17. Using SciPy’s ODEINT solver
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Multi-Degree of Freedom Dynamics, Modal Analysis and Seismic Response
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1. Welcome and preliminaries
1. Introduction and course overview
3
2. Course prerequisites and do I need to know Python?
Support and Lecture Q&A (Please read!)
3. Getting your coding environment set up
2. Introduction to ground motion modelling
4. Section overview
5. Overview of earthquake ground motion
6. Capturing the influence of ground motion
3
6.1 Jupyter Notebook - (lecture 6)
7. Motion transmissibility and isolation
7.1 Jupyter Notebook - (lecture 7)
8. Simulating ground motion response
8.1 Jupyter Notebook - (lecture 8)
9. Realistic ground motion response
10. Integrating ground acceleration
10.1 Jupyter Notebook - (lectures 9-10)
11. Introduction to response spectra
3. Modelling Multi-DoF Dynamic Systems
12. Section overview
13. Introduction to MDoF systems
3
14. MDoF Equations of Motion
3
15. Direct integration of the coupled EoM
16. Solving the coupled EoM by direct integration
6
17. Using SciPy’s ODEINT solver
9
17.1 Jupyter Notebook - (lectures 16-17)
Mid-course check-in
4. Modal Analysis and Decoupling the Equations of Motion
18. Section overview
19. What is modal analysis and how does it help us?
20. Finding natural frequencies and mode shapes
7
20.1 Jupyter Notebook - (lecture 20)
21. Matrix representation and the eigenproblem
2
21.1 Jupyter Notebook - (lecture 21)
22. Modal matrix and mass normalisation
5
22.1 Jupyter Notebook - (lecture 22)
23. Orthogonality and Decoupling Equations of Motion
24. Modal superposition - forced vibration
3
25. Comparing modal superposition with direct integration - forced response
10
26. Visualising the forced vibration response
3
26.1 Jupyter Notebook - (lecture 24-26)
27. Modal superposition - free vibration
28. Compare modal superposition with direct integration - free vibration
3
28.1 Jupyter Notebook - (lecture 27-28)
5. Damping Orthogonality
29. Section overview
3
30. Rayleigh damping
11
31. General determination of the damping matrix
32. Calculating the damping matrix
3
32.1 Jupyter Notebook - (lecture 32)
33. Direct integration versus modal superposition for a damped system
33.1 Jupyter Notebook - (lecture 33)
6. Bringing it all together: N-storey response to earthquake ground motion
34. Section overview
35. Equations of motion N-storey shear building
36. Automating modal analysis for NDoF
37. Ground motion response using modal superposition
3
38. Base shear and overturning moments
7
39. Visualising the structural response for NDoF
12
39.1 Jupyter Notebook - (lecture 35-39)
40. Course wrap up and completion certificate