Accession Number : AD0697736

Title :   LONGITUDINAL WAVE PROPAGATION ON A TRAVELING THREADLINE I,

Corporate Author : IOWA UNIV IOWA CITY DEPT OF MECHANICS AND HYDRAULICS

Personal Author(s) : Ames,W. F. ; Vicario,A. A. , Jr

Report Date : NOV 1968

Pagination or Media Count : 27

Abstract : The nonlinear equations of motion governing the longitudinal wave propagation on a moving elastic string are presented. These are analyzed using three mathematical techniques. The first employs a von Mises type of transformation from the physical to the particle function - time plane. The resulting equations are shown to be equivalent to the linear wave equation thus permitting construction of the general solution. Secondly, auxiliary functions are employed but the resulting Monge-Ampere equation is more difficult to solve than the original quasilinear equation. Lastly the quasilinear theory provides a vehicle for transforming the problem into a linear problem for time and space in the Riemann invariants plane. An example pure initial value problem, solved exactly, displays the effect of a critical velocity on the system. (Author)

Descriptors :   (*POWER TRANSMISSION BELTS, VIBRATION), (*MECHANICAL WAVES, PROPAGATION), WIRE, CORDAGE, OSCILLATION, WAVE FUNCTIONS, EQUATIONS OF MOTION, PROBLEM SOLVING, VELOCITY

Subject Categories : Machinery and Tools
      Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE