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

Abstract

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