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首页> 外文期刊>ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees >Fundamental frequency of a circular membrane with a strip of small length
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Fundamental frequency of a circular membrane with a strip of small length

机译：带长短的圆形膜的基本频率

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摘要

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.
机译：本文涉及一种带有任意长度的内部带的圆形膜片。当条带的长度接近零时，指定了膜基频的两个渐近展开。将其与具有内部圆形芯膜的推导[8]进行比较，发现内部约束的位置比内部约束的形状对基频的影响更大。渐近逼近也与通过双重边界元法[2]计算的数值数据进行了比较，该数值数据是半径为1的圆形膜片，径向放置的内部带长为2c。这两套数据非常吻合。对于带材的所有位置，当c小于或等于0.1时，相对误差小于3％。此外，当c小于或等于0.01时，相对误差小于1％。

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