Effects Of Foundation Parameters Research Articles

EFG meshless-ANN approach for free vibration analysis of functionally graded material plates on elastic foundation in thermal environments

This study focuses on free vibration analysis of functionally graded material (FGM) plates supported by Winkler–Pasternak elastic foundation in thermal environment using element-free Galerkin (EFG) meshless method. Plate kinematics depend on first-order shear deformation theory. Uniform, linear, and nonlinear temperature variations through the thickness direction are considered, along with the temperature-dependent material properties. The numerical outcomes obtained from EFG method are compared with those available in the published literature to validate the proposed method’s accuracy. An artificial neural network (ANN) model that can easily predict the natural frequencies of the plate is constructed from the EFG method outcomes. Further, the effect of foundation parameters, power law index, thickness ratio, temperature variations, and different boundary conditions are investigated; results show that these significantly influence the vibration response of FGM plates supported by the elastic foundation. Increasing the temperature of FGM plates supported by the Winkler–Pasternack foundation causes a decrease in the dimensionless fundamental natural frequency, and the uniform temperature influence is greater than that of linear and nonlinear temperature variation. The proposed EFG-ANN prediction model saves approximately 98.80% computation time when predicting the natural frequency with an accuracy of approximately 98.76% compared to that by EFG meshless method alone.

Nonlinear buckling and post-buckling of imperfect FG porous sandwich cylindrical panels subjected to axial loading on elastic foundation

This paper deals with the nonlinear buckling and post-buckling of sandwich cylindrical panels with non-uniform porous core and functionally graded face sheets. The imperfect sandwich cylindrical panels are subjected to axial loading on elastic foundation. Based on the Donnell shell theory, with von Kármán geometrical nonlinearity, the governing equations are derived. The effects of elastic foundation, various panel geometrical characteristics, porosity parameters, and the thickness of the porous core are investigated. The effects of foundation parameters, porosity parameters, the thickness of the porous core, and material parameters are investigated.

Size-dependent nonlinear bending analysis of nonlocal magneto-electro-elastic laminated nanobeams resting on elastic foundation

Employing Reddy’s third-order shear deformation theory (RTSDT) and nonlocal elasticity theory, a nonlinear bending model of the nonlocal three-layer magneto-electro-elastic (MEE) laminated nanobeam resting on elastic foundation is established by considering von Karman’s geometrically nonlinear equations. Nonlinear higher order partial differential governing equations of MEE laminated nanobeams can be obtained employing Hamilton variational principle. The three-layered MEE laminated nanobeam is considered to have simply supported boundary condition in the present paper. Meanwhile, the electric and magnetic potential distributions in the laminated nanobeam are determined through Maxwell’s magnetic-electro equations and boundary conditions. The governing equations of laminated nanobeams are re-expressed in the dimensionless form by introducing the non-dimensional terms. Employing Galerkin method, the nonlinear higher order partial differential governing equations are simplified into lower order equations. Several cases are explored to indicate the effects of foundation parameters, nonlocal parameter, stacking sequence, external electric voltage and external magnetic potential on bending behaviors of MEE laminated nanobeams.

Dynamic behaviour of pavement on a two-parameter viscoelastic foundation subjected to loads moving with variable speeds

ABSTRACT The dynamic response of a multilayer finite plate resting on a two-parameter viscoelastic foundation to moving variable loads is obtained analytically/numerically. The governing differential equation of a multi-layer finite plate resting on a two-parameter viscoelastic foundation is derived firstly. Then, the dynamic response is derived analytically using mode superposition and Duhamel’s formula, followed by the solving of the numerical method. Next, the proposed solution is verified by comparing the degraded solution with both the field measurement data and the known theoretical results. Three different loading models are assessed to select the loading model that would provide insight into the effects of acceleration and deceleration. The effects of foundation parameters and vehicle parameters, especially the acceleration or deceleration and initial velocity of the moving load, on the dynamic response of the multilayer plate are compared through parametric studies. The numerical results suggest that acceleration and deceleration exert considerable effects on the dynamic response of the plate, and that the stiffness of pavement exposed to frequent acceleration and deceleration should be increased by at least 15% to counteract the effects of variable speed.

