A note on vibration of a cantilever plate immersed in water
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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TL;DR: In this paper, the free vibration analysis of a horizontal rectangular plate, either immersed in fluid or floating on its free surface, is studied, and the governing equations for a moderately thick rectangular plate are analytically derived based on the Mindlin plate theory (MPT), whereas the velocity potential function and Bernoulli's equation are employed to obtain the fluid pressure applied on the free surface of the plate.
61 citations
Additional excerpts
...[15] investigated the freely vibrating behavior of a cantilever square plate immersed in water....
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TL;DR: In this paper, a theoretical study on the hydroelastic vibration of two identical rectangular plates coupled with a bounded fluid is presented, where the plates are clamped along the plate edges and an ideal fluid is surrounded by the two rectangular plates and a rigid rectangular container.
59 citations
TL;DR: In this article, the authors proposed an analytical model for vibration analysis of partially cracked rectangular plates coupled with fluid medium, where the influence of surrounding fluid medium is incorporated in the governing equation in the form of inertia effects based on velocity potential function and Bernoulli's equations.
54 citations
TL;DR: In this paper, the authors presented the hydroelastic vibration analysis of clamped rectangular plates, vertically or horizontally submerged in fluid by using isogeometric finite element and boundary element methods.
33 citations
TL;DR: In this paper, the free flexural vibration of a cantilever plate partially submerged in a fluid is investigated and the virtual mass matrix is derived by solving the boundary-value problem related to the fluid motion using elliptical coordinates.
28 citations
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•
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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
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
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