LINEAR THEORY OF BOTTOM REFLECTIONS

Abstract

The report gives a detailed mathematical development of a linear, spherical wave theory for the reflection of underwater explosion shock waves from plane bottoms of either fluid or rigid materials. The Laplace transform method of L. Cagniard is used to obtain integral solutions for the pressure which can be evaluated numerically. The paper begins with linear equations of motion and proceeds in steps through the derivation of the wave equations and finally to solutions of the wave equations. Two methods of integrating the integral solution are discussed. First, the real part of the integral is separated from the imaginary part to allow integration using real arithmetic. Second, a method of integration using complex arithmetic is described.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 12, 1969
Accession Number
AD0691248

Entities

People

  • James R. Britt

Organizations

  • Naval Ordnance Laboratory

Tags

DTIC Thesaurus Topics

  • Acoustic Waves
  • Angle Of Incidence
  • Bessel Functions
  • Bottom Waters
  • Complex Variables
  • Computational Science
  • Convolution Integrals
  • Differential Equations
  • Equations
  • Explosions
  • Ordnance Laboratories
  • Plastic Explosives
  • Real Variables
  • Shock Waves
  • Square Roots
  • Theorems
  • Underwater Explosions

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Wave Propagation and Nonlinear Chaotic Dynamics.