Thursday, July 25
11:30 AM

Inverse Problems: Formulas for Finding Properties of Vibrating Systems from Nodal Lines and Surfaces

This presentation will focus on the inverse problem of finding properties of two and three dimensional vibrating systems. This problem has important applications in nondestructive testing and design. The speaker will discuss a new data set...the position of the nodal lines or nodal surfaces. The nodes are places where the system does not vibrate when it's excited at a natural frequency. The nodal positions are determined by a Doppler shift measurement. She will show three simple formulas for determining the amplitude of a force on a two dimensional membrane or a three dimensional acoustic medium, and conjecture similar simple formulas for finding the density or soundspeed and support the conjectures with numerical experiments. Previously measured data sets are the natural frequencies for the vibrating system or the displacement of a single modeshape at all points of the system.

Joyce R. McLaughlin
Ford Foundation Professor of Mathematics
Rensselaer Polytechnic Institute

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MMD, 5/20/96