Analytical solution for nonlocal buckling characteristics of higher-order inhomogeneous nanosize beams embedded in elastic medium

In this paper, buckling characteristics of nonhomogeneous functionally graded (FG) nanobeams embedded on elastic foundations are investigated based on third order shear deformation (Reddy) without using shear correction factors. Third-order shear deformation beam theory accounts for shear deformation effects by a parabolic variation of all displacements through the thickness, and verifies the stress-free boundary conditions on the top and bottom surfaces of the FG nanobeam. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam in deformation, which acts in tension as well as in compression. The material properties of FG nanobeam are supposed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. Nonlocal equations of motion are derived through Hamilton's principle and they are solved applying analytical solution. Comparison between results of the present work and those available in literature shows the accuracy of this method. The obtained results are presented for the buckling analysis of the FG nanobeams such as the effects of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.

Analysis of wave propagation in orthotropic microtubules embedded within elastic medium by Pasternak model

Microtubules are embedded within elastic medium in living cells, where they perform a wide variety of functions; in cell motility and division, in organelle transport, and in cell organization. Waves propagate along microtubules in performing their physiological functions, so, wave propagation along microtubules has been the topic of research in the past decade. In the present article, the wave propagation in microtubules embedded in the elastic medium has been investigated on the basis of orthotropic-Pasternak model. We considered microtubules as orthotropic elastic shell and its surrounding elastic matrix as Pasternak foundation. We found that the flexural rigidity of microtubules has been increased with the stiffening of the elastic medium. Moreover, we observed that due to the mechanical coupling of microtubules with the elastic medium, their radial wave velocity has increased considerably as compared to other two wave velocities, i.e., longitudinal wave velocity and torsional wave velocity. The effect of foundation parameters H and G is more pronounced on radial wave velocity, to a lesser extent on torsional wave velocity and least even negligible on longitudinal wave velocity.

Semi-Analytic Solutions of Dynamic Response of Pavement Plate on the Elastic Foundation

The dynamic characteristics of the pavement plate on the elastic foundation were investigated. Based on semi-analytic element method and variational principle, the dynamic equations of the pavement plate on the elastic foundation were deduced. Through the analysis and calculation, dynamic response of pavement plate placed on the elastic foundation with vertical load was calculated by the semi-analytic element method. The deflection time histories curve of the plate under load on the elastic foundation was given. The effects of foundation parameters and the plate parameters are examined through numerical examples. The results show that the deflection of the pavement plate decrease with the increasing of thickness and elastic module of pavement plate, in the same time, the deflection of the plate is decreasing with the increase of the damping coefficient and elastic modules of foundation. Those parameters have significant effects on the deflection of the pavement plate.

Effect of Pasternak Foundation on Axisymmetric Vibration of Polar Orthotropic Annular Plates of Varying Thickness

Free axisymmetric vibrations of polar orthotropic annular plates of variable thickness resting on a Pasternak-type elastic foundation have been studied based on the classical plate theory. Hamilton’s energy principle has been used to derive the governing differential equation of motion. Frequency equations for an annular plate for two different combinations of edge conditions have been obtained employing Chebyshev collocation technique. Numerical results thus obtained have been presented in the form of tables and graphs. The effect of foundation parameter and thickness variation together with various plate parameters such as rigidity ratio, radius ratio, and taper parameter on natural frequencies has been investigated for the first three modes of vibration. Mode shapes for specified plates have been presented. A close agreement of results with those available in the literature shows the versatility of the present technique.

Moderately Large Deflection of Laminated Thin Rectangular Plates

Studies are made on the elastic behaviour of laminated rectangular thin plates under uniform distributed transverse load with moderately large deflection. The effects of foundation parameters, the material parameters, edge conditions, and the aspect ratio of the plate are examined. In all the cases considered, the nonlinear load parameter increases with the maximum deflection-to-thickness ratio. The influence of in-plane boundary conditions (movable and immovable edges) on the large deflections is significant. The nonlinear load parameter for any specified maximum deflection increases with the elastic foundation parameters.

