A GENERALIZED TREATMENT OF THE ENERGETICS OF TRANSLATING CONTINUA, PART I: STRINGS AND SECOND ORDER TENSIONED PIPES

Abstract

The energetics of translating one-dimensional uniform strings and highly tensioned pipes with vanishing bending stiffness and flowing fluid are analyzed for fixed, free and damped boundary conditions. The interaction between the translating continua and the boundary supports causes energy transfer. At a fixed boundary, the transverse component of tension does work, and the Coriolis forces at a free-end cause energy flux into the second-order continuum. Under a symmetric boundary configuration, the total energy of free oscillation varies periodically at the fundamental natural frequency. Asymmetric boundary supports in the pipe-fluid system lead to damped or self-excited motions. At a viscously damped boundary, the condition for maximal energy dissipation, the destabilizing effect of dissipation and the stabilizing effect of negative damping are examined analytically using travelling wave solutions. The energies transferred at the different boundary supports are quantified by energy reflection coefficients which are determined completely by the boundary conditions. Numerical simulations verify the analytically predicted energy variations.