• Coupled systems mechanics
• /
• v.11 no.4
• /
• pp.357-371
• /
• 2022

This paper presents a parametric study on the free vibration analysis of a functionally graded material (FGM) circular plate with non-uniform thickness resting on a variable Pasternak elastic foundation. The mechanical properties of the material vary in the transverse direction through the thickness of the plate according to the power-law distribution to represent the constituent components. The equation of motion of the circular plate has been carried out based on the classical plate theory (CPT), and the differential quadrature method (DQM) is employed to solve the governing equations as a semi-analytical method. The grid points are chosen based on Chebyshev-Gauss-Lobatto distribution to achieve acceptable convergence and better accuracy. The influence of geometric parameters, variable elastic foundation, and functionally graded variation for clamped and simply supported boundary conditions on the first three natural frequencies are investigated. Comparisons of results with similar studies in the literature have been presented and two-dimensional mode shapes for particular plates have been plotted to illustrate the effect of variable thickness profile.

• Geomechanics and Engineering
• /
• v.33 no.3
• /
• pp.271-277
• /
• 2023

This article investigates the effect of viscoelastic foundations on the waves' dispersion in a beam made of ceramic-metal functionally graded material (FGM) with microstructural defects. The beam is considered to be shear deformable, and a simple three-unknown sinusoidal integral higher-order shear deformation beam theory is applied to represent the beam's displacement field. Novel to this study is the investigation of the impact of viscosity damping on imperfect FG beams, utilizing a few-unknowns theory. The stresses and strains are obtained using the two-dimensional elasticity relations of FGM, neglecting the normal strain in the beam's depth direction. The variational operation is employed to define the dispersion relations of the FGM beam. The influences of the material gradation exponent, the beam's thickness, the porosity, and visco-Pasternak foundation parameters are represented. Results showed that phase velocity was inversely proportional to the damping and porosity of the beams. Additionally, the foundation viscous damping had a stronger influence on wave velocity when porosity volume fractions were low.

• Structural Engineering and Mechanics
• /
• v.37 no.4
• /
• pp.367-383
• /
• 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.

• Structural Engineering and Mechanics
• /
• v.49 no.5
• /
• pp.661-672
• /
• 2014

Laminated Rectangular plates embedded in elastic foundations are used in many mechanical structures. This study presents an analytical approach for transverse bending analysis of an embedded symmetric laminated rectangular plate using Mindlin plate theory. The surrounding elastic medium is simulated using Pasternak foundation. Adopting the Mindlin plate theory, the governing equations are derived based on strain-displacement relation, energy method and Hamilton's principle. The exact analysis is performed for this case when all four ends are simply supported. The effects of the plate length, elastic medium and applied force on the plate transverse bending are shown. Results indicate that the maximum deflection of the laminated plate decreases when considering an elastic medium. In addition, the deflection of the laminated plate increases with increasing the plate width and length.

• Coupled systems mechanics
• /
• v.5 no.3
• /
• pp.255-267
• /
• 2016

To investigate the surface effects on vibration 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 nano scale effect. The governing equations are determined via the energy method. Analytically Navier method is utilized to solve the governing equations for simply supported at both ends. Solving these equations enables us to estimate the natural frequency for circular curved nanobeam including Winkler and Pasternak elastic foundations. The results determined are verified by comparing the results by available ones in literature. The effects of various parameters such as nonlocal parameter, surface properties, Winkler and Pasternak elastic foundations and opening angle of circular curved nanobeam on the natural frequency are successfully studied. The results reveal that the natural frequency of circular curved nanobeam is significantly influenced by these effects.

• Computers and Concrete
• /
• v.19 no.6
• /
• pp.677-687
• /
• 2017

The nonlinear buckling response of nano composite anti-symmetric functionally graded polymeric microplate reinforced by single-walled carbon nanotubes (SWCNTs) rested on orthotropic elastomeric foundation with temperature dependent properties is investigated. For the carbon-nanotube reinforced composite (CNTRC) microplate, a uniform distribution (UD) and four types of functionally graded (FG) distribution are considered. Based on orthotropic Mindlin plate theory, von Karman geometric nonlinearity and Hamilton's principle, the governing equations are derived. Generalized differential quadrature method (GDQM) is employed to calculate the non-linear buckling response of the plate. Effects of FG distribution type, elastomeric foundation, aspect ratio (thickness to width ratio), boundary condition, orientation of foundation orthotropy and temperature are considered. The results are validated. It is found that the critical buckling load without elastic medium is significantly lower than considering Winkler and Pasternak medium.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.22 no.8
• /
• pp.763-770
• /
• 2012

The free vibration characteristics of fluid-filled cylindrical shells on partial elastic foundations are investigated by an analytical method. The cylindrical shell is fully or partially surrounded by the elastic foundations, these are represented by the Winkler or Pasternak model. The motion of shell is represented by the first order shear deformation theory to account for rotary inertia and transverse shear strains. The steady flow of fluid is described by the classical potential flow theory. The fluid-structure interaction is considered in the analysis. The effect of internal fluid can be considered by imposing a relation between the fluid pressure and the radial displacement of the structure at the interface. To validate the present method, the numerical example is presented and compared with the available existing results.

• Smart Structures and Systems
• /
• v.19 no.6
• /
• pp.695-703
• /
• 2017

In this paper, based on first-order shear deformation theory, the governing equations of motion for a sandwich curved beam including an elastic core and two piezo-magnetic face-sheets are presented. The curved beam model is resting on Pasternak's foundation and subjected to applied electric and magnetic potentials on the piezo-magnetic face-sheets and transverse loading. The five equations of motion are analytically solved and the bending and vibration results are obtained. The influence of important parameters of the model such as direct and shear parameters of foundation and applied electric and magnetic potentials are studied on the electro-mechanical responses of the problem. A comparison with literatures was performed to validate our formulation and results.

• Smart Structures and Systems
• /
• v.21 no.1
• /
• pp.113-122
• /
• 2018

In this article, an exact analytical solution for mechanical buckling analysis of magnetoelectroelastic plate resting on pasternak foundation is investigated based on the third-order shear deformation plate theory. The in-plane electric and magnetic fields can be ignored for plates. According to Maxwell equation and magnetoelectric boundary condition, the variation of electric and magnetic potentials along the thickness direction of the plate is determined. The von Karman model is exploited to capture the effect of nonlinearity. Navier's approach has been used to solve the governing equations for all edges simply supported boundary conditions. Numerical results reveal the effects of (i) lateral load, (ii) electric load, (iii) magnetic load and (iv) higher order shear deformation theory on the critical buckling load have been investigated. These results must be the analysis of intelligent structures constructed from magnetoelectroelastic materials.

• Structural Engineering and Mechanics
• /
• v.4 no.2
• /
• pp.149-162
• /
• 1996

A postbuckling analysis is presented for a simply supported, moderately thick rectangular plate subjected to combined axial compression and uniform temperature loading and resting on a two-parameter elastic foundation. The two cases of thermal postbuckling of initially compressed plates and of compressive postbuckling of initially heated plates are considered. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the first order shear deformation effect, and including the plate-foundation interaction and thermal effect. The analysis uses a deflection-type perturbation technique to determine the buckling loads and postbuckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, moderately thick plates resting on Winkler or Pasternak-type elastic foundations. Typical results are presented in dimensionless graphical form.