Doubly Asymptotic Approximations for Submerged Structures With Internal Fluid Volumes: Evaluation

1994 ◽  
Vol 61 (4) ◽  
pp. 900-906 ◽  
Author(s):  
T. G. Geers ◽  
Peizhen Zhang
Keyword(s):  
Spherical Shell ◽  
Transient Response ◽  
Companion Paper ◽  
Second Order ◽  
Numerical Results ◽  
Asymptotic Approximations ◽  
Incident Plane ◽  
Internal Fluid ◽  
Plane Step

The accuracy of the doubly asymptotic approximations formulated in the previous companion paper is examined through the comparison of DAA and exact transient response histories for a fluid-filled, submerged spherical shell excited by an incident plane step-wave. The numerical results indicate that second-order DAAs are satisfactory for problems of this type.

Doubly Asymptotic Approximations for Submerged Structures With Internal Fluid Volumes: Formulation

1994 ◽  
Vol 61 (4) ◽  
pp. 893-899 ◽  
Author(s):  
T. L. Geers ◽  
Peizhen Zhang
Keyword(s):  
Exact Solutions ◽  
Numerical Solution ◽  
Complex Geometry ◽  
Spherical Geometry ◽  
Companion Paper ◽  
Boundary Integral ◽  
Asymptotic Approximations ◽  
Flexible Body ◽  
Structural Acoustics ◽  
Internal Fluid

Doubly asymptotic approximations (DAAs) are approximate temporal impedance relations for a medium in contact with a flexible body. In this paper, the method of operator matching previously used for external acoustic domains is used to develop first- and second-order boundary integral DAAs for internal acoustic domains. Corresponding boundary element forms permit the numerical solution of transient structural acoustics problems with complex geometry. The accuracy of the DAAs is assessed in the following companion paper by comparing DAA and exact solutions for a canonical problem with spherical geometry.

Asymptotic eigensolutions of Laplace’s tidal equation

1977 ◽  
Vol 353 (1674) ◽  
pp. 377-400 ◽  
Keyword(s):  
Angular Velocity ◽  
Vertical Structure ◽  
Angular Frequency ◽  
Numerical Results ◽  
Asymptotic Approximations ◽  
Equivalent Depth ◽  
Negative Eigenvalues ◽  
Hough Functions

Asymptotic approximations to the eigenfunctions of Laplace’s tidal equation (Hough functions) are obtained for prescribed λ = σ /2 ω ( σ = angular frequency, ω = angular velocity of planet) and large values of Lamb’s parameter, β = 4 ω 2 a 2 / gh ( a is the planetary radius, and h the equivalent depth for a particular vertical structure), qua eigenvalue. Both positive and negative eigenvalues are considered. The results are validated by comparison with the extensive numerical results of Flattery (1967) and Longuet-Higgins (1968). They should be useful in atmospheric tidal studies, especially for a rapidly rotating planet, and may be useful for studies of equatorial motions in the oceans.

Numerical solution of a source identification problem: Almost coercivity

2019 ◽  
Vol 27 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Abdullah Said Erdogan ◽  
Ali Ugur Sazaklioglu
Keyword(s):  
Numerical Solution ◽  
Source Identification ◽  
Identification Problem ◽  
Second Order ◽  
Numerical Results ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Accuracy Difference ◽  
Coercive Stability

Abstract The present paper is devoted to the investigation of a source identification problem that describes the flow in capillaries in the case when an unknown pressure acts on the system. First and second order of accuracy difference schemes are presented for the numerical solution of this problem. Almost coercive stability estimates for these difference schemes are established. Additionally, some numerical results are provided by testing the proposed methods on an example.

Transient Response of an Interface-Crack in a Layered Plate

1986 ◽  
Vol 53 (3) ◽  
pp. 579-586 ◽  
Author(s):  
T. Kundu
Keyword(s):  
Stress Field ◽  
Interface Crack ◽  
Transient Response ◽  
Singular Integrals ◽  
Fortran Program ◽  
Numerical Results ◽  
New Method ◽  
Layered Plate ◽  
Improved Method ◽  
Sample Problem

In this paper, the transient response of an interface crack, in a two layered plate subjected to an antiplane stress field, is analytically computed. The problem is formulated in terms of semi-infinite integrals following the technique developed by Neerhoff (1979). It has been shown that the major steps of Neerhoff’s technique, which was originally developed for layered half-spaces, can also be applied to layered plate problems. An improved method for manipulation of semi-infinite singular integrals is also presented here. Finally, the new method is coded in FORTRAN program and numerical results for a sample problem are presented.

On the spectra of non-self-adjoint realisations of second-order elliptic operators

1981 ◽  
Vol 90 (1-2) ◽  
pp. 71-105 ◽  
Author(s):  
W. D. Evans
Keyword(s):  
Spherical Shell ◽  
Essential Spectrum ◽  
Weighted Space ◽  
Elliptic Operators ◽  
Second Order ◽  
Sectorial Operator ◽  
Image Position ◽  
Second Order Elliptic Operators ◽  
Complex Valued

SynopsisLet τ denote the second-order elliptic expressionwhere the coefficients bj and q are complex-valued, and let Ω be a spherical shell Ω = {x:x ∈ ℝn, l <|x|<m} with l≧0, m≦∞. Under the conditions assumed on the coefficients of τ and with either Dirichlet or Neumann conditions on the boundary of Ω, τ generates a quasi-m-sectorial operator T in the weighted space L2(Ω;w). The main objective is to locate the spectrum and essential spectrum of T. Best possible results are obtained.

Large Amplitude Free Vibration of Shallow Spherical Shell on a Pasternak Foundation

1993 ◽  
Vol 115 (1) ◽  
pp. 70-74 ◽  
Author(s):  
D. N. Paliwal ◽  
V. Bhalla
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Large Amplitude ◽  
Free Vibrations ◽  
Numerical Results ◽  
Shallow Spherical Shell ◽  
Pasternak Foundation ◽  
New Approach ◽  
Foundation Parameters ◽  
Clamped Edges

Large amplitude free vibrations of a clamped shallow spherical shell on a Pasternak foundation are studied using a new approach by Banerjee, Datta, and Sinharay. Numerical results are obtained for movable as well as immovable clamped edges. The effects of geometric, material, and foundation parameters on relation between nondimensional frequency and amplitude have been investigated and plotted.

Interaction of a Second-Order Solitary Wave With a Vertical Permeable Plane Breakwater

2004 ◽  
Author(s):  
A. Basmat
Keyword(s):  
Solitary Wave ◽  
Water Waves ◽  
Boussinesq Equations ◽  
Second Order ◽  
Wave Loading ◽  
Coastal Structures ◽  
Transformation Techniques ◽  
Incident Plane ◽  
Impermeable Wall ◽  
Plane Barrier

The purpose of this paper is to develop mathematical models to investigate the interaction between long non-linear water waves and dissipative/absorbing coastal structures. The diffraction of a plane second-order solitary wave at a vertical permeable plane barrier standing in front of an impermeable wall, with calculation of the second-order wave loading is investigated. An incident plane second-order solitary wave is the Laitone solution of Boussinesq equations. The analytical solution is obtained by means of a small parameter development and Fourier transformation techniques. Computational results were performed using the software MATHEMATICA version 4.0.1.0.

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