University of Illinois Urbana-Champaign

Accurate finite-difference scheme for elastic wave propagation in circular disk

Cherukuri, Harish P.; Shawki, Tarek G.; El-Raheb, Michael

Permalink

https://hdl.handle.net/2142/112471

Description

Title
Accurate finite-difference scheme for elastic wave propagation in circular disk
Author(s)
  • Cherukuri, Harish P.
  • Shawki, Tarek G.
  • El-Raheb, Michael
Issue Date
1994-11
Keyword(s)
  • Finite-difference Scheme
  • Elastic Wave Propagation
  • Circular Disk
Abstract
A second-order accurate, explicit finite-difference scheme is presented for the numerical solution of elastic wave propagation in a circular disk subjected to traction boundary conditions. One face of the disk is subjected to an axisymmetric loading while the rest of the boundary is traction free. The temporal dependence of the forcing function is taken to be trapezoidal. The governing partial differential equations are discretized by using second-order accurate central difference schemes in both time and space. A stability criterion is derived by using the classical von Neumann analysis. The numerical results are compared with the analytical results from a modal analysis approach and the agreement is excellent till times as late as 60 microseconds where, the traversal time of a longitudinal wave across the thickness is approximately 4.5 microseconds. Further, for timedependent loading, the numerical results are compared with those from a corresponding mixed problem. Our results show that even for time-dependent loading, the solution to the mixed problem approximates the solution to the nonmixed problem accurately for large enough distances in the axial direction.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 777
  • 1994-6033
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112471
Sponsor(s)/Grant Number(s)
Dow Chemical Company Central Research-Engineering Lab 94/11
Copyright and License Information
Copyright 1994 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.