In-Plane Ice Structure Vibration Analysis by Two-Dimensional Elastic Wave Theory

1984 ◽  
Vol 106 (2) ◽  
pp. 160-168 ◽  
Author(s):  
C. H. Luk
Keyword(s):  
Elastic Wave ◽  
Wave Equations ◽  
Fourier Transforms ◽  
Ice Sheet ◽  
Elastic Solid ◽  
Radiation Condition ◽  
Wave Theory ◽  
Two Dimensional ◽  
Transverse Waves ◽  
Cylindrical Structure

This paper presents a theoretical analysis of an in-plane ice sheet vibration problem due to a circular cylindrical structure moving in the plane of an infinite ice sheet, and computes the ice forces exerted on the structure as the motion occurs. The basic equations are derived from two-dimensional elastic wave theory for a plane stress or plane strain problem. The ice material is treated as a homogeneous, isotropic and linear elastic solid. The resulting initial and boundary value problems are described by two wave equations. One equation governs the ice motion associated with longitudinal wave propagation, and the other governs propagation of transverse waves. The equations are subject to 1) either a fixed or a frictionless boundary condition at the ice structure interface, and 2) a radiation condition at large distance from the structure to ensure the existence of only outward traveling elastic waves. The governing equations are then solved by 1) Fourier transforms, or 2) Laplace transforms, depending on the problem. Closed-form solutions are obtained in terms of Bessel functions. Plots are provided for estimating the ice added mass, the damping, and the unit function response for a circular cylindrical structure vibrating in the horizontal plane of an infinite ice sheet.

A Two-Dimensional Numerical Wave Flume—Part 1: Nonlinear Wave Generation, Propagation, and Absorption

2001 ◽  
Vol 123 (2) ◽  
pp. 70-75 ◽  
Author(s):  
S. F. Baudic ◽  
A. N. Williams ◽  
A. Kareem
Keyword(s):  
Numerical Model ◽  
Fluid Motion ◽  
Radiation Condition ◽  
Wave Theory ◽  
Published Data ◽  
Computational Domain ◽  
Two Dimensional ◽  
Time Step ◽  
Numerical Wave Flume ◽  
Wave Flume

A numerical model is developed to simulate fully nonlinear transient waves in a semi-infinite, two-dimensional wave tank. A mixed Eulerian-Lagrangian formulation is adopted and a high-order boundary element method is used to solve for the fluid motion at each time step. Input wave characteristics are specified at the upstream boundary of the computational domain using an appropriate wave theory. At the downstream boundary, a damping region is used in conjunction with a radiation condition to prevent wave reflections back into the computational domain. The convergence characteristics of the numerical model are studied and the numerical results are validated through a comparison with previous published data.

The generation of waves in an infinite elastic solid by variable body forces

1956 ◽  
Vol 248 (955) ◽  
pp. 575-607 ◽  
Keyword(s):  
General Solution ◽  
Fourier Transforms ◽  
Equations Of Motion ◽  
Elastic Solid ◽  
Physical Nature ◽  
Graphical Form ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Numerical Work ◽  
Body Forces

This paper is concerned with the determination of the distribution of stress in an infinite elastic solid when time-dependent body forces act upon certain regions of the solid. It is assumed throughout that the strains are small. In §2 a general solution of the equations of motion for any distribution of body forces is derived by the use of four-dimensional Fourier transforms, and from that is derived the general solution for an isotropic solid (§ 3). From the latter solution are deduced the general solution of the statical problem (§4) and the two-dimensional problem (§5). The solution of the equations of motion in the case in which the distribution of body forces is symmetrical about an axis is derived in §6. The remainder of the paper consists in deducing the solution of special problems from these general solutions. In §§7 to 13 some typical two-dimensional problems are considered and exact analytical expressions found for the components of the stress tensor. In §§14 to 16 examples are given of the use of the general non-symmetrical three-dimensional solution derived in § 3, and in §§17 to 19 examples are given to illustrate the use of the general solution of the axially symmetrical problem. A certain amount of numerical work (presented in graphical form) is quoted to give some idea of the physical nature of the solutions.

A CALIBRATED MODEL SEISMIC SYSTEM

Geophysics ◽  
1972 ◽  
Vol 37 (3) ◽  
pp. 445-455 ◽  
Author(s):  
C. N. G. Dampney ◽  
B. B. Mohanty ◽  
G. F. West
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Waves ◽  
Critical Examination ◽  
Two Dimensional ◽  
Linear Filtering ◽  
Analog Model ◽  
Basic Assumptions ◽  
Electronic Circuitry ◽  
Seismic System

Simple electronic circuitry and axially polarized ceramic transducers are employed to generate and detect elastic waves in a two‐dimensional analog model. The absence of reverberation and the basic simplicity. of construction underlie the advantages of this system. If the form of the fundamental wavelet in the model itself, as modified by the linear filtering effects of the remainder of the system, can be found, then calibration is achieved. This permits direct comparison of theoretical and experimental seismograms for a given model if its impulse response is known. A technique is developed for calibration and verified by comparing Lamb’s theoretical and experimental seismograms for elastic wave propagation over the edge of a half plate. This comparison also allows a critical examination of the basic assumptions inherent in a model seismic system.

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