On the completeness of a method of potentials in elastodynamics

Authors:
Ronald Y. S. Pak and Morteza Eskandari-Ghadi

Journal:
Quart. Appl. Math. **65** (2007), 789-797

MSC (2000):
Primary 74B05, 35Q72; Secondary 35L05

DOI:
https://doi.org/10.1090/S0033-569X-07-01074-X

Published electronically:
October 17, 2007

MathSciNet review:
2370361

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, the theoretical foundation of a compact scalar potential method in three-dimensional classical elastodynamics is substantiated. Beginning with a derivation of two basic lemmas on the decomposition and integration of wave solutions and vector fields which are apt to be of interest to general mechanics and analysis, the treatment proceeds to a proof of the completeness of the proposed representation as well as its extension to non-zero body forces.

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Additional Information

**Ronald Y. S. Pak**

Affiliation:
Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, Colorado 80309-0428

Email:
pak@colorado.edu

**Morteza Eskandari-Ghadi**

Affiliation:
Civil Engineering Department, University of Science and Technology of Mazandaran, Iran

Email:
ghadi@ustmb.ac.ir

DOI:
https://doi.org/10.1090/S0033-569X-07-01074-X

Keywords:
Elasticity,
completeness,
potentials,
mechanics,
wave equation,
vector calculus,
elastodynamics,
Helmholtz,
solenoidal field,
Laplacian

Received by editor(s):
May 24, 2007

Published electronically:
October 17, 2007

Dedicated:
A tribute to Eli Sternberg

Article copyright:
© Copyright 2007
Brown University

The copyright for this article reverts to public domain 28 years after publication.