Step-by-step piece-wise exact method for linear SDOF systems using Python

Overview:

To use this method, consider an input waveform of frequency 1Hz sampled at 0.01 sec. We want to determine the displacement response using PEM.

Formulation:

The following following formulations is used. The constant are taken from Humar, 2002.

\[u_{n+1} = A\:u_n + B\:\dot{u}_{n} +C\:p_n + D\:p_{n+1}\] \[\dot{u}_{n+1} = A_1\:u_n + B_1\:\dot{u}_n + C_1\:p_n + D_1\:p_{n+1}\]

Code:

Example Response:

The following response is obtained: