On the solution of nonlinear vibration of truncated conical shells covered by functionally graded coatings

Abstract:The influence of hard coating on vibration characteristics of fiber-reinforced composite thin shell (FCTS) is investigated theoretically. The theoretical model of the hard coating FCTS is firstly established by using the classical laminated shell theory, Love's first approximation theory, Rayleigh-Ritz method, and strain energy method. The values of the natural frequency, modal shape, resonant response, and modal loss factor of the hard-coating shell are obtained, and the corresponding analysis procedure is also summarized. The verification of such a theoretical method is performed by a case study, and the analysis results show a good agreement between the presented method and finite element method. The main findings from this study include: (I) The natural frequencies of FCTS with hard coating firstly decrease and then increase with the increase of elastic modulus and loss factor of hard coating, and they also show an increasing tendency when the thickness of hard coating rises; (II) Increasing the values of elastic modulus, loss factor, and thickness of hard coating can help to reduce the vibration response of FCTS. However, with the increase of modal order of the composite shell, the reduction rates of resonant responses and the increased levels of modal loss factor will decrease.

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“…By substituting Equations (18) and (19) into Equation (17) the total strain energy U can be written as…”

Section: The Theoretical Model Of the Hard Coating Fctsmentioning

confidence: 99%

Theoretical Study on the Influence of Hard Coating on Vibration Characteristics of Fiber-Reinforced Composite Thin Shell

Zhou

Sun

et al. 2018

Coatings

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“…And we chose = V = = = 10 7 to simulate actual constraint boundary condition in Figure 3. Then, substituting displacement equation (16) into strain energy equation 12, kinetic energy equation 13, and elastic potential energy equation 14, we can get…”

Section: Vibration Characteristic Analysis Of Tcs With Hardmentioning

confidence: 99%

“…Transfer matrix method is used to calculate the high order modes and the moving wave characteristics of the shell, and it was observed that high order vibration characteristics of rotating thin shells and hard coating damping material had a more obvious effect on the natural frequency at the high vibration order. Najafov et al [16] investigated linear and nonlinear vibrations of a truncated conical shell covered with functionally graded coatings, and parametric studies are performed to illustrate the effect of different values of thickness and coating material on the frequency-amplitude relations. Sofiyev [17] investigated the vibration and buckling of cylindrical shells covered by different coatings, such as functionally graded, metal, and ceramic coatings.…”

Section: Introductionmentioning

confidence: 99%

Experimental Study on the Influence on Vibration Characteristics of Thin Cylindrical Shell with Hard Coating under Cantilever Boundary Condition

Sun

Zhu

et al. 2017

Shock and Vibration

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This research has experimentally investigated the influence on vibration characteristics of thin cantilever cylindrical shell (TCS) with hard coating under cantilever boundary condition. Firstly, the theoretical model of TCS with hard coating is established to calculate its natural frequencies and modal shapes so as to roughly understand vibration characteristic of TCS when it is coated with hard coating material. Then, by considering its nonlinear stiffness and damping influences, an experiment system is established to accurately measure vibration parameters of the shell, and the corresponding test methods and identification techniques are also proposed. Finally, based on the measured data, the influences on natural frequencies, modal shapes, damping ratios, and vibration responses of TCS with hard coating are analyzed and discussed in detail. It can be found that hard coating can play an important role in vibration reduction of TCS, and for the most modes of TCS, hard coating will result in the decrease of natural frequencies, but the decreased level is not very big, and its damping effects on the higher frequency range of the shell are weak and ineffective. Therefore, in order to make better use of this coating material, we must carefully choose the concerned antivibration frequency range of the shell; otherwise it may lead to some negative effects.

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“…The study was not limited to the cylindrical shell, but the conical shape was also evaluated for the nonlinear vibration. 28 A concentric cylindrical shell with thickness ''t s '', radius ''R o '', and coordinate system r, c, z with reference to the Cartesian coordinate has been considered for the vibration analysis as shown in Figure 3. By using the wave propagation approach, the equations of motion can be solved.…”

Section: Bubble-structure Interactionmentioning

confidence: 99%

“…The study was not limited to the cylindrical shell, but the conical shape was also evaluated for the nonlinear vibration. 28…”

Section: Bubble–structure Interactionmentioning

confidence: 99%

Bubble-induced noise and vibration in cylindrical shell filled with liquid nitrogen

Gupta

Sharma

Lakhera

2017

Proceedings of the Institution of Mechanical Engineers, Part C:

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Bubble-induced vibration is a very crucial aspect in some critical systems like laser interferometer gravitational-wave observatory. Recently, laser interferometer gravitational-wave observatory detected the gravitational wave produced due to the merger of two black holes. To detect the other universe collision event due to other binary pairs like neutron stars, black holes or combination, the sensitivity of the detector should be very high. The sensitivity depends on the reduction of the noise present in the detector system / components. Liquid nitrogen cryopump is also one of the sources for the noise. This noise has been produced due to the bubble structure interaction. The present work analyzes the bubble generated noise spectrum level and its acoustic effect due to induced vibration. The spectrum levels considering force, acceleration, velocity, and displacement effect have been studied in detail for a thin annular fluid (LN2) filled cylindrical shell. It is assumed that the structure of cylindrical shell is homogeneous as well as isotropic. The noise level generated due to radial force excitation resulting from bubble collision has been found to be in the range of −85 dB to −45 dB at a lower resonance frequency.

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On the solution of nonlinear vibration of truncated conical shells covered by functionally graded coatings

Cited by 26 publications

References 41 publications

Theoretical Study on the Influence of Hard Coating on Vibration Characteristics of Fiber-Reinforced Composite Thin Shell

Theoretical Study on the Influence of Hard Coating on Vibration Characteristics of Fiber-Reinforced Composite Thin Shell

Experimental Study on the Influence on Vibration Characteristics of Thin Cylindrical Shell with Hard Coating under Cantilever Boundary Condition

Bubble-induced noise and vibration in cylindrical shell filled with liquid nitrogen

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