Transfer
Function

Dr. Layer 1.0 Exercise 9 Time Stepping 
Introduction  
BackgroundIn addition to varying the layer properties, another tool that comes in handy is a variation on the computational side. It involves varying the time step, i.e. the time it takes to repeat each computation. The defining rule for the iteration used in the time stepping procedure for Dr. Layer is the central difference method. It is not an exact procedure but it ensures that the iteration converges, achieves stability, and is close enough to the exact solution. The central difference hinges on a finite difference approximation of velocity and acceleration. The central difference method will “blow up”, giving meaningless results, if the chosen time step is not small enough. Stability of the solution requires _{} Where Dt is the time for each iteration and T is the period (time it takes to complete one cycle of the input loading) The steps below summarize the central difference procedure as it was programmed in Dr. Layer. (Check the time stepping theory for a better understanding of this process) 1a. _{ } 1b. _{} 1c. _{} 1d. _{} 1e._{}
computations for each time step I 2a. _{} 2b. _{} 2c. _{} 2d. _{} Repetition for each time step Substitute i +1 for i and repeat the steps 2a, 2b and 2c. BACK TO TOPObjectiveIt shows on the computation side of the output how varying the time step can significantly affect the speed of result output and stability of our analysis.Things to Do
BACK TO TOPObservationThe numerical procedure becomes unstable at large time steps but it is still a function of the relationship _{}On Your Own
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