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Journal articles on the topic 'Winkler and Pasternak models'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

Muradova, Aliki D., and Georgios E. Stavroulakis. "Nonlinear Time Spectral Analysis for a Dynamic Contact Model with Buckling for an Elastic Plate." Key Engineering Materials 618 (July 2014): 227–39. http://dx.doi.org/10.4028/www.scientific.net/kem.618.227.

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In the present paper a dynamic nonlinear model with contact and buckling for an elasticplate is considered. The model consists of two coupled nonlinear hyperbolic type partial differentialequations. The plate is subjected to compressive and/or tensile moving loads on its edges. The foundationsare nonlinear elastic Winkler and Pasternak models. The initial-boundary value problems forthe model are solved with the use of the time spectral method for spatial discretization and after thediscretization the Newmark- time-stepping iterative scheme for the obtained system of nonlinear ordinarydifferent

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2

KOZEL, Anastasiya G. "COMPARISON OF SOLUTIONS TO THE BENDING PROBLEMS OF THREE-LAYER PLATES ON THE WINKLER AND PASTERNAK FOUNDATIONS." Mechanics of Machines, Mechanisms and Materials 1, no. 54 (2021): 30–37. http://dx.doi.org/10.46864/1995-0470-2021-1-54-30-37.

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Solutions of problems on axisymmetric bending of an elastic three-layer circular plate on the Winkler and Pasternak foundations are given. The bearing layers are taken as isotropic, for which Kirchhoff’s hypotheses are fulfilled. In a sufficiently thick lightweight, incompressible in thickness aggregate, the Timoshenko model is valid. The cylindrical coordinate system, in which the statements and solutions of boundary value problems are carried out, is connected with the median plane of the filler. On the plate contour, it is assumed that there is a rigid diaphragm that prevents the relative s

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3

Arani, Ali Ghorbanpour, Reza Kolahchi, Ali Akbar Mosallaie Barzoki, Mohammad Reza Mozdianfard, and S. Mosatafa Noudeh Farahani. "Elastic foundation effect on nonlinear thermo-vibration of embedded double-layered orthotropic graphene sheets using differential quadrature method." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 4 (2012): 862–79. http://dx.doi.org/10.1177/0954406212453808.

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In this article, transverse nonlinear vibration of orthotropic double-layered graphene sheets embedded in an elastic medium (spring and shear constants of the Winkler and Pasternak models) under thermal gradient is studied using nonlocal elasticity orthotropic plate theory. The equations of motion are derived based on application of Hamilton’s principles. These are coupled, two-dimensional and time-dependent equations, which cannot be solved analytically due to their nonlinear terms. Hence, differential quadrature method is employed to solve the governing differential equations for the two bou

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4

Ghannadiasl, Amin, and Hassan Rezaei Dolagh. "Vibration Response of Timoshenko Beam-Foundation Interaction Model under Accelerated Moving Load." Mathematical Problems in Engineering 2022 (August 17, 2022): 1–10. http://dx.doi.org/10.1155/2022/3979604.

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Simulation of an infinite Timoshenko beam subjected to accelerated moving load rested on the finite depth is assessed in this study. Then, the dynamic response of the infinite beam is illustrated on the various theoretical models, including the Winkler, Pasternak, and visco-elastic foundations. Furthermore, the effects of various damping, such as foundation damping, beam damping, and hysteretic damping (damping between soil grains), are also studied on the dynamic behavior of the beam. It has been worked out that the type of basement and its depth have a remarkable effect on the dynamic behavi

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5

Wani, Khair ul Faisal, and K. Nallasivam. "Static and free vibration analysis on rigid pavement resting on Winkler and Pasternak foundation." Structural Integrity and Life 24, no. 1 (2024): 49–60. http://dx.doi.org/10.69644/ivk-2024-01-0049.

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The main aim of this study is to find out the static and modal response of the rigid pavement resting on different soil models subjected to aircraft loading. The FEM employed in this work is validated by a closed-form numerical problem, which is in great accord with previous research findings with a maximum divergence of 1.76 %. Furthermore, it has been investigated how the static response and cyclic frequency change as a result of variations in the thickness and span length of pavement, the modulus of the subgrade, different boundary conditions, and element discretization. Limited previous re

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6

Veselý, Jakub, and Vít Šmilauer. "Hygro-mechanical model for concrete pavement with long-term drying analysis." Acta Polytechnica CTU Proceedings 40 (July 24, 2023): 104–10. http://dx.doi.org/10.14311/app.2023.40.0104.

