STABILITY AND LIMIT-CYCLES OF PARAMETRICALLY EXCITED, AXIALLY MOVING STRINGS

Tension fluctuations are the dominant source of excitation in automoti ve belts. In particular designs, these fluctuations may parametrically excite large amplitude transverse belt vibrations and adversely impac t belt life. This paper evaluates an efficient discrete model of a par ametrically excited translating belt. The efficiency derives from the use of translating string eigenfunctions as a basis for a Galerkin dis cretization of the equations of transverse belt response. Accurate and low-order models lead to simple closed-form solutions for the existen ce and stability of limit cycles near para metric instability regions. In particular, simple expressions are found for the stability boundar ies of the general nth-mode principal parametric instability regions a nd the first summation and difference parametric instability regions. Subsequent evaluation of the weakly nonlinear equation of motion leads to an analytical expression for the amplitudes (and stability) of non trivial limit cycles that exist around the nth-mode principal parametr ic instability regions, Example results highlight important conclusion s concerning the response of automotive belt drives.