Spectral analysis of a viscoelastic tube conveying fluid with generalized boundary conditions

We study the spectral problem associated with equation governing small transverse motions of a viscoelastic tube finite length conveying an ideal fluid. The boundary conditions considered are general form, accounting for combination elasticity and viscous damping acting on both slopes displacements ends tube. These include many standard as special cases such clamped, free, hinged, guided conditions. derive explicit asymptotic formulas eigenvalues case generalized specialize these results to clamped in which acts but not displacements. In particular, dependence parameters is investigated.