### ASA 127th Meeting M.I.T. 1994 June 6-10

## 4pSAb2. A tale of two approaches: The response of a beaded string.

**G. Maidanik
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J. Dickey
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**
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*CDNSWC, Bethesda, MD 20084-5000
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In one approach, the response is given by the superposition of two terms.
The first is merely the response of the unbeaded infinite string. The remaining
terms involve elements of the first term mingled with parameters that describe
the beads; e.g., the impedance that each bead presents to the infinite string
and the position of that bead on the string. In the other approach, the bays
(portions of the string that lie between adjacent beads) are treated as
individual dynamic systems. These dynamic systems are coupled at the beads. The
model is then a cascade of coupled one-dimensional dynamic systems. In this
approach, the response is a vector composed of the response in each bay. The
response vector is composed of the superposition of a direct response vector
and a reverberant response vector. The reverberant response itself is composed
of two distinct terms. The formalisms in the two approaches appear very
different although they yield identical responses when subjected to the same
external drive. This identity in the responses is illustrated by computations.
Unlike the Sommerfeld--Watson transformation that relates the modal and the
wave approaches to describing the response of a finite string, as yet, no
analogeous analytical transformation is found to relate the two approaches of
concern here.