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Concrete pavements are subjected to the combination of moisture transport, heat transport and traffic loading. A hygro-mechanical 3D finite element model was created in OOFEM software in order to analyse the stress field and deformed shape from a long-term non-uniform drying. The model uses a staggered approach, solving moisture transfer weakly coupled with MPS viscoelastic model for ageing concrete creep and shrinkage. Moisture transport and mechanical sub-models are calibrated with lab experiments, long-term monitoring on D1 highway and data from 40 year old highway pavement. The slab geomet

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Contreras, Juan, and Genner Villarreal Castro. "Interacción Suelo-Estructura de una edificación con losa de cimentación con los modelos estáticos de Winkler y Pasternak." Memoria Investigaciones en Ingeniería, no. 28 (July 22, 2025): 71–84. https://doi.org/10.36561/ing.28.7.

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Winkler y Pasternak establecieron que la interacción suelo estructura entre la base de una estructura y el suelo de cimentación, se puede idealizar como un conjunto de resortes de rigidez que se desplazan como resultado de la carga aplicada sobre su superficie (Ubani, 2022). El aporte de los modelos estáticos es la incorporación de las propiedades dinámicas del suelo mediante modelos de comportamiento elástico lineal del suelo, facilitando los procedimientos de cálculo en función a las propiedades mecánicas obtenidas del estrato del suelo de fundación. Mediante la incorporación de los coeficie

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8

Studziński, Robert. "Analytical Models of Axially Loaded Blind Rivets Used with Sandwich Beams." Energies 14, no. 3 (2021): 579. http://dx.doi.org/10.3390/en14030579.

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The paper presents the novel use of analytical models of a beam on an elastic foundation. The one-parameter model (Winkler model) and the two-parameter models (Filonenko-Borodich and Pasternak models) were investigated. These models were used to describe the elastic response of axially loaded blind rivets used with sandwich structures. The elastic response related to the elastic strain energy is mentioned in the paper as the resilience modulus of the connection. The databases from laboratory pull-out tests were used to verify these models. One type of blind rivet (aluminum, with three clamping

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9

Trien, Trang Tan, Le Thanh Phong, and Pham Tan Hung. "Isogeometric free vibration of the porous metal foam plates resting on an elastic foundation using a quasi-3D refined theory." Journal of Science and Technology in Civil Engineering (JSTCE) - HUCE 19, no. 1 (2025): 119–30. https://doi.org/10.31814/stce.huce2025-19(1)-10.

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This study investigates the free vibration behavior of porous metal foam plates using the Quasi-3D refined plate theory. We consider three types of pores across the plate thickness: uniform, symmetric, and asymmetric distributions. Besides, the metal foam plate is reinforced by a Winkler-Pasternak foundation. By employing the variational principle and Quasi-3D refined theory, we derive the weak form for free vibration analysis. The Quasi-3D theory is essential for analyzing plates, as it accurately captures transverse shear and normal deformations, which are vital for understanding the behavio

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10

Nemati, A. R., and M. J. Mahmoodabadi. "Effect of micromechanical models on stability of functionally graded conical panels resting on Winkler–Pasternak foundation in various thermal environments." Archive of Applied Mechanics 90, no. 5 (2019): 883–915. http://dx.doi.org/10.1007/s00419-019-01646-6.

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11

Sadeghian, Mostafa, Arvydas Palevicius, and Giedrius Janusas. "Nonlocal Strain Gradient Model for the Nonlinear Static Analysis of a Circular/Annular Nanoplate." Micromachines 14, no. 5 (2023): 1052. http://dx.doi.org/10.3390/mi14051052.

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A nonlinear static analysis of a circular/annular nanoplate on the Winkler–Pasternak elastic foundation based on the nonlocal strain gradient theory is presented in the paper. The governing equations of the graphene plate are derived using first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT) with nonlinear von Karman strains. The article analyses a bilayer circular/annular nanoplate on the Winkler–Pasternak elastic foundation. HSDT while providing a suitable distribution of shear stress along the thickness of the FSDT plate, eliminating the defects of th

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12

Kumar, Saurabh. "Natural Frequencies of Beams with Axial Material Gradation Resting on Two Parameter Elastic Foundation." Trends in Sciences 19, no. 6 (2022): 3048. http://dx.doi.org/10.48048/tis.2022.3048.

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Free vibration analysis is carried out on axially inhomogeneous beams resting on Winkler-Pasternak elastic foundation. The material properties of the beam like Young’s modulus, modulus of rigidity and material density are considered to be varying along the length direction following constant, linear and exponential material models. The beam is subjected to different combinations of clamped and simply supported boundary conditions. The formulation is based on Timoshenko beam theory and energy method along with Hamilton’s principle is used to derive the governing equations. The effect of materia

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13

Yudenko, Dmytro. "TUNNEL REACTION TO GROUND MOVEMENT USING A SIMPLIFIED MODEL." Geoengineering, no. 7 (December 5, 2022): 23–29. http://dx.doi.org/10.20535/2707-2096.7.2022.264271.

