Modeling Building Response to Earthquakes: ODE Approach

[aquabug918]

Hey, this isn't a homework question but is more for help with a project. For our D.E. class we decided to model a building while it is being impacted by an earthquake. We are going to make up a building to use. Anyway, we are having trouble relating the earthquake to the building. We know that it has something to do with the resonate frequency of the building. Basically, we just need an equation and a solution (it has to be an ode). We are allowed to exclude variables as long as we explain why. Any suggestions? Thank you!

 

[Nenad]

You can model vibrations using a spring and a damper. If you call the building your mass, take the spring as your foundation or steel memebrs, use the ground or air as your damper and your forcing function on the RHS would be a trigonometric function such as sin or cos. In order to get a solution, you will need to use MUC or VOP, or a Laplace transform. also remember, if you want a constinuous steady state vibration, then you don't need a damper. If you want to see resonance, you need to play around with paramaters until you have an increasing amplitude over time.

 

[J77]

Standard second-order mass-spring-stiffness equation is the way forward - periodic forcing as above.

You could also include effects such as nonlinear damping.