Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams

Akgöz, Bekir; Cívalek, Ömer

doi:10.1016/j.compositesb.2017.07.024

Cited by 153 publications

(40 citation statements)

References 108 publications

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“…In this comparison, the elastic modulus and density of the beam is variable through the beam length and the geometrical dimensions and material properties are

L = 1 normalm

b = 0.05 normalm

h = 0.02 normalm

E_{0} = 210 normalG normalp normala

ρ_{0} = 7,850 normalk normalg / m^{3},

and

ν = 0.3

. The comparison of non‐dimensional free vibration frequency parameters between present model and previous results is presented in Table and a good agreement is observed between them. As seen from Table , convergence to desired order of accuracy is achieved by taking N = 12.…”

Section: Resultssupporting

confidence: 54%

“…As previously mentioned, there is no work reported on the low velocity impact analysis of AFG CNT‐reinforced cantilever beam. For this reason, at first the comparison between the non‐dimensional free vibration frequency parameters of an AFG cantilever beam with available data are carried out to validate the mass and stiffness matrices of the Ritz method (Appendix). In this comparison, the elastic modulus and density of the beam is variable through the beam length and the geometrical dimensions and material properties are

L = 1 normalm

b = 0.05 normalm

h = 0.02 normalm

E_{0} = 210 normalG normalp normala

ρ_{0} = 7,850 normalk normalg / m^{3},

and

ν = 0.3

.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Low velocity impact analysis of an axially functionally graded carbon nanotube reinforced cantilever beam

Ranjbar

Feli

2017

Polymer Composites

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In this article, a new analytical model is presented for low velocity impact on an axially functionally graded (AFG) carbon nanotube (CNT) reinforced cantilever beam. In order to estimate the material properties of the composite media, the refined rule of mixtures approach containing the efficiency parameters is employed. Based on the third order shear deformation beam theory, the beam deformation is formulated and the contact force is obtained with the aid of the nonlinear Hertz contact law. To derive the equations of motion, energy method with combining the polynomial Ritz method and generalized Lagrange equations are employed. To validate the accuracy of the analytical model, the convergence and comparison studies are carried out with those are reported in the literature in the special cases and simulating the process with ABAQUS software. Afterward, the influences of CNTs distribution, CNTs volume fraction, impact position, impactor initial velocity, and beam geometrical parameters on the contact force and beam deflection at the impact position are studied in detail. POLYM. COMPOS., 39:E969–E983, 2018. © 2017 Society of Plastics Engineers

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“…In this comparison, the elastic modulus and density of the beam is variable through the beam length and the geometrical dimensions and material properties are

L = 1 normalm

b = 0.05 normalm

h = 0.02 normalm

E_{0} = 210 normalG normalp normala

ρ_{0} = 7,850 normalk normalg / m^{3},

and

ν = 0.3

Section: Resultssupporting

confidence: 54%

L = 1 normalm

b = 0.05 normalm

h = 0.02 normalm

E_{0} = 210 normalG normalp normala

ρ_{0} = 7,850 normalk normalg / m^{3},

and

ν = 0.3

.…”

Section: Resultsmentioning

confidence: 99%

Low velocity impact analysis of an axially functionally graded carbon nanotube reinforced cantilever beam

Ranjbar

Feli

2017

Polymer Composites

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“…Detailed formulation of discrete singular convolution and detail of application of this method to some solid and fluid mechanical problems are given by Wei . Vibration analysis of some mechanical components such as rods, plates, shells and beams are studied by discrete singular convolution . The method of discrete singular convolution (DSC) is an effective and simple approach for the numerical verification of singular convolutions, which occur commonly in mathematical physics and engineering .…”

Section: Discrete Singular Convolution (Dsc)mentioning

confidence: 99%

“…[56][57][58][59][60] Vibration analysis of some mechanical components such as rods, plates, shells and beams are studied by discrete singular convolution. [61][62][63][64][65][66][67][68][69][70][71][72][73][74] The method of discrete singular convolution (DSC) is an effective and simple approach for the numerical verification of singular convolutions, which occur commonly in mathematical physics and engineering. [75][76][77][78][79] The discrete singular convolution method has been extensively used in scientific computations in past 10 years.…”

Section: Discrete Singular Convolution (Dsc)mentioning

confidence: 99%

Vibration of functionally graded carbon nanotube reinforced quadrilateral plates using geometric transformation discrete singular convolution method

Cívalek

2019

Numerical Meth Engineering

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Summary Free vibration characteristics of thick skew plates reinforced by functionally graded carbon nanotubes (CNTs) reinforced composite are presented. Discrete singular convolution (DSC) method is used for the numerical solution of vibration problems via geometric mapping technique. Using the geometric transformation via a four‐node element, the straight‐sided quadrilateral physical domain is mapped into a square domain in the computational space. Then the method of discrete singular convolution with some singular kernels such as Regularized Shannon's delta (RSD) and Lagrange's delta kernels (LDK) have been used for spatial discretizing of the resulting governing equation of motion. Calculated results have been presented in order to show the effects of volume fraction of CNT, skew angles, CNT distribution types, plate aspect ratio and length‐to‐thickness ratio on the frequency of CNT reinforced skew plate. The current results are compared with the related results available in the literature and obtained by different methods. It is shown that reasonable accurate results are obtained for free vibration of nanocomposite plates with less computational effort for higher modes. Several test examples for different plate have been selected to demonstrate the convergence properties, accuracy, and simplicity in numerical implementation of DSC procedures. This approach has verified the accuracy and applicability of DSC method to the class of problem considered in this study. Furthermore, in the numerical examples in the scope of the study, the results obtained with DSC method using a coarser grid are more accurate than the values obtained by finite elements and differential quadrature (DQ) methods. It is also revealed that the method of discrete singular convolution is a promising and potential approach for computational mechanics of nonrectangular plates with nanocomposite reinforced.

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“…using MCST for Euler‐Bernoulli beam model, concerned the micro‐size effect which are laminated composite beams surrounded by hygrothermal environments. Akgöz and Civalek carried out vibration response of shear deformation and thermal of functionally graded (FG) thick composite microbeams. They used the MCST in FG micro size beams to show the influence of small scale parameter rise on the natural frequencies.…”

Section: Introductionmentioning

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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Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams

Cited by 153 publications

References 108 publications

Low velocity impact analysis of an axially functionally graded carbon nanotube reinforced cantilever beam

Low velocity impact analysis of an axially functionally graded carbon nanotube reinforced cantilever beam

Vibration of functionally graded carbon nanotube reinforced quadrilateral plates using geometric transformation discrete singular convolution method

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

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