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Purpose: the analysis is performed by modal superposition of the response of a simplified model containing connected bending and shear beams supported by Winkler-type springs. Objective: to present a simplified model using coupled Bernoulli and shear beams supported by Winkler-type springs for the systematic identification of tunnels subject to earthquake-induced ground motions. A model formulation is introduced and closed-form solutions for the modal characteristic equation and mode shape are derived. Research methods: the formulation of the model is introduced and closed-form sol

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14

Mazur, Olga, and Jan Awrejcewicz. "Ritz Method in Vibration Analysis for Embedded Single-Layered Graphene Sheets Subjected to In-Plane Magnetic Field." Symmetry 12, no. 4 (2020): 515. http://dx.doi.org/10.3390/sym12040515.

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Vibrations of single-layered graphene sheets subjected to a longitudinal magnetic field are considered. The Winkler-type and Pasternak-type foundation models are employed to reproduce the surrounding elastic medium. The governing equation is based on the modified couple stress theory and Kirchhoff–Love hypotheses. The effect of the magnetic field is taken into account due to the Lorentz force deriving from Maxwell’s equations. The developed approach is based on applying the Ritz method. The proposed method is tested by a comparison with results from the existing literature. The numerical calcu

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15

Marinca, Bogdan, Nicolae Herisanu, and Vasile Marinca. "Study on Nonlinear Vibration of Carbon Nanotube-Reinforced Composite Beam Using Nonlocal Beam Theory in a Complex Environment." Applied Sciences 15, no. 12 (2025): 6494. https://doi.org/10.3390/app15126494.

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The present research analyzed the nonlinear vibration of a CNTRC embedded in a nonlinear Winkler–Pasternak foundation in the presence of an electromagnetic actuator and mechanical impact. A higher-order shear deformation beam theory was applied to various models, as well as Euler–Bernoulli, Timoshenko, Reddy, and other beams, using a unified NSGT. The governing equations were obtained based on the extended shear and normal strain component of the von Karman theory and a Hamilton principle. The system was discretized by means of the Galerkin–Bubnov procedure, and the OAFM was applied to solve a

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16

Wu, Chih-Ping, and Jyun-Yu Liou. "RMVT-Based Nonlocal Timoshenko Beam Theory for Stability Analysis of Embedded Single-Walled Carbon Nanotube with Various Boundary Conditions." International Journal of Structural Stability and Dynamics 16, no. 10 (2016): 1550068. http://dx.doi.org/10.1142/s0219455415500686.

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On the basis of Reissner’s mixed variational theorem (RMVT), a nonlocal Timoshenko beam theory (TBT) is developed for the stability analysis of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium, with various boundary conditions and under axial loads. Eringen’s nonlocal elasticity theory is used to account for the small length scale effect. The strong formulations of the RMVT-based nonlocal TBT and its associated possible boundary conditions are presented. The interaction between the SWCNT and its surrounding elastic medium is simulated using the Pasternak foundation models.

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17

Kaplunov, J., and A. Nobili. "The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation." Journal of Vibration and Control 23, no. 12 (2015): 2014–22. http://dx.doi.org/10.1177/1077546315606838.

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In this paper, the bending waves propagating along the edge of a semi-infinite Kirchhoff plate resting on a two-parameter Pasternak elastic foundation are studied. Two geometries of the foundation are considered: either it is infinite or it is semi-infinite with the edges of the plate and of the foundation coinciding. Dispersion relations along with phase and group velocity expressions are obtained. It is shown that the semi-infinite foundation setup exhibits a cut-off frequency which is the same as for a Winkler foundation. The phase velocity possesses a minimum which corresponds to the criti

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18

Gulnar, Mirzayeva, and Rzayeva Vusala. "ANALYSIS FREE OSCILLATIONS OF A NON-HOMOGENEOUS PIPE ALONG'S THICKNESS AND LENGTH, TAKING INTO ACCOUNT THE RESISTANCE OF THE EXTERNAL ENVIRONMENT." TECHNOLOGY AUDIT AND PRODUCTION RESERVES 1, no. 5(55) (2020): 24–27. https://doi.org/10.15587/2706-5448.2020.213475.

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<em>Structural elements made of heterogeneous natural and artificial materials are widely used in the construction of modern building complexes and in many other areas. Among them is the use of boards and shells of different configurations.</em><em> </em><em>Currently, one of the most important requirements for designers and accountants is to properly assess the mechanical properties of the material of the structural element and the impact of the environment in contact during operation. Taking these into account, the mathematical solution of the problem becomes difficult, and if not, seri

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19

Skar, Asmus, Assaf Klar, and Eyal Levenberg. "Load-Independent Characterization of Plate Foundation Support Using High-Resolution Distributed Fiber-Optic Sensing." Sensors 19, no. 16 (2019): 3518. http://dx.doi.org/10.3390/s19163518.

