Analytical Solution for Long-Wave Scattering by a Circular Island Mounted on a General Shoal

2012 ◽  
Vol 138 (6) ◽  
pp. 425-434 ◽  
Author(s):  
Huan-Wen Liu ◽  
Jian-Jian Xie ◽  
Zhang-Hua Luo
Keyword(s):  
Analytical Solution ◽  
Wave Scattering ◽  
Long Wave ◽  
Circular Island

scholarly journals An Extended Analytic Solution of Combined Refraction and Diffraction of Long Waves Propagating over Circular Island

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yu-Shu Kuo ◽  
Tai-Wen Hsu ◽  
Chia-Cheng Tsai ◽  
Yu-Hsuan Huang
Keyword(s):  
Wave Scattering ◽  
Analytic Solution ◽  
Complex Variables ◽  
Long Waves ◽  
Wave Refraction ◽  
Long Wave ◽  
Present Solution ◽  
Circular Island ◽  
Frobenius Series ◽  
Independent Parameters

An analytic solution of long waves scattering by a cylindrical island mounted on a permeable circular shoal was obtained by solving the linear long wave equation (LWE). The solution is in terms of the Bessel function expressed by complex variables. The present solution is suitable for arbitrary bottom configurations described by a power function with two independent parameters. For the case of the paraboloidal shoal, there exists a singular point (α=2) which can be removed using Frobenius series, whereαis a real constant. The present solution is reduced to Yu and Zhang’s (2003) solution for impermeable circular shoal. The numerical results show some special features of the combined effect of wave refraction and diffraction caused by a porous circular island. The effect of key parameters of the island dimension, the shoal slope, and permeability on wave scattering was discussed based on the analytic solution.

Analytical Solution of Lamb Wave Scattering at Plate End

2011 ◽  
Vol 199-200 ◽  
pp. 949-952 ◽  
Author(s):  
Fei Long Feng ◽  
Jian Zhong Shen ◽  
Jing Jun Deng ◽  
Qiu Ping Wang
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Lamb Wave ◽  
Wave Scattering ◽  
Least Square Method ◽  
Least Square ◽  
Matrix Elements ◽  
Scattering Coefficients ◽  
Reflection Matrix ◽  
Analytical Expressions

An analytical solution based on modal decomposition is presented to investigate Lamb wave scattering at plate end. Take boundary condition into biorthogonality relation, a matrix equation is established with all matrix elements have analytical expressions. The scattering feature is then expressed in matrix form, named as reflection matrix, which has explicit expression composed of those matrixes. Calculation examples have be implemented when antisymmetric modes are reflected. Scattering coefficients are figured out in a range when frequency-thickness product vary from 0 to 8kHzm, to prove the calculation efficiency. The calculation precision is very close to the least square method based on model discretization.

A Series Solution for Wave Scattering by a Circular Island on a Shoal Based on the Mild-Slope Equation

2012 ◽  
Vol 28 (1) ◽  
pp. 41-51 ◽  
Author(s):  
Y.-M. Cheng ◽  
C.-T. Chen ◽  
L.-F. Tu ◽  
J.-F. Lee
Keyword(s):  
Analytical Solution ◽  
Wave Scattering ◽  
Present Method ◽  
Series Solution ◽  
Shallow Water Equation ◽  
Variable Coefficients ◽  
Fourier Cosine ◽  
Mild Slope Equation ◽  
Scattering Field ◽  
Run Up

ABSTRACTA series solution based on the mild-slope equation is produced in this study of wave scattering produced by a circular cylindrical island mounted on an axi-symmetrical shoal. The solution is presumed to be a Fourier cosine expansion with variable coefficients in the radial direction on account of the symmetric scattering field, which translates the original 2-D boundary-value problem to a 1-D one in which an ordinary differential equation is in effect treated. Approximations to the coefficients of the governing equation with the Taylor expansions enable the use of the Frobenius method, and consequently the solution is obtained in a combined Fourier and power series. For verification, the present method is mainly compared with Zhu and Zhang's [1] analytical solution of the linearised shallow water equation for a conical shoal, and with a different analytical solution of the mild-slope equation developed by Liu et al. [2] for a paraboloidal shoal. Fine agreements are achieved. The present method is then used to investigate the variation pattern of the wave run-up when the shoal profile varies from conical to paraboloidal, and some interesting phenomena are observed.

Analytical solution to the SH wave scattering problem caused by a circular cavity in a half space with inhomogeneous modulus

Meccanica ◽  
2021 ◽  
Vol 56 (3) ◽  
pp. 705-709
Author(s):  
Jinlai Bian ◽  
Zailin Yang ◽  
Guanxixi Jiang ◽  
Yong Yang ◽  
Menghan Sun
Keyword(s):  
Analytical Solution ◽  
Half Space ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Circular Cavity ◽  
Sh Wave
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