• Proceedings of the KSME Conference
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• 2004.11a
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• pp.551-556
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• 2004

The theoretical method is developed to investigate the vibration characteristics of the combined cylindrical shells with an annular plate joined to the shell at any arbitrary axial position. The structural rotational coupling between shell and plate is simulated using the rotational artificial spring. For the translational coupling, the continuity conditions for the displacements of shell and plate are used. For the uncoupled annular plate, the transverse motion is considered and the in-plane motions are not. And the additional transverse and in-plane motions of the coupled annular plate by shell deformation are considered in analysis. Theoretical formulations are based on Love's thin shell theory. The frequency equation of the combined shell with an annular plate is derived using the Rayleigh-Ritz approach. The effect of inner-to-outer radius ratio, axial position and thickness of annular plate on vibration characteristics of combined cylindrical shells is studied. To demonstrate the validity of present theoretical method, the finite element analysis is performed.

• Proceedings of the KSR Conference
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• 2010.06a
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• pp.13-17
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• 2010

This presentation examines the characteristics of torsional vibration in axisymmetric out-of-plane vibrations of an annular Mindin plate. The out-of-plane vibration of circular or annular plates have been investigated since a long years ago by many researchers. When the classical Kirchhoff plate theory neglecting the effect of transverse shear deformation is applied to a thick plate, its out-of-plane natural frequencies are much different from reality. And so, since Minlin presented a plate theory considering the effect of rotary inertia and transverse shear deformation, many researches for the out-of-plane natural vibration of circular or annular Mindin plates have been performed. But almost all researchers missed the torsional vibration due to transverse shear deformation in axisymmetric out-of-plane vibrations of the circular or annular Mindin plate. Therefore, in this presentation, we verify the existence of torsional vibration of an annular plate and present the natural frequencies of an annular plate with free outer boundary surface.

• Smart Structures and Systems
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• v.13 no.1
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• pp.25-39
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• 2014

The axisymmetric dynamic instability of polar orthotropic sandwich annular plate combined with electrorheological (ER) fluid core layer and constraining layer are studied in this paper. And, the ER core layer and constraining layer are used to improve the stability of the annular plate system. The boundaries of instability regions for the polar orthotropic sandwich annular plate system are obtained by discrete layer annular finite element and the harmonic balance method. The rheological property of an electrorheological material, such as viscosity, plasticity, and elasticity can be controlled by applying different electric field strength. Thus, the damping characteristics of the sandwich system are more effective when the electric field is applied on the sandwich structure. Additionally, variations of the instability regions for the polar orthotropic sandwich annular plate with different applying electric field strength, thickness of ER layer and some designed parameters are investigated and discussed in this study.

• Smart Structures and Systems
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• v.8 no.5
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• pp.487-499
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• 2011

The parametric resonance problems of axisymmetric sandwich annular plate with an electrorheological (ER) fluid core and constraining layer are investigated. The annular plate is covered an electrorheological fluid core layer and a constraining layer to improve the stability of the system. The discrete layer annular finite element and the harmonic balance method are adopted to calculate the boundary of instability regions for the sandwich annular plate system. Besides, the rheological property of an electrorheological material, such as viscosity, plasticity, and elasticity can be changed when applying an electric field. When the electric field is applied on the sandwich structure, the damping of the sandwich system is more effective. Thus, variations of the instability regions for the sandwich annular plate with different applying electric fields, thickness of ER layer, and some designed parameters are presented and discussed in this study. The ER fluid core is found to have a significant effect on the location of the boundaries of the instability regions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.5
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• pp.564-571
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• 2008

This paper is concerned with the free vibration analysis of an annular plate with boundary conditions of simply supported-free, clamped-free and free-free, respectively. Exact solutions for the natural frequency and mode of an annular plate can be obtained by solving the differential equation but other methods such as the Rayleigh-Ritz method and the finite element method can be also used. In this research, we applied the Independent Coordinate Coupling Method(ICCM) to the annular plate and prove that the ICCM can accurately predict the natural frequency and mode shape of the annular plate. The numerical results show that the ICCM can be used effectively for the free vibration problem of plate with a hole compared to the Rayleigh-Ritz method and the finite element method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.3 s.234
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• pp.439-446
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• 2005

