TRAVELING-WAVE DYNAMICS IN A TRANSLATING STRING COUPLED TO STATIONARYCONSTRAINTS - ENERGY-TRANSFER AND MODE LOCALIZATION

Energy transfer and mode localization in a translating string, coupled to a stationary spring-mass-damper system, are analyzed using traveli ng waves. The string tension and the non-conservative centrifugal forc e at the constraint lead to energy transfer between the translating co ntinuum and the stationary constraint. By calculating energy contained in a harmonic wave before and after interacting with the constraint, energy transferred at the constraint is quantified in terms of constra int parameters. At an undamped constraint, energy is transmitted when a downstream (forward) wave impinges on the constraint. At a damped co nstraint, energy dissipated by damping, as well as energy flux by the tension and centrifugal force, contribute to the energy variation at t he coupling point. When the damping coefficient of the damped constrai nt equals twice the impedance of the string, vibration energy is maxim ally dissipated. Asymmetry caused by the constraint localizes vibratio n modes into a downstream or upstream region. The degree of localizati on in each vibration mode is described in terms of the reflection coef ficient and the constraint location. The effect of the constraint para meters on the mode localization and veering of natural frequency loci are also examined. (C) 1998 Academic Press Limited.