Free and forced vibrations of shear deformable functionally graded porous beams

Chen, Da; Yang, Jie; Kitipornchai, S.

doi:10.1016/j.ijmecsci.2016.01.025

Cited by 361 publications

(115 citation statements)

References 29 publications

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“…Chen et al [28] studied the elastic buckling and static bending problems of shear deformable FG porous beams within the frame of Timoshenko beam theory, considering two different non-uniform porosity distribution patterns and four types of boundary conditions. They [29] also employed the Lagrange equation method with Ritz trial functions in the space domain and Newmark-β method in the time domain to examine the free and forced vibrations of FG porous beams under various loading conditions.…”

Section: Introductionmentioning

confidence: 99%

“…A larger value of e 0 corresponds to lower elastic moduli and mass density due to the increased size and density of internal pores. It should be achieved since in this case, all material property values are reduced to zero.The typical mechanical property of an open-cell metal foam[1,28,29,37] expressed in Eq. (6) is used to determine the relationship between e 0 and e m in Eq (7)…”

mentioning

confidence: 99%

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Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core

Chen

Kitipornchai

Yang

2016

Thin-Walled Structures

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311

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a b s t r a c tThe nonlinear free vibration behavior of shear deformable sandwich porous beam is investigated in this paper within the context of Timoshenko beam theory. The proposed beam is composed of two face layers and a functionally graded porous core which contains internal pores following different porosity distributions. Two non-uniform functionally graded distributions are considered in this paper based on the equivalent beam mass, associated with a uniform distribution for purpose of comparison. The elastic moduli and mass density are assumed to vary along the thickness direction in terms of the coefficients of porosity and mass density, whose relationship is determined by employing the typical mechanical characteristic of an open-cell metal foam. The Ritz method and von Kármán type nonlinear strain-displacement relationships are applied to derive the equation system, which governs the nonlinear vibration behavior of sandwich porous beams under hinged or clamped end supports. A direct iterative algorithm is then used to solve the governing equation system to predict the linear and nonlinear frequencies which are presented by a detailed numerical study to discuss the effects of porosity coefficient, slenderness ratio, thickness ratio and to compare the varying porosity distributions and boundary conditions, providing a feasible way to improve the vibration behavior of sandwich porous beams.

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core

Chen

Kitipornchai

Yang

2016

Thin-Walled Structures

Self Cite

311

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“…It is well‐known that Young's elasticity and shear moduli are related to each other as

G = E / 2 (1 + ν)

. Also e 0 and

e_{m}

are the coefficients of porosity and mass density that are defined as:

e_{0} = 1 - \frac{E_{2}}{E_{1}},

e_{m} = 1 - \frac{ρ_{2}}{ρ_{1}}

The mechanical property of an open‐cell metal foam model is shown as:

\frac{E_{2}}{E_{1}} = {((), \frac{ρ_{2}}{ρ_{1}})}^{2}

Using the Equations , and the relationship between e 0 and

e_{m}

can be obtained as:

e_{m} = 1 - \sqrt{1 - e_{0}}

The variations of density in the thickness direction are shown in Figure .…”

Section: Materials Properties Of Sandwich Beammentioning

confidence: 99%

Size‐dependent free vibration of sandwich micro beam with porous core subjected to thermal load based on SSDBT

2019

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In this study, free vibration of the sandwich microbeam with porous core and FG carbon nanotubes reinforced composite face sheets which is rested on Winkler‐Pasternak substrate is investigated. It is assumed the beam is in thermal environment and is subjected to thermal load and the displacement components are described based on sinusoidal shear deformation beam theory. The small scale effects are taken into account according to the modified couple stress theory. The core and face sheets properties are diffused through the thickness. The motion equations are derived and solved using Hamilton's principle and Navier's method, respectively. Effect of different parameters such as porosity coefficient and distributions, different types of CNTs distribution, small scale and geometrical size of the beam is considered. The results show by enhancing the porosity, the frequency decreased. The findings of the current study can be used to design prominent role in modern engineering applications.

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“…Some researchers mainly focused on studying the properties [7] and design methods [8] of cross section of reinforced concrete structures, such as beams. And some other researchers mainly devoted themselves to studying the response [9][10][11][12][13][14] of the beams, consisting of different materials, under special load and their fatigue behavior [15], etc. In addition, some scholars have put forward some methods, based on the displacement monitoring, that can be good for obtaining the internal force of different engineering structures [16], and someone even proposed a new finite element model of beam [17].…”

Section: Introductionmentioning

confidence: 99%

An Improved Method for Calculating Bending Moment and Shearing Force of Beam in Numerical Modelling

Yuan

Wang

et al. 2018

Teh. vjesn.

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Abstract:In view of the problem that it is difficult to obtain the displacement, internal force and damage status from one beam model established in most numerical analysis models, an improved method for calculating bending moment and shearing force is presented in this paper, which can change this situation. This method portrays how to obtain the internal force from model established using 3-D solid element which can be able to show the failure process easily. The research results are as follows:(1) Deflection equation of beam established using 3-D solid element can be fitted by extracting displacement value of each node on the axis, thus bending moment and shearing force value can be directly figured out by putting the equation of deflection curve into approximately differential equation of deflection curve. (2) The reliability of the results calculated in this method would be easily affected by force, shape of cross section and the highest degree of polynomial, etc. When the beam is in a state of small deformation and the highest degree of polynomial is kept between 20 and 30, the results will be more reliable, besides, beam model whose shape of the cross section is rectangular is more suitable for the method than the circular one. (3) This method can always be applied to beam model, no matter its constraint conditions and loading conditions are complex or not.

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Free and forced vibrations of shear deformable functionally graded porous beams

Cited by 361 publications

References 29 publications

Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core

Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core

Size‐dependent free vibration of sandwich micro beam with porous core subjected to thermal load based on SSDBT

An Improved Method for Calculating Bending Moment and Shearing Force of Beam in Numerical Modelling

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