Nonlinear Vibration Analysis of Thin Laminated Rectangular Plates on Elastic Foundations

Studies are made on the elastic behaviour of laminated rectangular thin plates with non-linear vibration. The effects of foundation parameters, the material parameters, edge conditions, and the aspect ratio of the plate are examined. In all the cases considered, the nonlinear frequency increases with the amplitude and a hardening type of non-linearity is noted. The influence of in-plane boundary conditions (movable and immovable edges) on non-linear frequency is significant. The non-linear frequency for any specified amplitude increases with the elastic foundation parameters.

Influence of Foundation Nonlinearity on Offshore Towers Response

The response of a fixed, offshore tower is greatly affected by the nonlinear behavior of the supporting piles. An analysis of the foundation piles response to transient dynamic loading that accounts for soil nonlinearity, discontinuity conditions at the pile-soil interface, and group effect is used to assemble the stiffness matrix of the foundation piles. A foundation stiffness matrix is added to the global structural stiffness matrix at the pertinent degrees of freedom (DOF). A model for the evaluation of wave forces on the tower members that takes into account the spatial incoherence effect on wave forces is used in the analysis. Hydrodynamic damping is evaluated, and the effect of the tower foundation behavior on it is assessed. Furthermore, the tower response to random wave forces is conducted, and the effect of foundation parameters on the tower response is examined. It was found that both the hydrodynamic damping and tower response to wave forces are greatly influenced by the foundation nonlinearity and by pile-soil-pile interaction.

A refined model for dynamic analysis of circular plates on elastic foundations

A two-parameter model is developed to represent the supporting foundation in analyzing the axially symmetric free vibrations of a finite circular plate resting on an elastic foundation of finite depth. In this analytical process, a rigorous theoretical basis is presented, using Hamilton's principle, for deriving the equations governing the interaction between the plate and the elastic foundation. Here, the decay rate of the foundation displacement components through the depth appears as a new parameter. This new parameter, normally taken as contant by other researchers, is shown to depend on other foundation parameters. The incoming waves in the horizontal direction are eliminated by considering the foundation to be infinite in the horizontal direction and a general solution is presented in terms of Bessel functions. The application of the model is illustrated by examples and the effect of foundation parameters on the natural frequencies and corresponding decay rates are studied for the first and second modes of vibrations.

Non-linear vibration of orthotropic thin rectangular plates on elastic foundations

This study deals with the large amplitude free vibrations of rectilinearly orthotropic thin rectangular plates resting on elastic foundations. The von Kármán-type of governing equations are employed. The displacements are assumed to be harmonic in time and are expanded space-wise in terms of polynomial basis functions which satisfy the boundary conditions exactly. The time co-ordinate is eliminated by the Kantorovich averaging method. The orthogonal point collocation method is used to obtain the discretised equations. The non-linear eigenvalue problem is solved by an iterative method. Numerical results are presented for the linear frequency of the fundamental mode and for the ratio of the non-linear frequency to the linear frequency. Plates with opposite edges clamped or simply supported with immovable in-plane conditions and resting on Winkler, Pasternak and non-linear Winkler foundations are considered. The effects of foundation parameters, material parameters, edge conditions and the aspect ratio on the non-linear vibration behaviour have been investigated.

Non-linear axisymmetric vibration of orthotropic thin circular plates on elastic foundations

This study deals with the large amplitude axisymmetric free vibrations of cylindrically orthotropic thin circular plates resting on elastic foundations. Geometric non-linearity due to moderately large deflections has been included. Movable and immovable simply supported plates and immovable clamped plates resting on Winkler, Pasternak and non-linear Winkler foundations have been considered. The von Kármán type governing equations have been employed. Harmonic vibrations are assumed and the time t is eliminated by the Kantorovich averaging method. An orthogonal point collocation method is used for spatial discretization. Numerical results are presented for the linear natural frequency of the first axisymmetric mode and for the ratio of the non-linear period to the linear period of natural vibration. The effects of foundation parameters, the orthotropic parameter and the edge conditions on the non-linear vibration behaviour have been investigated.