10.15. Programming Implementation (MATLAB/Python)

Try these first

1. 1.

   What is the purpose of discretizing the time vector in programming?

   Hint

   Think about how we measure time in programming.

2. 2.

   Name a function used for numerical integration in MATLAB.

   Hint

   It's short for a mathematical operation.

3. 3.

   What is the Duhamel Integral primarily used for?

   • Analyzing signals
   • Determining system response to dynamic loading
   • Calculating static loads

   Hint

   Think about dynamic versus static conditions.

4. 4.

   Is discretization necessary for numerical integration in programming?

   • True
   • False

   Hint

   Consider how we break down complex calculations.

5. 5.

   A bridge experiences ground motion data recorded at 0.1-second intervals. If the total duration of the recorded data is 10 seconds, outline how you would implement Duhamel's Integral using Python, including necessary steps.

   Hint

   Think about the sequential steps you take when programming.

6. 6.

   Using MATLAB, explain how you would numerically integrate an arbitrary force function over a time vector using Duhamel's approach, detailing at least two functions used.

   Hint

   How do you set up your input values and process them using built-in functions?