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The evaluation of soil reaction in geotechnical foundation systems such as concrete pavements, mat- and raft foundations is a challenging task, as the process involves both the selection of a representative mechanical model (e.g., Winkler, Continuum, Pasternak, etc.) and identify its prevailing parameters. Moreover, the support characteristics may change with time and environmental situation. This paper presents a new method for the characterization of plate foundation support using high-resolution fiber-optic distributed strain sensing. The approach involves tracking the location of distinct

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20

Gao, X. L., and G. Y. Zhang. "A non-classical Mindlin plate model incorporating microstructure, surface energy and foundation effects." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2191 (2016): 20160275. http://dx.doi.org/10.1098/rspa.2016.0275.

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A non-classical model for a Mindlin plate resting on an elastic foundation is developed in a general form using a modified couple stress theory, a surface elasticity theory and a two-parameter Winkler–Pasternak foundation model. It includes all five kinematic variables possible for a Mindlin plate. The equations of motion and the complete boundary conditions are obtained simultaneously through a variational formulation based on Hamilton's principle, and the microstructure, surface energy and foundation effects are treated in a unified manner. The newly developed model contains one material len

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21

Hasrati, E., R. Ansari, and H. Rouhi. "A numerical approach to the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 19-20 (2019): 7041–61. http://dx.doi.org/10.1177/0954406219867726.

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Presented herein is the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation under radial loading based on a variational numerical method named as variational differential quadrature. To accomplish this aim, a first-order shear deformable plate model is developed in the context of incremental theory of plasticity (IT) (with the Prandtl-Reuss constitutive equations) and the deformation theory of plasticity (DT) (with the Hencky constitutive equations). It is considered that the material of plates exhibits strain hardening characterized by t

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22

Ghorbanpour Arani, A., M. Mohammadimehr, A. R. Saidi, A. Arefmanesh, and Q. Han. "Pasternak effect on the buckling of embedded single-walled carbon nanotubes using non-local cylindrical shell theory." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 12 (2011): 3045–59. http://dx.doi.org/10.1177/0954406211409511.

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In this article, the buckling analysis of a single-walled carbon nanotube using the non-local cylindrical shell theory under general loading embedded on the Winkler- and Pasternak-type foundations is presented. The effect of the surrounding elastic medium such as the Winkler-type spring constant and the Pasternak-type shear constant is taken into account in the present formulations. The non-local and local critical buckling loads are obtained under general loading such as the axial compression, lateral pressure, and torsional loading, and it is concluded from the results that the non-local cri

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23

Amirian, B., R. Hosseini-Ara, and H. Moosavi. "Thermo-Mechanical Vibration of Short Carbon Nanotubes Embedded in Pasternak Foundation Based on Nonlocal Elasticity Theory." Shock and Vibration 20, no. 4 (2013): 821–32. http://dx.doi.org/10.1155/2013/281676.

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This study is concerned with the thermal vibration analysis of a short single-walled carbon nanotube embedded in an elastic medium based on nonlocal Timoshenko beam model. A Winkler- and Pasternak-type elastic foundation is employed to model the interaction of short carbon nanotubes and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, high temperature change, Winkler modulus parameter, Pasternak shear parameter, vibration mode and aspect ratio of short carbon nanotubes on the vibration frequency are analyzed and discussed. The present study show

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24

Salhi, Mohamed, Omar Safer, Mouloud Dahmane, et al. "Finite element method numerical modeling of the crack's impact on the free vibration of 2D functionally graded beams on the Pasternak-Winkler elastic foundation." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 2 (2024): e6562. http://dx.doi.org/10.54021/seesv5n2-087.

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The study's contribution is to examine, while taking into account pinned-pinned boundary conditions, the free vibration response of multi-cracks Euler-Bernoulli perfect FG beams structure on Pasternak-Winkler elastic foundations. The finite element approach is used to discretize the equations. The material properties are taken into account using a power-law form, and they differ in the thickness and width directions of the beam structure. The 2D FG beam's reduced cross section is used to calculate the stiffness of the cracked structure. On the other hand, the Pasternak-Winkler type foundation

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25

Huang, Xiaolin, Nengguo Wei, Chengzhe Wang, and Xuejing Zhang. "Nonlinear Free Vibration Analysis of Functionally Graded Porous Conical Shells Reinforced with Graphene Nanoplatelets." Strojniški vestnik - Journal of Mechanical Engineering 70, no. 3-4 (2024): 181–93. http://dx.doi.org/10.5545/sv-jme.2023.825.

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The nonlinear vibration analysis of functionally graded reinforced with graphene platelet (FG-GRC) porous truncated conical shells surrounded by the Winkler-Pasternak elastic foundation is presented in this paper. An improved model for evaluating the material properties of porous composites is proposed. Three types of porous distribution and three patterns of graphene nanoplatelets (GPLs) dispersion are estimated. Coupled with the effect of the Winkler-Pasternak elastic foundation, the nonlinear governing equations are developed by using the Hamilton principle. The Galerkin integrated techniqu

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26

Shah, Abdul Ghafar, Tahir Mahmood, Muhammad Nawaz Naeem, and Shahid Hussain Arshad. "Vibrational Study of Fluid-Filled Functionally Graded Cylindrical Shells Resting on Elastic Foundations." ISRN Mechanical Engineering 2011 (April 26, 2011): 1–13. http://dx.doi.org/10.5402/2011/892460.

