Seminar Series - 1996-1997

Spectral Analysis of Constrained Translating Continua

Dr. Weidong Zhu
Department of Mechanical and Automation Engineering
The Chinese University of Hong Kong
 
Sponsored by the Department of Engineering Mechanics

Date:  Friday, November 15, 1996
Time:  3:30 p.m.
Place:  306 Bancroft Hall


Flexible machine components such as high speed transmission belts, band saws, magnetic tapes, textile fibers, and tramway cables are commonly referred to as axially moving materials. When they are coupled to stationary constraints, such as a recording head in tape drives and a guide bearing in band saws, dependence of the natural frequencies and damping rates on the constraint parameters becomes an important design consideration. In control of axially moving material vibration, though some criteria have been previously derived for design of pointwise controllers which ensure that all eigenvalues lie strictly in the left half plane, the distances of eigenvalues of controlled continuous systems from the imaginary axis, especially the infinite number of high modes, remain unknown. These distances measure the degree of controllability of the distributed systems considered herein.

In the present study new spectral analyses are developed for constrained translating strings and tensioned Euler-Bernoulli beams. Closed-form, asymptotic solutions to all the eigenvalues are derived explicitly from the characteristic equations of the constrained systems. Influences of the system parameters on the distribution of eigenvalues are identified. Necessary and sufficient conditions which ensure a uniform stability margin for all the modes of vibration are determined. Other research activities on the dynamics and control of translating continua will also be discussed.


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