Calculation of the phase velocities of three-dimensional flexural waves in isotropic cylindrical bars and shells using the Debye and Debye-type potentials

Using the Debye and Debye-type potentials, two representations of the vector potential of the displacement vector are considered for isotropic cylindrical bars and shells. With this approach, characteristic equations are obtained for the wavenumbers of three-dimensional flexural waves propagating in the aforementioned bodies; the phase velocities of such waves are calculated.