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Vibrational characteristics of functionally graded cylindrical shells filled with fluid and placed on Winkler and Pasternak elastic foundations are investigated. Love's thin-shell theory is utilized for strain-displacement and curvature-displacement relationships. Shell dynamical equations are solved by using wave propagation approach. Natural frequencies for both empty and fluid-filled functionally graded cylindrical shells based on elastic foundations are determined for simply-supported boundary condition and compared to validate the present technique. Results obtained are in good agreement

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Pratap Singh, Piyush, Mohammad Sikandar Azam, and Vinayak Ranjan. "Vibration analysis of a thin functionally graded plate having an out of plane material inhomogeneity resting on Winkler–Pasternak foundation under different combinations of boundary conditions." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 8 (2018): 2636–62. http://dx.doi.org/10.1177/0954406218796040.

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In the present research article, classical plate theory has been adopted to analyze functionally graded material plate, having out of plane material inhomogeneity, resting on Winkler–Pasternak foundation under different combinations of boundary conditions. The material properties of the functionally graded material plate vary according to power law in the thickness direction. Rayleigh–Ritz method in conjugation with polynomial displacement functions has been used to develop a computationally efficient mathematical model to study free vibration characteristics of the plate. Convergence of frequ

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Kafkas, Uğur. "A COUPLED MCST-FEM INVESTIGATION OF SIZE-DEPENDENT BUCKLING OF PERFORATED NANOBEAMS ON WINKLER-PASTERNAK FOUNDATION." Konya Journal of Engineering Sciences 13, no. 2 (2025): 368–83. https://doi.org/10.36306/konjes.1587217.

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The buckling behavior of perforated nanobeams on elastic foundations has become increasingly important, mainly due to their widespread use in nanostructures and nanotechnology systems. This study investigates the buckling behavior of perforated nanobeams resting on Winkler-Pasternak elastic foundations using Modified Couple Stress Theory (MCST) and the Finite Element Method (FEM). The analysis examines the effects of various parameters, including foundation elasticity, MCST internal length scale, perforation properties, and beam length, on critical buckling loads. Results indicate that increas

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Ghorbanpour Arani, A., S. Amir, A. R. Shajari, M. R. Mozdianfard, Z. Khoddami Maraghi, and M. Mohammadimehr. "Electro-thermal non-local vibration analysis of embedded DWBNNTs." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226, no. 5 (2011): 1410–22. http://dx.doi.org/10.1177/0954406211422619.

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In this article, electro-thermal transverse vibration behaviour of double-walled boron nitride nanotubes embedded in a surrounded elastic medium is investigated using non-local piezoelasticity cylindrical shell theory. The effects of the elastic medium including Winkler spring and Pasternak shear constants and van der Waals interaction between inner and outer nanotubes are taken into account. The higher order governing equations of motion are derived based on Hamilton's principle. Effects of parameters such as Winkler spring constant, Pasternak shear constant, electric field, and temperature c

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Saadatnia, Zia, Hassan Askari, and Ebrahim Esmailzadeh. "Multi-frequency excitation of microbeams supported by Winkler and Pasternak foundations." Journal of Vibration and Control 24, no. 13 (2017): 2894–911. http://dx.doi.org/10.1177/1077546317695463.

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The multi-frequency excitation of a microbeam, resting on a nonlinear foundation, is investigated and the governing equation of motion of the microbeam system is developed. The viscoelastic-type foundation is considered by assuming nonlinear parameters for both Pasternak and Winkler coefficients. The well-known Galerkin approach is utilized to discretize the governing equation of motion and to obtain its nonlinear ordinary differential equations. The multiple time-scales method is employed to study the multi-frequency excitation of the microbeam. Furthermore, the resonant conditions due to the

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Veselý, Jakub, and Vít Šmilauer. "THERMO-MECHANICAL MODEL FOR CONCRETE PAVEMENT." Acta Polytechnica CTU Proceedings 30 (April 22, 2021): 121–25. http://dx.doi.org/10.14311/app.2021.30.0121.

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This paper describes a numerical thermo-mechanical model for concrete pavement, implemented in OOFEM software. The thermal part is a heat transfer problem with appropriate initial and boundary conditions (sun irradiation, radiation and convection), calibrated from experimental data. Heat release from cement hydration is also included, calibrated for commonly used cements to demonstrate the difference that can be achieved with the binder selection. The mechanical part of the problem is composed of a 3D elastic concrete slab, subsoil Winkler-Pasternak elements and 1D interface elements, allowing

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Parida, Smita, and Sukesh Chandra Mohanty. "Free Vibration and Buckling Analysis of Functionally Graded Plates Resting on Elastic Foundation Using Higher Order Theory." International Journal of Structural Stability and Dynamics 18, no. 04 (2018): 1850049. http://dx.doi.org/10.1142/s0219455418500499.

