• Title/Summary/Keyword: Winkler foundation

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Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity

  • Hadj, Bekki;Rabia, Benferhat;Daouadji, Tahar Hassaine
    • Coupled systems mechanics
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    • v.10 no.1
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    • pp.61-77
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    • 2021
  • The porosity of functionally graded materials (FGM) can affect the static and dynamic behavior of plates, which is important to take this aspect into account when analyzing such structures. The present work aims to study the effect of the distribution shape of porosity on the free vibration response of simply supported FG plate reposed on the Winkler-Pasternak foundation. A refined theory of shear deformation is expanded to study the influence of the distribution shape of porosity on the free vibration behavior of FG plates. The findings showed that the distribution shape of porosity significantly influences the free vibration behavior of thick rectangular FG plates for small values of Winkler-Pasternak elastic foundation parameters.

Elastic wave propagation analysis in sandwich nanoplate assuming size effects

  • Amir Behshad;Maryam Shokravi;Akbar Shafiei Alavijeh;Hamed, Karami
    • Steel and Composite Structures
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    • v.47 no.1
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    • pp.71-77
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    • 2023
  • This paper presents a study on the wave propagation of functionally graded material (FGM) sandwich nanoplates with soft core resting on a Winkler foundation. The structure is modelled by classical theory. Motion equations are derived by the assumption of nonlocal Eringen theory and energy method. Then, the equations are solved using an exact method for finding phase velocity responses. The effects of Winkler foundation, nonlocal parameters, thickness and mode number on the dispersion of elastic waves are shown. With the increase of spring constant, the speed of wave propagation increases and reaches a uniform state at a higher wave number.

Thermo-mechanical behavior of porous FG plate resting on the Winkler-Pasternak foundation

  • Rabia, Benferhat;Tahar, Hassaine Daouadji;Abderezak, Rabahi
    • Coupled systems mechanics
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    • v.9 no.6
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    • pp.499-519
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    • 2020
  • The effect of porosity on the thermo-mechanical behavior of simply supported functionally graded plate reposed on the Winkler-Pasternak foundation is investigated analytically in the present paper using new refined hyperbolic shear deformation plate theory. Both even and uneven distribution of porosity are taken into account and the effective properties of FG plates with porosity are defined by theoretical formula with an additional term of porosity. The present formulation is based on a refined higher order shear deformation theory, which is based on four variables and it still accounts for parabolic distribution of the transverse shearing strains and stresses through the thickness of the FG plate and takes into account the various distribution shape of porosity. The elastic foundation is described by the Winkler-Pasternak model. Anew modified power-law formulation is used to describe the material properties of FGM plates in the thickness direction. The closed form solutions are obtained by using Navier technique. The present results are verified in comparison with the published ones in the literature. The results show that the dimensionless and stresses are affected by the porosity volume fraction, constituent volume fraction, and thermal load.

Natural frequency analysis of joined conical-cylindrical-conical shells made of graphene platelet reinforced composite resting on Winkler elastic foundation

  • Xiangling Wang;Xiaofeng Guo;Masoud Babaei;Rasoul Fili;Hossein Farahani
    • Advances in nano research
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    • v.15 no.4
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    • pp.367-384
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    • 2023
  • Natural frequency behavior of graphene platelets reinforced composite (GPL-RC) joined truncated conical-cylindrical- conical shells resting on Winkler-type elastic foundation is presented in this paper for the first time. The rule of mixture and the modified Halpin-Tsai approach are applied to achieve the mechanical properties of the structure. Four different graphene platelets patterns are considered along the thickness of the structure such as GPLA, GPLO, GPLX, GPLUD. Finite element procedure according to Rayleigh-Ritz formulation has been used to solve 2D-axisymmetric elasticity equations. Application of 2D axisymmetric elasticity theory allows thickness stretching unlike simple shell theories, and this gives more accurate results, especially for thick shells. An efficient parametric investigation is also presented to show the effects of various geometric variables, three different boundary conditions, stiffness of elastic foundation, dispersion pattern and weight fraction of GPLs nanofillers on the natural frequencies of the joined shell. Results show that GPLO and BC3 provide the most rigidity that cause the most natural frequencies among different BCs and GPL patterns. Also, by increasing the weigh fraction of nanofillers, the natural frequencies will increase up to 200%.

Free vibration analysis of FG porous spherical cap reinforced by graphene platelet resting on Winkler foundation

  • Xiangqian Shen;Tong Li;Lei Xu;Faraz Kiarasi;Masoud Babaei;Kamran Asemi
    • Advances in nano research
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    • v.16 no.1
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    • pp.11-26
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    • 2024
  • In this study, free vibration analysis of FG porous spherical cap reinforced by graphene platelets resting on Winkler-type elastic foundation has been surveyed for the first time. Three different types of porosity patterns are considered for the spherical cap whose two types of porosity patterns in the metal matrix are symmetric and the other one is uniform. Besides, five GPL patterns are assumed for dispersing of GPLs in the metal matrix. Tsai-Halpin and extended rule of the mixture are used to determine the Young modulus and mass density of the shell, respectively. Employing 3D FEM elasticity in conjunction with Hamilton's Principle, the governing motion equations of the structure are obtained and solved. The impact of various parameters including porosity coefficient, various porosity distributions in conjunction with different GPL patterns, the weight fraction of graphene Nano fillers, polar angles and stiffness coefficient of elastic foundation on natural frequencies of FG porous spherical cap reinforced by GPLs have been reported for the first time.

