IJPAM: Volume 27, No. 1 (2006)

EXACT AND ASYMPTOTIC SOLUTIONS OF THE ELASTIC
WAVE PROPAGATION PROBLEM IN A ROD

Faiz Ahmad$^1$, F.D. Zaman$^2$
$^1$Department of Mathematics
Faculty of Science
King Abdulaziz University
P.O. Box 80203, Jeddah, 21589, KINGDOM OF SAUDI ARABIA
$^2$Department of Mathematical Sciences
King Fahd University of Petroleum and Minerals
P.O. Box 1839, Dhahran, 31261, KINGDOM OF SAUDI ARABIA


Abstract.An exact solution to the problem of elastic wave propagation in a bar of finite length with variable Young's modulus is presented. The problem is reduced to a Bessel equation using the Laplace transform and asymptotic form of the Bessel function is used to obtain the solution in the final form.

Received: March 1, 2006

AMS Subject Classification: 73D05

Key Words and Phrases: elastic waves, variables Young's modulus, exact solution, asymptotic approximation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 27
Issue: 1