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Journal ArticleDOI

A note on vibration of a cantilever plate immersed in water

08 Apr 1979-Journal of Sound and Vibration (Academic Press)-Vol. 63, Iss: 3, pp 385-391
TL;DR: In this article, the first few mode shapes and the respective natural frequencies of a submerged cantilever plate are found by using a finite element procedure, eigenvalues being obtained by a simultaneous iteration technique.
About: This article is published in Journal of Sound and Vibration.The article was published on 1979-04-08. It has received 32 citations till now. The article focuses on the topics: Cantilever & Added mass.
Citations
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Journal ArticleDOI
TL;DR: In this article, the in-vacuo dynamic properties of cantilever plates were investigated, such as natural frequencies and mode shapes, of the plates, partially in contact with a fluid.

124 citations

Journal ArticleDOI
Moon K. Kwak1
TL;DR: In this paper, the authors used the Rayleigh-Ritz method combined with the Green function method to estimate the virtual mass effect on the natural frequencies and mode shapes of rectangular plates in the presence of water on one side of the plate.
Abstract: This paper is concerned with the virtual mass effect on the natural frequencies and mode shapes of rectangular plates due to the presence of the water on one side of the plate. The approximate formula, which mainly depends on the so-called nondimensionalized added virtual mass incremental factor, can be used to estimate natural frequencies in water from natural frequencies in vacuo. However, the approximate formula is valid only when the wet mode shapes are almost the same as the one in vacuo. Moreover, the nondimensionalized added virtual mass incremental factor is in general a function of geometry, material properties of the plate and mostly boundary conditions of the plate and water domain. In this paper, the added virtual mass incremental factors for rectangular plates are obtained using the Rayleigh-Ritz method combined with the Green function method. Two cases of interfacing boundary conditions, which are free-surface and rigid-wall conditions, and two cases of plate boundary conditions, simply supported and clamped cases, are considered in this paper. It is found that the theoretical results match the experimental results. To investigate the validity of the approximate formula, the exact natural frequencies and mode shapes in water are calculated by means of the virtual added mass matrix. It is found that the approximate formula predicts lower natural frequencies in water with a very good accuracy.

113 citations

Journal ArticleDOI
TL;DR: In this article, a numerical simulation to analyze the influence of the surrounding water in a turbine runner has been carried out using finite element method (FEM), and the added mass effect due to the fluid structure interaction has been discussed in detail.

104 citations

Journal ArticleDOI
TL;DR: In this article, the authors presented a simple procedure to determine the vibration frequencies and mode shapes of submerged cantilever plates based on an empirical added mass formulation, which can be used to analyze free vibration response easily.

103 citations

Journal ArticleDOI
TL;DR: In this article, the flexural vibrations of an electrostatically actuated cantilever microbeam in an incompressible inviscid stationary fluid have been investigated and the inertial effects of fluid on microbeam dynamics have been modeled as a mass added to microbeam mass.
Abstract: In this paper flexural vibrations of an electrostatically actuated cantilever microbeam in an incompressible inviscid stationary fluid have been studied. By applying “Three dimensional aerodynamic theory” pressure jump across the microbeam has been investigated and the inertial effects of fluid on microbeam dynamics have been modeled as a mass added to microbeam mass. Magnitude of the added mass has been calculated for various aspect ratios of cantilever microbeams and compared with those of clamped-clamped microbeams. To investigate the dynamic characteristics, it has been considered that the microbeam has been deflected by a DC voltage, V DC and then the dynamic characteristics and forced response of the system have been considered about these conditions. Galerkin-based step by step linearization method (SSLM) and Galerkin-based reduced order model have been applied to solve the nonlinear static and dynamic governing equations, respectively. Water by neglecting viscidity effects, as an instant has been considered as a surrounding fluid and the frequency response of the microbeam has been compared with that of vacuum conditions. It has been shown that because of the added mass effects in watery environment, the natural frequencies of the microbeam decrease. Because of the higher dielectric coefficient and increasing electrical stiffness and decreasing total stiffness consequently, maximum amplitude of the microbeam vibrations increases in watery environment, compared with vacuum. Moreover, it has been shown that increasing the DC voltage, increases the electrical stiffness and maximum amplitude of the microbeam vibrations, consequently, It has been shown that in higher voltages (near pull-in voltage), the rate of variation of resonance frequency and maximum amplitude is stronger than lower voltages.

63 citations


Cites methods from "A note on vibration of a cantilever..."

  • ...Muthuveerappan et al. (1979) and Rao et al. (1993) have used the finite-element method to solve the fluid‐structure interaction problems for completely submerged elastic plates....

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References
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Book
01 Jan 1971
TL;DR: In this paper, the authors describe how people search numerous times for their favorite books like this the finite element method in engineering science, but end up in malicious downloads, and instead they cope with some infectious bugs inside their computer.
Abstract: Thank you very much for downloading the finite element method in engineering science. Maybe you have knowledge that, people have search numerous times for their favorite books like this the finite element method in engineering science, but end up in malicious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they cope with some infectious bugs inside their computer.

3,688 citations

Book
01 Jan 1969
TL;DR: The fundamental equation of classical plate theory can be found in this article, where anisotropic and variable-thickness versions of the classical plates are considered, as well as other considerations.
Abstract: : Contents: Fundamental Equations of Classical Plate Theory; Circular Plates; Elliptical Plates; Rectangular Plates; Parallelogram Plates; Other Quadrilateral Plates; Triangular Plates; Plates of Other Shapes; Anisotropic Plates; Plates With Inplane Forces; Plates With Variable Thickness; and Other Considerations.

2,137 citations

Journal ArticleDOI
TL;DR: In this paper, the simultaneous iteration method of obtaining eigenvalues and eigenvectors is employed for the solution of undamped vibration problems, and a method of allowing for body freedom is given and some numerical tests are discussed.
Abstract: The simultaneous iteration method of obtaining eigenvalues and eigenvectors is employed for the solution of undamped vibration problems. This method is of significance when a few of the dominant eigenvalues and eigenvectors are required from a large matrix, and hence is particularly suitable for vibration problems involving a large number of degrees of freedom. It is shown that advantage may be taken of both the symmetry and the band form of the mass and stiffness matrices, thus making it feasible to process on a computer larger order vibration problems than can be processed using transformation methods. A method of allowing for body freedom is given and some numerical tests are discussed.

69 citations

Book
01 Jan 1961

42 citations

Journal ArticleDOI
TL;DR: In this paper, the equations for the free undamped vibration of a structure in an ideal incompressible fluid medium and their finite element formulation are briefly reviewed and the relevant matrices (stiffness and loading) for two prismatic fluid elements are given explicitly and some numerical results are presented.
Abstract: The equations for the free undamped vibration of a structure in an ideal incompressible fluid medium and their finite element formulation are briefly reviewed. The relevant matrices (stiffness and loading) for two prismatic fluid elements are given explicitly and some numerical results are presented.

18 citations