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This paper deals with the free vibration and buckling analysis of functionally graded material (FGM) plates, resting on the Winkler–Pasternak elastic foundation. The higher order shear deformation plate theory (HSPT) is adopted for the realistic variation of transverse displacement through the thickness, using the power law distribution to describe the variation of the material properties. Both the effects of shear deformation and rotary inertia are considered. In the present model, the plate is discretised into [Formula: see text] eight noded serendipity quadratic elements with seven nodal de

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Wang, Yan Qing, Yun Fei Liu, and T. H. Yang. "Nonlinear Thermo-Electro-Mechanical Vibration of Functionally Graded Piezoelectric Nanoshells on Winkler–Pasternak Foundations Via Nonlocal Donnell’s Nonlinear Shell Theory." International Journal of Structural Stability and Dynamics 19, no. 09 (2019): 1950100. http://dx.doi.org/10.1142/s0219455419501001.

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The thermo-electro-mechanical nonlinear vibration of circular cylindrical nanoshells on the Winkler–Pasternak foundation is investigated. The nanoshell is made of functionally graded piezoelectric material (FGPM), which is simulated by the nonlocal elasticity theory and Donnell’s nonlinear shell theory. The Hamilton’s principle is employed to derive the nonlinear governing equations and corresponding boundary conditions. Then, the Galerkin’s method is used to obtain the nonlinear Duffing equation, to which an approximate analytical solution is obtained by the multiple scales method. The result

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CİVALEK, ÖMER. "LARGE DEFLECTION STATIC AND DYNAMIC ANALYSIS OF THIN CIRCULAR PLATES RESTING ON TWO-PARAMETER ELASTIC FOUNDATION: HDQ/FD COUPLED METHODOLOGY APPROACHES." International Journal of Computational Methods 02, no. 02 (2005): 271–91. http://dx.doi.org/10.1142/s0219876205000478.

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An analysis of the geometrically nonlinear dynamics of thin circular plates on a two parameter elastic foundation is presented in this paper. The nonlinear partial differential equations obtained from von Karman's large deflection plate theory have been solved by using the harmonic differential quadrature method in the space domain and the finite difference numerical integration method in the time domain. Winkler-Pasternak foundation model is considered and the influence of stiffness of Winkler (K) and Pasternak (G) foundation on the geometrically nonlinear analysis of the circular plates has

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Kafkas, Uğur. "Size-Dependent Bending Response of Perforated Nanobeams on Winkler-Pasternak Foundation." International Journal of Engineering and Applied Sciences 17, no. 1 (2025): 1–16. https://doi.org/10.24107/ijeas.1590000.

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This study investigates the bending response of perforated nanobeams resting on Winkler-Pasternak elastic foundation (WPEF), using Eringen's theory of nonlocal elasticity (ENET). The analysis examines how various parameters affect the mechanical response of the nanobeam, including the nonlocal parameter, foundation parameters, filling ratio, and number of holes. Results indicate that an increase in the nonlocal parameter produces larger transverse displacements compared to classical beam theory, while the stiffness decreases due to nanoscale effects. The elastic foundation parameters significa

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Asanjarani, A., S. Satouri, A. Alizadeh, and MH Kargarnovin. "Free vibration analysis of 2D-FGM truncated conical shell resting on Winkler–Pasternak foundations based on FSDT." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 5 (2014): 818–39. http://dx.doi.org/10.1177/0954406214539472.

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Based on the first-order shear deformation theory, this paper focuses on the free vibration behavior of two-dimensional functionally graded material truncated conical shells resting on Winkler–Pasternak foundations. The materials are assumed to be isotropic and inhomogeneous in the length and thickness directions of truncated conical shell. The material properties of the truncated conical shell are varied in these directions according to power law functions. The derived governing equations are solved using differential quadrature method. Convergence of this method is checked and the fast rate

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A., Asanjarani, Satouri S., Alizadeh A., and H. Kargarnovin M. "Free vibration analysis of 2D-FGM truncated conical shell resting on Winkler–Pasternak foundations based on FSDT." Mechanical Engineering Science 229, no. 5 (2014): 818–39. https://doi.org/10.1177/0954406214539472.

