Comparison of the present results with the published results in the literature for the special case confirmed the accuracy of the proposed theory.

• Geomechanics and Engineering
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• v.22 no.5
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• pp.415-431
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• 2020

In this study, dynamics responses of advanced composite plates resting variable elastic foundations via a quasi-3D theory are developed using an analytical approach. This higher shear deformation theory (HSDT) is included the shear deformation theory and effect stretching that has five unknowns, which is even inferior to normal deformation theories found literature and other theories. The quasi-three-dimensional (quasi-3D) theory accounts for a parabolic distribution of the transverse shear deformation and satisfies the zero traction boundary conditions on the surfaces of the advanced composite plate without needing shear correction factors. The plates assumed to be rest on two-parameter elastic foundations, the Winkler parameter is supposed to be constant but the Pasternak parameter varies along the long side of the plate with three distributions (linear, parabolic and sinusoidal). The material properties of the advanced composite plates gradually vary through the thickness according to two distribution models (power law and Mori-Tanaka). Governing differential equations and associated boundary conditions for dynamics responses of the advanced composite plates are derived using the Hamilton principle and are solved by using an analytical solution of Navier's technique. The present results and validations of our modal with literature are presented that permitted to demonstrate the accuracy of the present quasi-3D theory to predict the effect of variables elastic foundation on dynamics responses of advanced composite plates.

• Geomechanics and Engineering
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• v.31 no.1
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• pp.99-112
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• 2022

The present study examines the natural frequencies (NFs) of perfect/imperfect functionally graded sandwich beams (P/IP-FGSBs), which are composed of a porous core constructed of functionally graded materials (FGMs) and a homogenous isotropic metal and ceramic face sheets resting on elastic foundations. To accomplish this, the material properties of the FGSBs are assumed to vary continuously along the thickness direction as a function of the volume fraction of constituents expressed by the modified rule of the mixture, which includes porosity volume fraction represented using four distinct types of porosity distribution models. Additionally, to characterize the reaction of the two-parameter elastic foundation to the Perfect/Imperfect (P/IP) FGSBs, the medium is assumed to be linear, homogeneous, and isotropic, and it is described using the Winkler-Pasternak model. Furthermore, the kinematic relationship of the P/IP-FGSBs resting on the Winkler-Pasternak elastic foundations (WPEFs) is described using trigonometric shear deformation theory (TrSDT), and the equations of motion are constructed using Hamilton's principle. A closed-form solution is developed for the free vibration analysis of P/IP-FGSBs resting on the WPEFs under four distinct boundary conditions (BCs). To validate the new formulation, extensive comparisons with existing data are made. A detailed investigation is carried out for the effects of the foundation coefficients, mode numbers (MNs), porosity volume fraction, power-law index, span to depth ratio, porosity distribution patterns (PDPs), skin core skin thickness ratios (SCSTR), and BCs on the values of the NFs of the P/IP-FGSBs.

• Geomechanics and Engineering
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• v.8 no.2
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• pp.283-303
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• 2015

To research and analyze the differential settlements of foundations specifically, site investigations of existing railways and metro were firstly carried out. Then, the centrifugal test was used to observe differential settlements in different position between foundations on the basis of investigation. The theoretical model was established according to the stress diffusion method and Fourier method to establish an analytical solution of embankment differential settlement between different foundations. Finally, theoretical values and experimental values were analyzed comparatively. The research results show that both in horizontal and vertical directions, evident differential settlement exists in a limited area on both sides of the vertical interface between different foundations. The foundation with larger elastic modulus can transfer more additional stress and cause relatively less settlement. Differential settlement value decreases as the distance to vertical interface decreases. In the vertical direction of foundation, mass differential settlement also exists on both sides of the vertical interface and foundation with larger elastic modulus can transfer more additional stress. With the increase of relative modulus of different foundations, foundation with lower elastic modulus has larger settlement. Meanwhile, differential settlement is more obvious. The main error sources in theoretical and experimental values include: (a) different load form; (b) foundation characteristics differences; (c) modulus conversion; (d) effect of soil internal friction.

• Structural Engineering and Mechanics
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• v.50 no.6
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• pp.773-796
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• 2014

This paper deals with free vibration analysis of continuous grading fiber reinforced (CGFR) and bi-directional FG annular sector plates on two-parameter elastic foundations under various boundary conditions, based on the three-dimensional theory of elasticity. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. Results indicate that the non-dimensional natural frequency parameter of a functionally graded fiber volume fraction is larger than that of a discrete laminated and close to that of a 2-layer. It results that the CGFR plate attains natural frequency higher than those of traditional discretely laminated composite ones and this can be a benefit when higher stiffness of the plate is the goal and that is due to the reduction in spatial mismatch of material properties. Moreover, it is shown that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional one-dimensional functionally graded material. The multidirectional graded material can likely be designed according to the actual requirement and it is a potential alternative to the unidirectional functionally graded material. The new results can be used as benchmark solutions for future researches.

