A GENERALIZED TREATMENT OF THE ENERGETICS OF TRANSLATING CONTINUA .1.STRINGS AND 2ND-ORDER TENSIONED PIPES

The energetics of translating one-dimensional uniform strings and high ly tensioned pipes with vanishing bending stiffness and flowing fluid are analyzed for fixed, free and damped boundary conditions. The inter action between the translating continua and the boundary supports caus es energy transfer. At a fixed boundary, the transverse component of t ension does work, and the Coriolis forces at a free-end cause energy f lux into the second-order continuum. Under a symmetric boundary config uration, the total energy of free oscillation varies periodically at t he fundamental natural frequency. Asymmetric boundary supports in the pipe-fluid system lead to damped or self-excited motions. At a viscous ly damped boundary, the condition for maximal energy dissipation, the destabilizing effect of dissipation and the stabilizing effect of nega tive damping are examined analytically using travelling wave solutions . The energies transferred at the different boundary supports are quan tified by energy reflection coefficients which are determined complete ly by the boundary conditions. Numerical simulations verify the analyt ically predicted energy variations. (C) 1997 Academic Press Limited.