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Based on the first-order shear deformation theory, this paper focuses on the free vibration behavior of two-dimensional functionally graded material truncated conical shells resting on Winkler–Pasternak foundations. The materials are assumed to be isotropic and inhomogeneous in the length and thickness directions of truncated conical shell. The material properties of the truncated conical shell are varied in these directions according to power law functions. The derived governing equations are solved using differential quadrature method. Convergence of this method is checked and the fast

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Uzodinma, Franklin, Onodagu P. Dinwoke, Aginam C. Henry, and Ubani U. Obinna. "General Solution of Thick Plates on Winkler-Pasternak Foundation Using Orthogonal Polynomial Displacement Functions." European Journal of Engineering Science and Technology 4, no. 4 (2021): 1–14. http://dx.doi.org/10.33422/ejest.v4i4.591.

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A solution for thick plates on Winkler-Pasternak foundation using characteristic orthogonal polynomials (COPs) displacement functions was presented in this study. A shear deformation function was developed from Soldatos’ (1992) trigonometric function and the Ritz energy approach was used to determine the total potential energy of the thick plate on elastic foundation. This method presents a simple and efficient method where only definite integration is required to obtain solutions. Results for non-dimensional in-plane and out-of-plane displacements for simply supported (SSSS) thick plates were

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Zenkour, AM, and AF Radwan. "Free vibration analysis of multilayered composite and soft core sandwich plates resting on Winkler–Pasternak foundations." Journal of Sandwich Structures & Materials 20, no. 2 (2016): 169–90. http://dx.doi.org/10.1177/1099636216644863.

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Free vibration of laminated composite and soft core sandwich plates resting on Winkler–Pasternak foundations using four-variable refined plate theory are presented. The theory accounts for the hyperbolic distribution of the transverse shear strains through the plate thickness, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Equations of motion are derived from the dynamic version of the principle of virtual work. Navier technique is employed to obtain the closed-form solutions of antisymmetric cross-ply, angle-ply, and so

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Wang, Xiancheng, Wei Li, Jianjun Yao, Zhenshuai Wan, Yu Fu, and Tang Sheng. "Free Vibration of Functionally Graded Sandwich Shallow Shells on Winkler and Pasternak Foundations with General Boundary Restraints." Mathematical Problems in Engineering 2019 (March 13, 2019): 1–19. http://dx.doi.org/10.1155/2019/7527148.

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In this investigation, an exact method based on the first-order shear deformation shallow shell theory (FSDSST) is performed for the free vibration of functionally graded sandwich shallow shells (FGSSS) on Winkler and Pasternak foundations with general boundary restraints. Vibration characteristics of the FGSSS have been obtained by the energy function represented in the orthogonal coordinates, in which the displacement and rotation components consisted of standard double Fourier cosine series and several closed-form supplementary functions are introduced to eliminate the potential jumps and b

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Oliveira Santos, Larissa, Fabio Carlos da Rocha, and Leslie Darien Pérez Fernández. "Static Analysis of Isotropic Beams Resting on Elastic Foundations of the Winkler-Pasternak Type." VETOR - Revista de Ciências Exatas e Engenharias 33, no. 1 (2023): 114–23. http://dx.doi.org/10.14295/vetor.v33i1.15133.

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Beams resting on elastic foundations are widely used in engineering projects, so analyzing their displacement fields is very important. The present work presents solutions for the deflection of isotropic beams resting on elastic foundations of the Winkler-Pasternak type. The proposed formulation is based on the Euler-Bernoulli beam theory, and the governing equations and the boundary conditions are derived from the principle of virtual work. The direct integration method can decouple the deflections from axial displacement and twists. The system of deflection equations decouples into two princ

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Seyfi, Ali, Amir Teimouri, Rossana Dimitri, and Francesco Tornabene. "Dispersion of Elastic Waves in Functionally Graded CNTs-Reinforced Composite Beams." Applied Sciences 12, no. 8 (2022): 3852. http://dx.doi.org/10.3390/app12083852.

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This work deals with the wave propagation analysis in functionally graded carbon nanotubes (CNTs)-reinforced composite beams lying on an elastic medium. Despite the large amount of experimental and theoretical studies in the literature on the mechanical behavior of composite structures strengthened with CNTs, limited attention has been paid to the effect of an axial graduation of the reinforcing phase on the mechanical response of CNTs-reinforced composite beams. In this paper, CNT fibers are graded across the beam length, according to a power-law function, which expresses a general variation

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Ebrahimi, Farzad, and Mohsen Daman. "Investigating Surface Effects on Thermomechanical Behavior of Embedded Circular Curved Nanosize Beams." Journal of Engineering 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/9848343.

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To investigate the surface effects on thermomechanical vibration and buckling of embedded circular curved nanosize beams, nonlocal elasticity model is used in combination with surface properties including surface elasticity, surface tension, and surface density for modeling the nanoscale effect. The governing equations are determined via the energy method. Analytically Navier method is utilized to solve the governing equations for simply supported nanobeam at both ends. Solving these equations enables us to estimate the natural frequency and critical buckling load for circular curved nanobeam

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Akhzary, Ali, and Ahmad Reza Khorshidvand. "A MIXED DQ-NEWMARK METHOD FOR DYNAMIC RESPONSE AND STRESS ANALYSIS OF POROUS FG RECTANGULAR PLATES UNDER MOVING LOAD." Special Topics & Reviews in Porous Media: An International Journal 14, no. 6 (2023): 27–51. http://dx.doi.org/10.1615/specialtopicsrevporousmedia.v14.i6.30.

