Linear transverse vibration of an axially moving string-particle system

• Published in: The Journal of the Acoustical Society of America Vol. 84; no. 3; pp. 963 - 969
• Main Authors: WICKERT, J. A, MOTE, C. D. JR
• Format: Journal Article
• Language: English
• Published: Woodbury, NY Acoustical Society of America 01-09-1988; American Institute of Physics
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Transversal vibration; Vibration; Point mass; Cable transportation; Mechanical system; String; Modeling
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/1.396611

A monocable ropeway system is modeled as an axially moving string that transports an attached mass particle. The linear transverse equation of motion is derived, and the response of the string–particle system is represented as d’Alembert waves that are scattered by the point mass. Three solutions of an approximate eigenvalue problem that is valid for small transport speed and particle mass are presented: a closed-form asymptotic solution for vanishing particle mass, roots of a characteristic equation, and solutions obtained from a Galerkin discretization. In general, the spectrum is complex and depends on the axial position of the particle. The discretized equations of motion are numerically integrated, and the free response of the discrete model is compared to that predicted by the approximate eigensolutions.