The theoretical method is developed to investigate the vibration characteristics of the combined cylindrical shells with an annular plate joined to the shell at any arbitrary axial position. The structural rotational coupling between shell and plate is simulated using the rotational artificial spring. For the translational coupling, the continuity conditions for the displacements of shell and plate are used. For the uncoupled annular plate, the transverse motion is considered and the in-plane motions are not. And the additional transverse and in-plane motions of the coupled annular plate by shell deformation are considered in analysis. Theoretical formulations are based on Love's thin shell theory. The frequency equation of the combined shell with an annular plate is derived using the Rayleigh-Ritz approach. The effect of inner-to-outer radius ratio, axial position and thickness of annular plate on vibration characteristics of combined cylindrical shells is studied. To demonstrate the validity of present theoretical method, the finite element analysis is performed.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.10
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• pp.767-776
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• 2003

The theoretical method is developed to Investigate the nitration characteristics of the combined cylindrical shells with an annular plate joined to the shell at any arbitrary axial position. The structural coupling between shell and plate is simulated using two types of artificial springs a translational spring is introduced for translational coupling and a rotational spring is used for rotational coupling. The springs are continuously distributed along circumferential direction. Using the Rayleigh-Ritz method the natural frequencies and mode shapes of the combined shell with an annular plate examine. The effect of Inner-to-outer radius ratio, axial position of annular plate and length-to-radius ratio of shell on vibration characteristics of combined cylindrical shells is studied. The theoretical results are verified by comparison with FEM results.

• Structural Engineering and Mechanics
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• v.30 no.4
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• pp.501-512
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• 2008

The axisymmetric problem of a functionally graded annular plate is considered by extending the theory of functionally graded materials plates suggested by Mian and Spencer (1998). In particular, their expansion formula for displacements is adopted and the hypothesis that the material parameters can vary along the thickness direction in an arbitrary continuous fashion is retained. However, their analysis is extended here in two aspects. First, the material is assumed to be transversely isotropic, rather than isotropic. Second, the plate is no longer tractions-free on the top and bottom surfaces, but subject to uniform loads applied on the surfaces. The elasticity solutions are given for a uniformly loaded annular plate of functionally graded materials for a total of six different boundary conditions. Numerical results are given for a simply supported functionally graded annular plate, and good agreement with those by the classical plate theory is obtained.

• Coupled systems mechanics
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• v.12 no.2
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• pp.127-149
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• 2023

A theoretical method is developed to analyze the free vibration of an elastic annular plate in contact with an ideal liquid. The displacement potential functions of the contained liquid are expressed as a combination of the Bessel functions that satisfy the Laplace equation and the liquid boundary conditions. The compatibility condition along the interface between the annular plate and the contained liquid is taken into account to consider the fluid-structure coupling. The dynamic displacement of the wet annular plate is assumed to be a combination of dry eigenfunctions, allowing for prediction of the natural frequencies using the Rayleigh-Ritz method. The study investigates the effect of radial liquid boundary conditions on the natural frequencies of the wet annular plate, considering four types of liquid bounding: outer container bounded, outer and inner bounded, inner bounded, and radially unbounded. The proposed theoretical method is validated by comparing the predicted wet natural frequencies with those obtained from finite element analysis, showing excellent accuracy. The results indicate that the radial liquid bounding effect on the natural frequencies is negligible for the axisymmetric vibrational mode, but relatively significant for the mode with one nodal diameter (n =1) and no nodal circle (m' = 0). Furthermore, the study reveals that the wet natural frequencies are the largest for the plate with an inner bounded cylinder among the radial liquid boundary cases, regardless of the vibration mode.

• Journal of Advanced Marine Engineering and Technology
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• v.22 no.3
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• pp.353-361
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• 1998

The study on the vibration characteristics of annular sector plates is important for structural engineers. In this study the vibration modes and their natural frequencies of annular sector plates clamped along the inner circumferential edge are obtained by the time average holographic interferometer according to the varying sector angle. The experimental results agree well with those obtained by the numerical analysis. The vibration characteristics of annular sector plates shows great dependence on the sector angle. The radial nodal lines converge to the center of annular sector plate.