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In this paper, the stress analysis and dynamic behavior of porous functionally graded rectangular plates under moving concentrated load when supported on the Winkler-Pasternak model of elastic foundations are considered. The mechanical properties of functionally graded plates, such as their elasticity modulus and density, are varied in accordance with the power law, while the constant Poisson's ratio is taken into consideration, and porosity is assumed to be classified into two categories: evenly and unevenly distributed. On the basis of first-order shear deformation theory and Hamilton's prin

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Fiedler, Josef, and Tomáš Koudelka. "Nonlinear Behaviour of Concrete Foundation Slab." Applied Mechanics and Materials 821 (January 2016): 495–502. http://dx.doi.org/10.4028/www.scientific.net/amm.821.495.

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A layered model is used for nonlinear analysis of a foundation concrete slab. Calculation is performed using interaction with elastic Winkler-Pasternak subsoil model and considering plastic yielding of slab layers. Two Drucker-Prager yield criterions define a nonlinear material model for concrete. Computation is done by the SIFEL solver using the Finite Element Method.

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Omar, Marouf, Bendahane Khaled, Sehoul Mohammed, and Bouguenina Otbi. "Analytical modeling contribution of the vibration dynamics of FGM plates placed on elastic foundations." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 3 (2024): e12589. https://doi.org/10.54021/seesv5n3-044.

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The present article uses the non-polynomial refined shear deformation theory (NP-RSDT) with four unknowns in order to determine the natural frequencies of functionally graded material (FGM) plates that are made with advanced materials without integrating a shear correction factor. These plates rest on elastic foundations. This study aims to analyze the effects of an elastic system, which is supposed to be represented by the two Pasternak and Winkler parameters on the dynamics of free vibrations of the FGM plates, while taking into account the fact that the Winkler springs have a variable modul

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Li, X. F., G. J. Tang, Z. B. Shen, and K. Y. Lee. "Vibration of nonclassical shear beams with Winkler-Pasternak-type restraint." Acta Mechanica 223, no. 5 (2012): 953–66. http://dx.doi.org/10.1007/s00707-011-0604-x.

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Bozyigit, Baran. "Transfer matrix formulation for dynamic response of Timoshenko beams resting on two-parameter elastic foundation subjected to moving load." Journal of Structural Engineering & Applied Mechanics 4, no. 2 (2021): 99–110. http://dx.doi.org/10.31462/jseam.2021.04099110.

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In this study, the dynamic response of beams resting on two-parameter elastic foundation subjected to moving load is investigated by using the transfer matrix method (TMM). The Timoshenko beam theory (TBT) which considers shear deformation and rotational inertia is used to model the beam. The two-parameter elastic foundation model is selected as Pasternak foundation that takes into account a shear layer at the end of linear springs of Winkler foundation. The TMM which uses the relation between analytically obtained state vectors of each end of the beam is applied to solve the free vibration pr

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Hu, Haibo, Lina Luo, Gang Lei, et al. "The Transverse Bearing Characteristics of the Pile Foundation in a Calcareous Sand Area." Materials 15, no. 17 (2022): 6176. http://dx.doi.org/10.3390/ma15176176.

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Reviewing literature revealed that the studies on the bearing characteristics of pile foundations mainly focuses on clay, ordinary sand, loess, saline soil, and other areas. However, few studies on the bearing characteristics of the pile foundation in calcareous sand were conducted. Besides, existing traditional studies ignored the variation of soil compression modulus with depth, and the effect of void ratio on the transverse bearing characteristics of the pile foundation in a calcareous sand area were not well understood. In response of these problems, this study conducted a theoretical inve

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Oveissi, Soheil, Davood Toghraie, S. Ali Eftekhari, and Ali J. Chamkha. "Instabilities of SWCNT conveying laminar, incompressible and viscous fluid flow." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 4 (2019): 1773–94. http://dx.doi.org/10.1108/hff-10-2018-0563.

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Purpose This study aims to study the transverse vibration and instabilities of the fluid-conveying single-walled carbon nanotubes (CNTs). To this purpose, the Euler–Bernoulli beam model is used. Also, the surface effects, small-size effects of the both fluid and structure and two different elastic mediums viscoelastic and Pasternak elastic are investigated. Design/methodology/approach To consider the nano-scale for the CNT, the strain-inertia gradient theory is used and to solve the governing equation of motion for the system, the Galerkin’s method is used. The effect of the flow velocity, asp

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