• Geomechanics and Engineering
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• v.28 no.1
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• pp.49-64
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• 2022

In this work, the bending and dynamic behaviors of advanced composite plates resting on variable visco-Pasternak foundations are studied using a simple shear deformation integral plate model. The research is carried out with a view to a three-parameter foundation including the influences of the variable Winkler coefficient, the constant Pasternak coefficient and the damping coefficient of the elastic medium. The present theory uses a displacement field with integral terms instead of derivative terms by including also the shear deformation effect without introducing the shear correction factors. The equations of motion for advanced composite plates are obtained using the Hamilton principle. Analytical solutions for the bending and dynamic analysis are deduced for simply supported plates resting on variable visco-Pasternak foundations. Some numerical results are presented to demonstrate the impact of material index, elastic foundation type, and damping coefficient of the foundation, on the bending and dynamic responses of advanced composite plates.

• Structural Engineering and Mechanics
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• v.85 no.4
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• pp.433-443
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• 2023

The current paper discusses the dynamic and stability responses of cross-ply composite laminated plates by employing a refined quasi-3D trigonometric shear deformation theory. The proposed theory takes into consideration shear deformation and thickness stretching by a trigonometric variation of in-plane and transverse displacements through the plate thickness and assures the vanished shear stresses conditions on the upper and lower surfaces of the plate. The strong point of the new formulation is that the displacements field contains only 4 unknowns, which is less than the other shear deformation theories. In addition, the present model considers the thickness extension effects (ε_z≠0). The presence of the Winkler-Pasternak elastic base is included in the mathematical formulation. The Hamilton's principle is utilized in order to derive the four differentials' equations of motion, which are solved via Navier's technique of simply supported structures. The accuracy of the present 3-D theory is demonstrated by comparing fundamental frequencies and critical buckling loads numerical results with those provided using other models available in the open literature.

• Earthquakes and Structures
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• v.14 no.2
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• pp.117-128
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• 2018

In this research work, free vibrations of simply supported functionally graded plate resting on a Winkler-Pasternak elastic foundation are investigated by a new shear deformation theory. The influence of alternative micromechanical models on the macroscopic behavior of a functionally graded plate based on shear-deformation plate theories is examined. Several micromechanical models are tested to obtain the effective material properties of a two-phase particle composite as a function of the volume fraction of particles which continuously varies through the thickness of a functionally graded plate. Present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. The energy functional of the system is obtained using Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. Finally, the numerical results are provided to reveal the effect of explicit micromechanical models on natural fundamental frequencies.

• Advances in nano research
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• v.17 no.3
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• pp.221-234
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• 2024

In this paper, dynamic response of annular nanoplates in improving sports equipment with surface effect embedded by visco Pasternak fractional foundation is studied. Size effects are evaluated by modified couple stress theory (MCST) and the surface effects are considered by the Gurtin-Murdoch theory. The structural damping effect is considered in this research using Kelvin-Voigt model. Sinusoidal shear deformation theory (SSDT) is applied for mathematical modelling of the nanostructure system. The numerical procedure of differential quadrature (DQ) is presented to determine the dynamic deflection as well as dynamic response of the annular nanoplates. The numerical results dynamic deflection of the nanostructure is considering, including material length scale parameter, spring and damper constants of visco-pasternak fractional foundation, geometrical parameters of annular nanoplates, surface stress effects.

• Structural Engineering and Mechanics
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• v.83 no.6
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• pp.757-770
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• 2022

In this paper, the vibration of a moderately thick plate to a moving mass is investigated. Pasternak foundation with a variable subgrade modulus is considered to tackle the shortcomings of Winkler model, and an analytical-numerical solution is proposed based on the eigenfunction expansion method. Parametric studies by using both CPT (Classical Plate Theory) and FSDT (First-Order Shear Deformation Plate Theory) are carried out, and, the differences between them are also highlighted. The obtained results reveal that utilizing FSDT without considering the rotary inertia leads to a smaller deflection in comparison with CPT pertaining to a thin plate, while it demonstrates a greater response for plates of higher thicknesses. Moreover, it is shown that CPT is unable to properly capture the variation of the plate thickness, thereby diminishing the accuracy as the thickness increases. The outcomes also indicate that the presence of a foundation contributes more to the dynamic response of thin plates in comparison to moderately thick plates. Furthermore, the findings suggest that the performance of the moving force approach for a moderately thick plate, in contrast to a thin plate, appears to be acceptable and it even provides a much better estimation in the presence of a foundation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.706-711
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• 2000

This paper deals with the free vibrations of horizontally curved beams on an elastic foundation. Taking into account the effects of rotatory inertia and shear deformation, the differential equations governing free vibrations of noncircular curved beams resting on Pasternak-type foundations are derived and solved numerically. The lowest three natural frequencies for parabolic curved beams with hinged-hinged and clamped-clamped end restraints are calculated. Numerical results are presented to show the effects on the natural frequencies of the non-dimensional system parameters: the horizontal rise to span length ratio, the Winkler foundation parameter, the shear foundation parameter, and the width ratio of contact area between the beam and foundation.

