In the industrial film casting process with the two-stage cascade (velocity and tension controlled) loop, various aspects of nonlinear dynamics and chaotic motion have been investigated solving simple 1-D viscoelastic model. Most of the extensional deformation processes exhibit sustained-periodic oscillations or stable limit cycles of state variables (called draw resonance instability) beyond the critical onset, even if they are conventionally controlled systems. Besides such well-known instability, some intriguing nonlinear dynamic phenomena such as period-doubling and eventual chaotic motion of film thickness and width could be observed when a disturbance is imposed in the second tension-controlled system. In other words, the bifurcation mode is dramatically changed by a sinusoidal disturbance under the combined velocity-tension control condition in contrast to only constant take-up velocity condition inducing a supercritical Hopf bifurcation of draw resonance.

Frequency response of the nonisothermal viscoelastic film blowing process to the ongoing sinusoidal disturbances has been investigated using transient simulation techniques. Of the many state variables exhibiting resonant peaks with the input frequency, amplitude ratio of the film cross-sectional area at the freezeline height has been used as an indicator of the process sensitivity. The effects of operating conditions and viscoelasticity on the sensitivity have been scrutinized around the middle point of three multiple steady states under the given conditions. The sensitivity results have been interpreted through their correlation with results from linear stability analysis. Increasing draw ratio generally makes the system more sensitive to sinusoidal disturbances, whereas the cooling induces more sensitive or less sensitive system, according to the location of a steady state. Also, the viscoelasticity makes the system of extensional thickening fluids more sensitive at low Deborah number and less sensitive at high Deborah number.