What is Dynamic Analysis and Simulation ?

 Long elastic bodies such as conveyor belts operate on rolling objects such as idlers or pulleys.  As a result, the system not only exhibits distributed mass and elasticity along its length due to rolling friction, it also contains variable mass on the material carrying side comapred to the return side.

 On starting such a complex mass (or its rapid stopping) creates a distributed stress front of high and lower relative tensions.  High tensions can cause belts to fail, while low dynamic tensions can cause severe buckling and structure destruction.

 Analysis using the  "Wave Equation"  in 1982 (Harrison) shows wave action at frequencies that differ with frequencies that are not "pi" commensurate.  Differential equations like Uxx - kUtt = F(x,t) (the wave equation) predict displacements U, velocities Ut and dynamic tensions sUx (added to the steady state or running tensions).  Here, s = stress, k = 1/v^2 where v is the speed of sound in a belt material - typically 1000 to 3000 m/s).

 However, the treatment of moveable boundary conditions such as take-ups is tricky, mathematically, with wave equations.   Use of connected mass-spring elements with the appropriate dampling can be used to simulate dynamic forces using an algorithm that progressively tracks and stabilizes the displacements vereywhere along the simulated belt.  Mass differences are accommodated.

 In vibration theory, Continuum vs. Mass-Spring methods are identical, if set up correctly.

 The slide show aside : Demonstrates the mass-spring simulation method with the added feature of dynamic look-ahead convergence equations (Harrison 2007).

 The new model is fast  : A 16 element mass-spring simulation can compute all velocities and forces in the 16 springs in less than 1 second.  Eliminates need for a separate "Static Analysis"