Natural frequencies of rotating functionally graded cylindrical shells

Xiang, Song; Li, Guangchao; Zhang, Wei; Yang, Mingsui

doi:10.1007/s10483-012-1554-6

Cited by 20 publications

(5 citation statements)

References 15 publications

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“…natural frequencies (Hz) versus tube thickness-to-radius ratio h/R shows a good agreement with those results evaluated for the vibration of cylindrical shell. Behavior of these variation of natural frequencies versus tube thickness-to-radius ratios is similar to that is observed for vibrating cylindrical shells by Xiang et al (2012), who analyzed the natural frequency versus to thickness-to-radius ratios for these shells. Effect of these boundary conditions is seen moderately more pronounced for higher values of h/R ratio.…”

Section: Resultssupporting

confidence: 73%

Vibration analysis of single-walled carbon nanotubes using wave propagation approach

Hussain

2017

Mech. Sci.

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Abstract. In this paper, influence of boundary conditions on free vibrations of single-walled carbon nanotubes (SWCNTs) is examined. The Flügge's shell dynamical equations are utilized for governing vibrations for carbon nanotubes. The wave propagation approach (WPA) is engaged to determine vibration frequency equation in standard eigenvalue form. The axial modal dependence is measured by the complex exponential functions implicating the axial modal numbers. These numbers are associated with boundary conditions specified at edges of a carbon nanotube. Computer programming is performed to obtain solutions of vibration frequency equation. In our new investigation, the vibration frequency spectra are obtained and analyzed for various physical parameters e.g., length and thickness-to-radius ratio. A number of results are presented to influence of different boundary conditions on SWCNTs. They are shown graphically and have been compared with those available in the literature.

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Section: Resultssupporting

confidence: 73%

Vibration analysis of single-walled carbon nanotubes using wave propagation approach

Hussain

2017

Mech. Sci.

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“…In addition, some scholars have studied on the vibration frequency of other structures (Jia et al 2005;Adhikari 2006). Xiang et al (2012) calculated the natural frequency of rotating functionally graded cylindrical shells by Love's first approximation theory. Zhou et al (2012) analyzed the natural frequency of nonlinear transverse vibrations for pipes conveying fluid by multiple scale method.…”

Section: Introductionmentioning

confidence: 99%

Simulation on Vibration Characteristics of Fractured Rock

Yan

et al. 2015

Rock Mech Rock Eng

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Modal analysis theory of rock is proposed and the modeling of vibration characteristics of fractured rock is undertaken in this study. The modeling includes two aspects, namely, the natural frequency of rock with a single fracture and the crack expansion energy of rock with multiple fractures. Also, the results of numerical analysis are presented. Four main control parameters are considered, including the material properties, crack size, crack trend and the number of cracks. It is confirmed that the natural frequency of rock will be reduced by the cracks in it. The expansion energy of a single crack is inversely proportional to the number of such cracks in the rock. Namely, the more the similar cracks are, the less the energy required for a single crack expansion is and the smaller the excitation frequency needed for rock resonance is. The vibration characteristics of fractured rock are validated by numerical analysis. The natural frequency of rock increases with the increase of elastic modulus, and decreases with the increase of the angle, the length, the width and the number of cracks.

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“…The material properties of the nickel are E ni = 205.098 GPa, ν ni = 0.31, and ρ ni = 8 900 kg/m 3 . Tables 1 and 2 show comparisons of the natural frequencies of simplysupported FGM cylindrical shells with those of Loy et al [27], Jin et al [22], and Xiang et al [43]. The dimensions of the cylindrical shells are: radius (R) = 1 m, length to radius ratio (L/R) = 20, thickness to radius ratio (h/R) = 0.05 (results in Table 1), and h/R = 0.002 (results in Table 2).…”

Section: Validation Studiesmentioning

confidence: 99%

“…The circular cylinders have stainless steel on their outer surface and nickel on their inner surface. The results of [21,27,43] are based on the classical shell theory, while the results of [22,31] are based on the elasticity approach. As can be seen from Tables 1 to 3, the current results are in good agreement with the existing results of [22,27,31,43].…”

Section: Validation Studiesmentioning

confidence: 99%

Natural frequencies analysis of functionally graded circular cylindrical shells

Alshabatat

Zannon

2021

ACM

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In the present work, a study on natural frequencies of functionally graded materials (FGM) circular cylindrical shells is presented. TheFGM is considered to be a mixture of two materials. The volumetric fractions are considered to vary in the radial direction (i.e., through the thickness) in compliance with a conventional power-law distribution. The equivalent material properties are estimated based on the Voigt model. The analysis of the FGM cylindrical shells is performed using the third-order shear deformation shell theory and the principle of virtual displacements. Moreover, the third-order shear deformation shell theory coupled with Carrera’s unified formulation is applied for the derivation of the governing equations associated with the free vibration of circular cylindrical shells. The accuracy of this method is examined by comparing the obtained numerical results with other previously published results. Additionally, parametric studies are performed for FGM cylindrical shells with several boundary conditions in order to show the effect of several design variables on the natural frequencies such as the power-law exponent, the circumferential wave number, the length to radius ratio and the thickness to radius ratio.

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Natural frequencies of rotating functionally graded cylindrical shells

Cited by 20 publications

References 15 publications

Vibration analysis of single-walled carbon nanotubes using wave propagation approach

Vibration analysis of single-walled carbon nanotubes using wave propagation approach

Simulation on Vibration Characteristics of Fractured Rock

Natural frequencies analysis of functionally graded circular cylindrical shells

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