No abstract

No abstract

No abstract

No abstract

No abstract

No abstract

The recent trend towards micro-patterning of thin film webs brought stricter manufacturing tolerances than traditionally admissible vibration levels. Therefore, one has to consider roll-to-roll (R2R) systems with their system dynamics model encompassing all systems' components, namely, the axially moving web(s), the rotating rolls and other accessories. In this study, the dynamic characteristics of an axially moving web in a two-span R2R system are investigated. Influence of geometrical parameters on the R2R dynamics and the parametric resonances of the moving web is presented. The time variations of web axial speed and webtransmitted tension are rigorously obtained by solving the web tension-roller angular speed equation, which is obtained from the conservation of mass law. The effects of system parameters such as length of the web, inertia of idler roll and radius of the rewinding/unwinding roll on the angular speed and web-transmitted tension have been discussed. The axially moving web was modelled as a string, which was mathematically represented by a second-order hyperbolic partial differential equation. The effect of the frequency of the disturbance at the roll on the web dynamics is also discussed. The transverse vibration response at selected points on the web shows higher frequency fluctuations corresponding to lower transport axial speed. It is noted that instability in the transverse response will occur when the first and second frequencies of the oscillation converge.

A structure with two periodicities can couple up to six modes under a case of simultaneous resonance resulting in a stop-band interaction. The method of multiple scales is employed to analyze the modal coupling in a two-dimensional acoustic duct with rigid periodically undulated walls as well as in an elastic plate having periodically corrugated outerfaces, leading to the coupled-mode equations. The comparison between the three possible cases of interaction under simultaneous resonance are given in terms of the power reflection coefficient spectrum as a function of frequency. The strength of the stop-band interaction is found to be strongly related to the number of direct couplings between the incident and reflected modes.