Fundamental frequency of a circular membrane with a strip of small length |
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Authors: | L H Yu |
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Institution: | (1) Department of Mathematics, National Chung Cheng University, 621 Minghsiung, Chiayi, Taiwan, R. O. C. |
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Abstract: | A circular membrane with an arbitrarily placed internal strip of small length is
concerned in this article. A two-term asymptotic expansion for the fundamental frequency of the
membrane, as the length of the strip approaching to zero, is specified. Comparing it with the one
8] derived for the membrane with an internal circular core, it is found that the position of
the internal constraint has more effect than the shape of the internal constraint on the
fundamental frequency. The asymptotic approximation is also compared with the numerical data
computed by the dual boundary element method 2] for a circular membrane of radius 1 with a
radially placed internal strip of length
2c. These two sets of data are in good agreement. The
relative error is less than 3 % as
c
is less than or equal to 0.1, for all positions of the
strip. Moreover, the relative error is less than 1 % as c is less than or equal to 0.01. |
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Keywords: | asymptotic approximation fundamental frequency strip circular membrane |
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