On the natural frequencies of standing water waves in a canal of arbitrary shape

1972 ◽  
Vol 23 (6) ◽  
pp. 881-888 ◽  
Author(s):  
Shih-chih Chang ◽  
S. T. Wu
Keyword(s):  
Water Waves ◽  
Arbitrary Shape ◽  
Natural Frequencies ◽  
Standing Water

A Finite Element Approach to Plate Vibration Problems

1965 ◽  
Vol 7 (1) ◽  
pp. 28-32 ◽  
Author(s):  
D. J. Dawe
Keyword(s):  
Finite Element ◽  
Arbitrary Shape ◽  
Natural Frequencies ◽  
Isotropic Plate ◽  
Uniform Thickness ◽  
Flat Plates ◽  
Finite Element Approach ◽  
Various Boundary Conditions ◽  
Element Approach ◽  
Vibration Problems

A method of computing the natural frequencies of vibration of flat plates of arbitrary shape is outlined in which the plate is considered as an assemblage of elements. Both stiffness and inertia matrices are derived for a rectangular isotropic plate element of uniform thickness, and these matrices are used to find the natural frequencies of square plates subject to various boundary conditions. Comparison of finite element frequencies with known exact, experimental and energy solutions shows the method to give good results even for relatively few elements.

Sloshing in Regular Polygonal Basins—Frequencies, Modes, and Tileability

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Helmholtz Equation ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
Small Amplitude ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Mode Shapes ◽  
Shallow Water Waves ◽  
First Time

Abstract The classical theory of small amplitude shallow water waves is applied to regular polygonal basins. The natural frequencies of the basins are related to the eigenvalues of the Helmholtz equation. Exact solutions are presented for triangular, square, and circular basins while pentagonal, hexagonal, and octagonal basins are solved, for the first time, by an efficient Ritz method. The first five eigenvalues of each basin are tabulated and the corresponding mode shapes are discussed. Tileability conditions are presented. Some modes (eigenmodes) can be tiled into larger domains.

A Nash-Moser Theorem for Standing Water Waves

Equadiff 99 ◽  
2000 ◽  
pp. 1379-1384
Author(s):  
P.I. Plotnikov ◽  
J.F. Toland
Keyword(s):  
Water Waves ◽  
Standing Water

Computation of three-dimensional standing water waves

2013 ◽  
Vol 255 ◽  
pp. 612-638 ◽  
Author(s):  
Chris H. Rycroft ◽  
Jon Wilkening
Keyword(s):  
Water Waves ◽  
Three Dimensional ◽  
Standing Water
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