An exact solution to the problems of flexo-poro-elastic structures rested on elastic beds acted upon by moving loads

Nikkhoo, Ali; Tafakor, Reza; Mofid, Massood

doi:10.24200/sci.2019.51365.2135

“…In the current section, the DQM is employed as a well-accepted and well-known numerical approach to provide an approximate solution for the set of the governing equations (28) with any combination of the boundary conditions (29) at both ends of the shell (x=0,L). Based on the main idea in the DQM, each derivative of a function like P(x) can be estimated in terms of the weighted sum of its values at a set of grid points as below:…”

Section: Solution Methodologymentioning

confidence: 99%

“…( 24) into Eq. ( 25) and employing the following solution: (28) where prime indicates derivative with respect to the spatial variable x. Likewise, by substituting Eq.…”

Section: Governing Equationsmentioning

confidence: 99%

“…They studied the dependency of the thermoelastic characteristics of such beams on the pore fluid. An exact solution was presented by Nikkhoo et al [28] for the dynamic response of flexo-poro-elastic structures subjected to moving loads. The influences of the porosity parameter, viscosity of the pore fluid, the velocity of the moving loads, and stiffness of the foundation on the dynamic response of the beam were examined by them.…”

mentioning

confidence: 99%

See 1 more Smart Citation

The Vibration Study of A Sandwich Conical Shell With A Saturated FGP Core

Esfahani

¹

,

Hashemian

²

,

Aghadavoudi

³

2021

Preprint

0

View full text Add to dashboard Cite

This paper is provided to analyze the free vibration of a sandwich truncated conical shell with a saturated functionally graded porous (FGP) core and two same homogenous isotropic face sheets. The mechanical behavior of the saturated FGP is assumed based on Biot’s theory, the shell is modeled via the first-order shear deformation theory (FSDT), and the governing equations and boundary conditions are derived utilizing Hamilton’s principle. Three different porosity distribution patterns are studied including one homogenous uniform distribution pattern and two non-homogenous symmetric ones. The porosity parameters in mentioned distribution patterns are regulated to make them the same in the shell’s mass. The equations of motion are solved exactly in the circumferential direction via proper sinusoidal and cosinusoidal functions, and a numerical solution is provided in the meridional direction utilizing the differential quadrature method (DQM). The precision of the model is approved and the influences of several parameters such as circumferential wave number, the thickness of the FGP core, porosity parameter, porosity distribution pattern, the compressibility of the pore fluid, and boundary conditions on the shell’s natural frequencies are investigated. It is shown that the highest natural frequencies usually can be achieved when the larger pores are located close to the shell’s middle surface and in each vibrational mode, there is a special value of the porosity parameter which leads to the lowest natural frequencies. It is deduced that in most cases, natural frequencies decrease by increasing the thickness of the FGP core. In addition, reducing the compressibility of the porefluid a small growth in the natural frequencies can be seen.

show abstract

“…Rofooei et al [24] collated the Von Karman and Kirchhoff plate theory to explore the deflection of rectangular plates subjected to a moving mass. In another research attempt, Nikkhoo et al [25], explored the excitations of flexo poro elastic structures resting on the elastic foundations subjected to the moving loads. In another study, Nikkhoo et al [26], evaluated effects of the moving mass' weights, velocities, plates' aspect ratios, inclined crack angles, and crack lengths.…”

Section: Introductionmentioning

confidence: 99%

On non-stationary response of cracked thin rectangular plates acted upon by a moving random force

Nikkhoo

¹

,

Banihashemi

²

,

Kiani

³

2023

View full text Add to dashboard Cite

This paper is aimed to examine the dynamics of cracked thin rectangular plates subjected to a moving non-stationary random load. A random load is considered with a constant mean value, a constant moving velocity, and five different covariance patterns namely the white noise, constant, exponential, cosine wave, and exponential cosine covariance. Accordingly, an intact plate's orthogonal polynomials in combination with the well-known corner functions are employed to explore the mechanical behavior of the cracked plate. As the non-dimensional deflection values, the functions of the squared mean values are obtained for the damped and undamped cracked plates at different points. Then an inclusive parametric study is performed to explore effects of the inclined crack angles and the crack lengths on the non-dimensional functions of squared mean values at middle point of the undamped and damped cracked plates. Based on the obtained results, there are non-monotonous nonlinear relations between increasing the incline crack angles as well as the crack lengths and the non-dimensional functions of squared mean values. Furthermore, it is found that in the exponential covariance cases, the effects of increasing crack angles and lengths on the non-dimensional squared mean values are profounder than the other four patterned covariance cases.

show abstract

“…They studied the dependency of the thermoelastic characteristics of such beams on the pore fluid. An exact solution was presented by Nikkhoo et al 27 for the dynamic response of flexo-poro-elastic structures subjected to moving loads. The influences of the porosity parameter, viscosity of the pore fluid, the velocity of the moving loads, and stiffness of the foundation on the dynamic response of the beam were examined by them.…”

Section: Introductionmentioning

confidence: 99%

The vibration study of a sandwich conical shell with a saturated FGP core

Esfahani

¹

,

Hashemian

²

,

Aghadavoudi

³

2022

Sci Rep

View full text Add to dashboard Cite

This paper is provided to analyze the free vibration of a sandwich truncated conical shell with a saturated functionally graded porous (FGP) core and two same homogenous isotropic face sheets. The mechanical behavior of the saturated FGP is assumed based on Biot’s theory, the shell is modeled via the first-order shear deformation theory (FSDT), and the governing equations and boundary conditions are derived utilizing Hamilton’s principle. Three different porosity distribution patterns are studied including one homogenous uniform distribution pattern and two non-homogenous symmetric ones. The porosity parameters in mentioned distribution patterns are regulated to make them the same in the shell’s mass. The equations of motion are solved exactly in the circumferential direction via proper sinusoidal and cosinusoidal functions, and a numerical solution is provided in the meridional direction utilizing the differential quadrature method (DQM). The precision of the model is approved and the influences of several parameters such as circumferential wave number, the thickness of the FGP core, porosity parameter, porosity distribution pattern, the compressibility of the pore fluid, and boundary conditions on the shell’s natural frequencies are investigated. It is shown that the highest natural frequencies usually can be achieved when the larger pores are located close to the shell’s middle surface and in each vibrational mode, there is a special value of the porosity parameter which leads to the lowest natural frequencies. It is deduced that in most cases, natural frequencies decrease by increasing the thickness of the FGP core. In addition, reducing the compressibility of the porefluid a small growth in the natural frequencies can be seen.

show abstract

An exact solution to the problems of flexo-poro-elastic structures rested on elastic beds acted upon by moving loads

Cited by 4 publications

References 74 publications

The Vibration Study of A Sandwich Conical Shell With A Saturated FGP Core

The Vibration Study of A Sandwich Conical Shell With A Saturated FGP Core

On non-stationary response of cracked thin rectangular plates acted upon by a moving random force

The vibration study of a sandwich conical shell with a saturated FGP core

Contact Info

Product

Resources

About