Nonlinear Hydroelastic Vibration of a Cylindrical Tank with an Elastic Bottom, Containing Liquid. Part II: Linear Axisymmetric Vibration Analysis

Chiba, Masakatsu

doi:10.1006/jfls.1993.1005

Cited by 51 publications

(14 citation statements)

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“…The same Galerkin equation was obtained by Gonc7 alves & Ramos (1996), using the Galerkin method, and by Amabili (1999) and Amabili et al (1998) by using the Rayleigh}Ritz method. Chiba (1993Chiba ( , 1995 and Chiba and Osumi (1998) obtained another nonsymmetric Galerkin equation. It can easily be shown that equation (1) can give complex eigenvalues.…”

Section: Amabilimentioning

confidence: 96%

“…Recently, Amabili (1997Amabili ( , 1999, Amabili et al (1998), Gonialves & Ramos (1996), Chiba (1993Chiba ( , 1995 and Chiba & Osumi (1998) solved vibration of plates and shells coupled with sloshing, quiescent and inviscid liquid by inserting the sloshing condition into the eigenvalue problem. In their formulation, all the authors cited obtained an eigenvalue problem for non-symmetric matrices for which the problem of the existence of complex eigenvalues arises.…”

Section: Amabilimentioning

confidence: 98%

See 1 more Smart Citation

On the Real Eigenvalues for Vibrating Structures Coupled With Quiescent Liquids With Free Surface

Amabili

Frosali

Landucci

2000

Journal of Fluids and Structures

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Section: Amabilimentioning

confidence: 96%

Section: Amabilimentioning

confidence: 98%

On the Real Eigenvalues for Vibrating Structures Coupled With Quiescent Liquids With Free Surface

Amabili

Frosali

Landucci

2000

Journal of Fluids and Structures

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“…Furthermore, Bauer (1981Bauer ( , 1995 investigated the hydroelastic vibration of liquid in a rectangular container and a circular cylindrical container, respectively, of which the free liquid surface is covered by a #exible membrane or an elastic plate. Recently, Chiba (1993Chiba ( , 1994 studied the hydroelastic vibration of the #exural bottom in a circular cylindrical container under the consideration of the e!ect of in-plane force in the plate due to the static liquid pressure. Amabili (1997) and Amabili & Dalpiaz (1998) studied the bulging modes of an elastic bottom in circular and annular cylindrical containers partially "lled with liquid by using the Ritz method.…”

Section: Introductionmentioning

confidence: 99%

Hydroelastic Vibration of a Circular Container Bottom Plate Using the Galerkin Method

Cheung

Zhou

2002

Journal of Fluids and Structures

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“…Such a problem was further studied by Amabili and Kwak [5] using the Rayleigh}Ritz approach. Chiba [16] studied the linear axisymmetric vibration of a cylindrical tank with rigid wall and elastic bottom. Amabili [10] studied the vibrations of plates placed in a circular (or annular) aperture of an in"nite rigid wall in contact with an unbounded #uid of "nite depth on one side by using the Rayleigh}Ritz method.…”

Section: Introductionmentioning

confidence: 99%

Vibration of vertical rectangular plate in contact with water on one side

Zhou

Cheung

2000

Earthquake Engng. Struct. Dyn.

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SUMMARYIn this paper, the vibratory characteristics of a rectangular plate in contact with water on one side are studied. The elastic plate is considered to be a part of a vertical rectangular rigid wall in contact with water, the edges of which are elastically restrained and parallel to those of the rigid wall. The location and size of the plate on the rigid wall may vary arbitrarily. The water with a free surface is in a rectangular domain in"nite in the length direction. The e!ects of free surface waves, compressibility of the water and the hydrostatic water pressure are neglected in the analysis. An analytical-Ritz method is developed to analyse the interaction of the plate}water system. First of all, by using the method of separation of variables and the method of Fourier series expansion, the exact expression of the motion of water is derived in the form of integral equations including the dynamic deformation of the plate. Then the Rayleigh}Ritz approach is used to derive the eigenfrequency equation of the system via the variational principle of energy. By selecting beam vibrating functions as the admissible functions of the plate, the added virtual mass incremental (AVMI) matrices for plate vibration are obtained. The convergency studies are carried out. The e!ects of some parameters such as the depth and width of water, the support sti!nesses, location and aspect ratio of the plate and the plate}water size and density ratios on the eigenfrequencies of the plate}water system are investigated. Several numerical examples are given. The validity of AVMI factor approach is also con"rmed by comparing the AVMI factor solutions with the analytical-Ritz solutions. The results show that the approach presented here can also be used as excellent approximate solutions for rectangular plates in contact with water of in"nite width and/or in"nite depth.

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Nonlinear Hydroelastic Vibration of a Cylindrical Tank with an Elastic Bottom, Containing Liquid. Part II: Linear Axisymmetric Vibration Analysis

Cited by 51 publications

References 0 publications

On the Real Eigenvalues for Vibrating Structures Coupled With Quiescent Liquids With Free Surface

On the Real Eigenvalues for Vibrating Structures Coupled With Quiescent Liquids With Free Surface

Hydroelastic Vibration of a Circular Container Bottom Plate Using the Galerkin Method

Vibration of vertical rectangular plate in contact with water on one side

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