Free vibration analysis of tapered beam-column with pinned ends embedded in Winkler-Pasternak elastic foundation

  • Civalek, Omer;Ozturk, Baki
    • Geomechanics and Engineering
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    • v.2 no.1
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    • pp.45-56
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    • 2010
  • The current study presents a mathematical model and numerical method for free vibration of tapered piles embedded in two-parameter elastic foundations. The method of Discrete Singular Convolution (DSC) is used for numerical simulation. Bernoulli-Euler beam theory is considered. Various numerical applications demonstrate the validity and applicability of the proposed method for free vibration analysis. The results prove that the proposed method is quite easy to implement, accurate and highly efficient for free vibration analysis of tapered beam-columns embedded in Winkler- Pasternak elastic foundations.

Nonlinear vibration of hybrid composite plates on elastic foundations

  • Chen, Wei-Ren;Chen, Chun-Sheng;Yu, Szu-Ying
    • Structural Engineering and Mechanics
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    • v.37 no.4
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    • pp.367-383
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    • 2011
  • In this paper, nonlinear partial differential equations of motion for a hybrid composite plate subjected to initial stresses on elastic foundations are established to investigate its nonlinear vibration behavior. Pasternak foundation and Winkler foundations are used to represent the plate-foundation interaction. The initial stress is taken to be a combination of pure bending stress plus an extensional stress in the example problems. The governing equations of motion are reduced to the time-dependent ordinary differential equations by the Galerkin's method. Then, the Runge-Kutta method is used to evaluate the nonlinear vibration frequency and frequency ratio of hybrid composite plates. The nonlinear vibration behavior is affected by foundation stiffness, initial stress, vibration amplitude and the thickness ratio of layer. The effects of various parameters on the nonlinear vibration of hybrid laminated plate are investigated and discussed.

Generalized curved beam on elastic foundation solved by transfer matrix method

  • Arici, Marcello;Granata, Michele Fabio
    • Structural Engineering and Mechanics
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    • v.40 no.2
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    • pp.279-295
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    • 2011
  • A solution of space curved bars with generalized Winkler soil found by means of Transfer Matrix Method is presented. Distributed, concentrated loads and imposed strains are applied to the beam as well as rigid or elastic boundaries are considered at the ends. The proposed approach gives the analytical and numerical exact solution for circular beams and rings, loaded in the plane or perpendicular to it. A well-approximated solution can be found for general space curved bars with complex geometry. Elastic foundation is characterized by six parameters of stiffness in different directions: three for rectilinear springs and three for rotational springs. The beam has axial, shear, bending and torsional stiffness. Numerical examples are given in order to solve practical cases of straight and curved foundations. The presented method can be applied to a wide range of problems, including the study of tanks, shells and complex foundation systems. The particular case of box girder distortion can also be studied through the beam on elastic foundation (BEF) analogy.

Seismic response of foundation-mat structure subjected to local uplift

  • El Abbas, Nadia;Khamlichi, Abdellatif;Bezzazi, Mohammed
    • Coupled systems mechanics
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    • v.5 no.4
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    • pp.285-304
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    • 2016
  • The effects of large rotations and p-delta on the dynamic response of a structure subjected to seismic loading and local uplift of its foundation were analyzed in this work. The structure was modeled by an equivalent flexible mat mounted on a rigid foundation that is supported either by a Winkler soil type or a rigid soil. The equations of motion of the system were derived by taking into account the equilibrium of the coupled foundation-mat system where the structure was idealized as a single-degree-of-freedom. The obtained nonlinear coupled system of ordinary differential equations was integrated by using an adequate numerical scheme. A parametric study was performed then in order to evaluate the maximum response of the system as function of the intensity of the earthquake, the slenderness of the structure, the ratio of the mass of the foundation to the mass of the structure. Three cases were considered: (i) local uplift of foundation under large rotation with the p-delta effect, (ii) local uplift of foundation under large rotation without including the p-delta effect, (iii) local uplift of foundation under small rotation. It was found that, in the considered ranges of parameters and for moderate earthquakes, assuming small rotation of foundation under seismic loading can yield more adverse structural response, while the p-delta effect has almost no effect.

Free Vibrations of Horizontally Curved Beams with Multiple Elastic Springs (여러 개의 스프링으로 탄성 지지된 수평 곡선보의 자유진동)

  • 이병구;진태기;최규문;이태은
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.11 no.5
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    • pp.101-107
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    • 2001
  • This paper deals with the free vibrations of horizontally curved beams with mu1tiple elastic springs. Taking into account the effects of rotatory Inertia and shear deformation. differential equations governing the free vibrations of such beams are derived, In which each e1astic spring is modeled as a discrete Winkler foundation with very short longitudinal length. Differential equations are solved numerically to calculate natural frequencies and mode shapes. In numerical examples, the circular, Parabolic. sinusoidal and elliptic curved beams are considered. The parametric studies are conducted and the lowest four frequency parameters are reported In tables and figures as the non-dimensional forms. Also the typical mode shapes are presented.

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