Fundamental frequency of a circular membrane with a strip of small length

A circular membrane with an arbitrarily placed internal strip of small length isconcerned in this article. A two-term asymptotic expansion for the fundamental frequency of themembrane, 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 ofthe internal constraint has more effect than the shape of the internal constraint on thefundamental frequency. The asymptotic approximation is also compared with the numerical datacomputed by the dual boundary element method [2] for a circular membrane of radius 1 with aradially placed internal strip of length 2c. These two sets of data are in good agreement. Therelative error is less than 3 % as cis less than or equal to 0.1, for all positions of thestrip. Moreover, the relative error is less than 1 % as c is less than or equal to 0.01.