• Geomechanics and Engineering
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• v.32 no.2
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• pp.159-177
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• 2023

In the present work, a simple and refined shear deformation theory is used to analyze the effect of visco-elastic foundation on the buckling response of exponentially-gradient sandwich plates under various boundary conditions. The proposed theory includes indeterminate integral variables kinematic with only four generalized parameters, in which no shear correction factor is used. The visco-Pasternak's foundation is taken into account by adding the influence of damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's foundation modulus. The four governing equations for FGM sandwich plates are derived by employing principle of virtual work. To solve the buckling problem, Galerkin's approach is utilized for FGM sandwich plates for various boundary conditions. The analytical solutions for critical buckling loads of several types of powerly graded sandwich plates resting on visco-Pasternak foundations under various boundary conditions are presented. Some numerical results are presented to indicate the effects of inhomogeneity parameter, elastic foundation type, and damping coefficient of the foundation, on the critical buckling loads.

• Structural Engineering and Mechanics
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• v.69 no.4
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• pp.439-455
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• 2019

This research deals with thermo-electro-mechanical buckling analysis of the sandwich nano-beams with face-sheets made of functionally graded carbon nano-tubes reinforcement composite (FG-CNTRC) based on the nonlocal strain gradient elasticity theory (NSGET) considering various higher-order shear deformation beam theories (HSDBT). The sandwich nano-beam with FG-CNTRC face-sheets is subjected to thermal and electrical loads while is resting on Pasternak's foundation. It is assumed that the material properties of the face-sheets change continuously along the thickness direction according to different patterns for CNTs distribution. In order to include coupling of strain and electrical field in equation of motion, the nonlocal non-classical nano-beam model contains piezoelectric effect. The governing equations of motion are derived using Hamilton principle based on HSDBTs and NSGET. The differential quadrature method (DQM) is used to calculate the mechanical buckling loads of sandwich nano-beam as well as critical voltage and temperature rising. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various HSDBTs, length scale parameter (strain gradient parameter), the nonlocal parameter, the CNTs volume fraction, Pasternak's foundation coefficients, various boundary conditions, the CNTs efficiency parameter and geometric dimensions on the buckling behaviors of FG sandwich nano-beam. The numerical results indicate that, the amounts of the mechanical critical load calculated by PSDBT and TSDBT approximately have same values as well as ESDBT and ASDBT. Also, it is worthy noted that buckling load calculated by aforementioned theories is nearly smaller than buckling load estimated by FSDBT. Also, similar aforementioned structure is used to building the nano/micro oscillators.

• Steel and Composite Structures
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• v.30 no.1
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• pp.13-29
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• 2019

This work presents the buckling investigation of functionally graded plates resting on two parameter elastic foundations by using a new hyperbolic plate theory. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only four unknowns and which is even less than the first order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT) by introducing undetermined integral terms, hence it is unnecessary to use shear correction factors. The governing equations are derived using Hamilton's principle and solved using Navier's steps. The validation of the proposed theoretical model is performed to demonstrate the efficacy of the model. The effects of various parameters like the Winkler and Pasternak modulus coefficients, inhomogeneity parameter, aspect ratio and thickness ratio on the behaviour of the functionally graded plates are studied. It can be concluded that the present theory is not only accurate but also simple in predicting the critical buckling loads of functionally graded plates on elastic foundation.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.9
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• pp.835-846
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• 2007

This paper deals with the flexural free vibrations of circular strip foundation with the variable breadth on Pasternak soil. The breadth of strip varies with the linear functional fashion, which is symmetric about the mid-arc. Differential equations governing flexural free vibrations of such strip foundation are derived, in which the elastic soil with the shear layer, i.e. Pasternak soil, is considered. Effects of the rotatory and shear deformation are included in the governing equations. Differential equations are numerically solved to calculate the natural frequencies and mode shapes. In the numerical examples, the hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. Four lowest frequency parameters accompanied with their corresponding mode shapes are reported and parametric studies between frequency parameters and various system parameters are investigated.