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.