Using a Convolution Integral to Compute Earthquake Response
This model illustrates how to use a Convolution element to compute the response of a building to an earthquake given a time history of ground acceleration. The input signal is the time history of acceleration (or accelerogram). In this case the input signal comes from the 1940 El Centro earthquake in Southern California. A Convolution element is used to calculate the building displacement from the earthquake accelerogram.
The Convolution element takes a transfer function and the input signal and produces or calculates the output signal (building displacement in this case). For a transfer function in this example case, the building is treated as a damped spring. A plot of this transfer function is provided in the "Transfer_Function" sub model . The transfer function represents the ratio of a displacement response to the input ground velocity pulse. The result of the convolution and displacement estimate is contained in the Result element "Result_Structure_Response". This shows that the building oscillates during the earthquake with the oscillations dying out in about 15 seconds.