Propagation of Longitudinal Tension in a Slender Moving Web
Strain propagation in a web that isn’t moving
Current models
Then, why consider propagation?
Earlier work
Assumptions
Assumptions (Cont.)
The dependent variable
Independent variables
The boundary conditions
The PDE Model
The Euler Description
The Euler description (Cont.)
The transformation equations
The transformation equations (Cont.)
The Wave equation for a moving medium
The solution
The P.D.E. solution (Cont.)
Step input
Step response
Comparison with the O.D.E. model
O.D.E. comparison (Cont.)
O.D.E comparison (Cont.)
A high-resolution view of the solutions
Propagation along the span
Step response at high speed
Propagation at high speed
Response to a single pulse
Response to a single pulse (Cont.)
Transport damping
Energy transfers
A high-speed view
Repetitive pulses
Sinusoidal disturbances
Sinusoidal disturbances (Cont.)
High speed behavior
High speed behavior (Cont.)
Conclusions
Conclusions (Cont.)
Condlusions (Cont.)
When is a web slender?
PPT Slide
How much does web speed affect longitudinal natural frequencies?
What are typical values for longitudinal resonant frequencies?
What frequencies can be expected for disturbances?
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