• Steel and Composite Structures
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• v.33 no.2
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• pp.195-208
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• 2019

Based on a four-variable shear deformation shell theory, the free vibration analysis of functionally graded graphene platelet-reinforced composite (FGGPRC) doubly-curved shallow shells with different boundary conditions is investigated in this work. The doubly-curved shells are composed of multi nanocomposite layers that are reinforced with graphene platelets. The graphene platelets are uniformly distributed in each individual layer. While, the volume faction of the graphene is graded from layer to other in accordance with a novel distribution law. Based on the suggested distribution law, four types of FGGPRC doubly-curved shells are studied. The present shells are assumed to be rested on elastic foundations. The material properties of each layer are calculated using a micromechanical model. Four equations of motion are deduced utilizing Hamilton's principle and then converted to an eigenvalue problem employing an analytical method. The obtained results are checked by introducing some comparison examples. A detailed parametric investigation is performed to illustrate the influences of the distribution type of volume fraction, shell curvatures, elastic foundation stiffness and boundary conditions on the vibration of FGGPRC doubly-curved shells.

• Advances in nano research
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• v.16 no.3
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• pp.313-324
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• 2024

The main aims of this study are to develop a new nonlocal quasi-3D theory for the free vibration behaviors of the functionally graded sandwich nanobeams. The sandwich beams consist of a ceramic core and two functionally graded material layers resting on elastic foundations. The two layers, linear spring stiffness and shear layer, are used to model the effects of the elastic foundations. The size-effect is considered using nonlocal elasticity theory. The governing equations of the motion of the functionally graded sandwich nanobeams are obtained via Hamilton's principle in combination with nonlocal elasticity theory. Then the Navier's solution technique is used to solve the governing equations of the motion to achieve the nonlocal free vibration behaviors of the nanobeams. A deep parametric study is also provided to demonstrate the effects of some parameters, such as length-to-height ratio, power-law index, nonlocal parameter, and two parameters of the elastic foundation, on the free vibration behaviors of the functionally graded sandwich nanobeams.

• Steel and Composite Structures
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• v.11 no.5
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• pp.403-421
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• 2011

In the present manuscript, geometrically nonlinear free vibration analysis of thin laminated plates resting on non-linear elastic foundations is investigated. Winkler-Pasternak type foundation model is used. Governing equations of motions are obtained using the von Karman type nonlinear theory. The method of discrete singular convolution is used to obtain the discretised equations of motion of plates. The effects of plate geometry, boundary conditions, material properties and foundation parameters on nonlinear vibration behavior of plates are presented.

• Structural Engineering and Mechanics
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• v.83 no.6
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• pp.771-788
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• 2022

This research investigates the free vibration of porous advanced composite plates resting on Winkler/Pasternak/ Kerr foundations by using a new hyperbolic quasi three dimensional (quasi-3D) shear deformation theory. The present theory, which does not require shear correction factor, accounts for shear deformation and thickness stretching effects by parabolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate. In this work, we consider imperfect FG plates with porosities embedded within elastic Winkler, Pasternak or Kerr foundations. Implementing an analytical approach, the obtained governing equations from Hamilton's principle according to FG plates are derived. The closed form solutions are obtained by using Navier technique, and natural frequencies of FG plates are found, for simply supported plates, by solving the results of eigenvalue problems. A comprehensive parametric study is presented to evaluate effects of the geometry of material, mode numbers, porosity volume fraction, Power-law index and stiffness of foundations parameters on free vibration characteristics of FG plates.

• Advances in materials Research
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• v.5 no.1
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• pp.35-53
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• 2016

Flexural bending analysis of perfect and imperfect functionally graded materials plates under hygro-thermo-mechanical loading are investigated in this present paper. Due to technical problems during FGM fabrication, porosities and micro-voids can be created inside FGM samples which may lead to the reduction in density and strength of materials. In this investigation, the FGM plates are assumed to have even and uneven distributions of porosities over the plate cross-section. The modified rule of mixture is used to approximate material properties of the FGM plates including the porosity volume fraction. In order the elastic coefficients, thermal coefficient and moisture expansion coefficient of the plate are assumed to be graded in the thickness direction. The elastic foundation is modeled as two-parameter Pasternak foundation. The equilibrium equations are given and a number of examples are solved to illustrate bending response of Metal-Ceramic plates subjected to hygro-thermo-mechanical effects and resting on elastic foundations. The influences played by many parameters are investigated.