A GENERALIZED TREATMENT OF THE ENERGETICS OF TRANSLATING CONTINUA, PART II: BEAMS AND FLUID CONVEYING PIPES

✍ Scribed by S.-Y. Lee; C.D. Mote; Jr.

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 265 KB
• Volume: 204
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1996.0946

✦ Synopsis

The energetics of translating tensioned beams and fluid transporting pipes under fixed, simply supported and free boundary conditions are analyzed in a generalized manner. The conservative and non-conservative forces acting at the boundaries lead to energy transfer between the translating continua and the boundary supports. The forces and associated convective velocities are identified from the one-dimensional transport theorem. The group velocity and the wavenumbers of propagating and evanescent waves in the dispersive continua are defined. The time variation of total energy is represented in terms of the impedances and the reflection coefficients of the propagating waves in the continuum and the dynamic stability of the translating continua is discussed based on the energy expressions. The critical fluid speed in a cantilevered pipe, at which the resultant energy flux into the pipe at the free end vanishes, is determined by the use of travelling wave solutions.