Free Vibrations of Circular Plates Coupled With Liquids: Revising the Lamb Problem

Amabili, Marco; Kwak, Moon Kyu

doi:10.1006/jfls.1996.0051

Cited by 156 publications

(106 citation statements)

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“…Probably this can be due to the different boundary condition. In the cases of MonteroGallego [1984] and Amabili-Kwak [1996], the plate is situated in a hole of a rigid wall that separates the fluid on the lower and upper sides of the plate, and even in the case of MonteroGallego [1984] the fluid domain is not infinite because it is immersed in a tank of finite dimensions. In the modes with nodal circles this difference should be more measurable due to the change in sign on the vibration amplitude and therefore on the pressures exerted by the fluid.…”

Section: Resultsmentioning

confidence: 99%

Induced Damping on Vibrating Circular Plates Submerged in Still Fluid

Gascón-Pérez

García-Fogeda

2015

Int. J. Appl. Mechanics

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Received RevisedWhen a structure vibrates immersed in a fluid it is known that the dynamic properties of the system are modified. The surrounding fluid will, in general, contributes to the inertia, the rigidity and the damping coefficient of the coupled fluid-structure system. For light structures, like spacecraft antennas, even when the fluid is air the contribution to the dynamic properties can be important. For not so light structures the ratio of the equivalent fluid/structure mass and rigidity can be very small and the fluid contribution could be neglected. For the ratio of equivalent fluid/structure damping both terms are of the same order and therefore the fluid contribution must be studied. The working life of the spacecraft structure would be on space and so without any surrounding fluid. The response of a spacecraft structure on its operational life would be attenuated by the structural damping alone but when the structure is dynamically tested on the earth the dynamic modal test is performed with the fluid surrounding it. The results thus are contaminated by the effects of the fluid. If the damping added by the fluid is of the same order as the structural damping the response of the structure in space can be quite different to the response predicted on earth. It is therefore desirable to have a method able to determine the amount of damping induced by the fluid and that should be subtracted of the total damping measured on the modal vibration test. In this work a method for the determination of the effect of the surrounding fluid on the dynamic characteristics of a circular plate has been developed. The plate is assumed to vibrate harmonically with the vacuum modes and the generalized forces matrix due to the fluid is thus computed. For a compressible fluid this matrix is formed by complex numbers indicating that include terms of inertia, rigidity and damping. The matrix due to the fluid loading is determined by a boundary element method (BEM). The BEM used is of circular rings on the plate surface so the number of elements to obtain an accurate result is very low. The natural frequencies of the system are computed by an iteration procedure one by one and also the damping fluid contribution. Comparisons of the present method with various experimental data and other theories show the efficiency and accuracy of the method for any support condition of the plate.

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Section: Resultsmentioning

confidence: 99%

Induced Damping on Vibrating Circular Plates Submerged in Still Fluid

Gascón-Pérez

García-Fogeda

2015

Int. J. Appl. Mechanics

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“…Isshiki and Nagata [4] derived the governing equations of a oating plate by assuming Hamilton's principle for plate and Kelvin's principle for water. Amabili and Kwak [5] utilized Hankel transformation to analyze the vibrational properties of circular plates with di erent forms of uniform boundary conditions. Investigations were continued by Matsui, who employed FourierBessel series to derive the governing equations of motion for a base excited storage tank with doubledeck [6] and single-deck [7] oating roofs.…”

Section: Introductionmentioning

confidence: 99%

Stress Analyses in Single Deck and Double Deck Floating Roofs Subjected to Earthquake Ground Motions

2017

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Abstract. This paper investigates the stress patterns in circular single-and double-deck oating roofs excited by earthquake ground motions. Variational formulation is employed to derive the governing equations. Response of the oating roofs to di erent classes of ground motions including near-eld and far-eld records is evaluated. Results indicate that far-eld earthquakes produce larger wave elevation but smaller bending stresses in the oating roof. Moreover, the bending stresses in double-deck roofs emerge in a smooth and approximately symmetric pattern with a peak around the mid-span radius while the peak values of bending stress in single-deck oating roofs occur at the vicinity of deck center and at the deck-pontoon interface. The results can have practical implications in the design process of oating-roof cylindrical tanks.

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“…In recent works, Kwak [1991]; Kwak and Kim [1991]; Amabili et al [1995] and Amabili and Kwak [1996] have developed a method to determine the dynamic properties of circular plates surrounded by a liquid. The modes of vibration in all of the cases studied were taken as the modes of the plate in vacuum (see, e.g., Leissa [1969]), and these modes satisfy the exact boundary conditions at the plate edges.…”

Section: Introductionmentioning

confidence: 99%

“…In Kwak [1991] and Kwak and Kim [1991], the influence of the free surface of the fluid compared with the rigid wall was investigated, and it was concluded that for the cases of clamped and simply supported boundary conditions, the nondimensional added virtual mass increment (NAVMI) factors were lower for the free surface than for the rigid surface. Additionally, in Amabili and Kwak [1996] the influence of the coupling fluid-structure on the vibration mode was studied. In the results presented, it was shown that small differences occur with regard to the mode shape in both cases, with the small deviation depending on the boundary condition on the plate edges.…”

Section: Introductionmentioning

confidence: 99%

“…In the results presented, it was shown that small differences occur with regard to the mode shape in both cases, with the small deviation depending on the boundary condition on the plate edges. It was concluded in Amabili and Kwak [1996] that the use of the modes in vacuum for the plate vibration can be a good approximation for most of the cases. Therefore, in this paper, the consideration that the plate is in a hole on a rigid surface will be taken into account while keeping in mind that this condition will be different from the case of a plate on a free surface.…”

Section: Introductionmentioning

confidence: 99%

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Influence of a Liquid on the Natural Frequencies of Almost Circular Plates

Gascón-Pérez

García-Fogeda

2014

Int. J. Appl. Mechanics

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In this work, the influence of the surrounding fluid on the dynamic characteristics of almost circular plates is investigated. First the natural frequencies and normal modes for the plates in vacuum are calculated by a perturbation procedure. The method is applied for the case of elliptical plates with a low value of eccentricity. The results are compared with other available methods for this type of plates with good agreement. Next, the effect of the fluid is considered. The normal modes of the plate in vacuum are used as a base to express the vibration mode of the coupled plate-fluid system. By applying the Hankel transformation the nondimensional added virtual mass 2 increment (NAVMI) are calculated for elliptical plates. Results of the NAVMI factors and the effect of the fluid on the natural frequencies are given and it is shown that when the eccentricity of the plate is reduced to zero (circular plate) the known results of the natural frequencies for circular plates surrounded by liquid are recovered.

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Free Vibrations of Circular Plates Coupled With Liquids: Revising the Lamb Problem

Cited by 156 publications

References 0 publications

Induced Damping on Vibrating Circular Plates Submerged in Still Fluid

Induced Damping on Vibrating Circular Plates Submerged in Still Fluid

Stress Analyses in Single Deck and Double Deck Floating Roofs Subjected to Earthquake Ground Motions

Influence of a Liquid on the Natural Frequencies of Almost Circular Plates

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