A GENERALIZED TREATMENT OF THE ENERGETICS OF TRANSLATING CONTINUA .2.BEAMS AND FLUID CONVEYING PIPES

The energetics of translating tensioned beams and fluid transporting p ipes under fixed, simply supported and free boundary conditions are an alyzed in a generalized manner. The conservative and non-conservative forces acting at the boundaries lead to energy transfer between the tr anslating continua and the boundary supports. The forces and associate d convective velocities are identified from the one-dimensional transp ort theorem. The group velocity and the wavenumbers of propagating and evanescent waves in the dispersive continua are defined. The time Var iation of total energy is represented in terms of the impedances and t he reflection coefficients of the propagating waves in the continuum a nd the dynamic stability of the translating continua is discussed base d on the energy expressions. The critical fluid speed in a cantilevere d pipe, at which the resultant energy flux into the pipe at the free e nd vanishes, is determined by the use of travelling wave solutions. (C ) 1997 Academic Press Limited.