KRYLOV, V.V. and GEORGIEV, V., 2007. New approach to investigation of resonant vibrations of noncircular shells based on the theory of coupled waveguides. Journal of Mechanics of Materials and Structures, 2 (9), pp. 1761-1771.
In the present paper a new simple method of analytical description of resonant vibrations of finite noncircular cylindrical shells is developed. The method is based on the theory of coupled waveguides formed by quasiflat areas of the same noncircular shells having an infinite length (depth). The physical reason for guided wave propagation along quasiflat areas of such shells is the difference between flexural wave velocities in their quasiflat and curved areas, respectively. Using asymptotic expressions for flexural wave velocities in circular shells with different radii of curvature, approximate dispersion equations are derived for waves propagating in such waveguides and their corresponding coupling coefficients. After that, considering shells of finite length, the transition is made from the coupled guided modes to the coupled resonant vibrations of the shell. The obtained resonant frequencies and spatial distributions of the resulting vibration modes are in good agreement with the results of finite element calculations.