An asymptotic solution of the governing equation for the natural frequencies of a cantilevered, coupled beam model

An asymptotic solution is presented for the natural frequencies, mode shapes of a cantilevered, coupled beam model. A three-term expansion is obtained for the frequency, which shows good agreement with exact values over a wide range of the stiffness parameter α. The first three mode shapes are also presented for large α, and show good agreement for the first and second modes. Agreement for the third mode improves as α gets larger. The modeled structure behaves essentially as a shear beam except in the immediate neighborhood of the ends.