The state vector approach to the wave analysis of the forced vibration of a cylindrical shell. Part II: Finite cylinders in vacuum

The vibrational response of a circular cylindrical shell of a finite length in vacuum, excited by a point force of arbitrary orientation, is studied by using wave techniques and the state vector formalism. Because of the geometric symmetry, both the point excitation and the resulting vibrational response can be decomposed into Fourier circumferential components. The forced vibration is expressed as a linear superposition of ‘‘waveguide modes’’ with different circumferential numbers both propagating and attenuating. State vector techniques are used to identify the ‘‘reflection matrices,’’ characterizing, for each circumferential number, the linear relationship between the complex amplitudes of the waves ‘‘ingoing’’ to and ‘‘outgoing’’ from the end terminations. The discontinuity conditions at the point excitation provide the last set of equations needed for the complete identification of the vibrational response. A few particular cases, including a termination consisting of rigid disks having masses and moving as rigid bodies, are discussed in detail. Numerical results are presented. Because the approach is essentially analytical, the computational complexity is substantially reduced with respect to purely numerical methods, and largely independent of the cylinder length.