6.6. Derivation of Equation of Motion for Base Excitation

Try these first

1. 1.

   Define base excitation in your own words.

   Hint

   Think of how earthquakes affect buildings.

2. 2.

   What is a pseudo-force?

   Hint

   Consider forces acting on a mass during ground acceleration.

3. 3.

   What is the equation of motion for a mass under base excitation?

   Hint

   Recall the forces acting on the system.

4. 4.

   True or False: Base excitation affects the inertial response of structures during earthquakes.

   • True
   • False

   Hint

   Consider how structures respond when the base moves.

5. 5.

   Consider a mass-spring-damper system with a mass of 100 kg, a damping coefficient of 10 Ns/m, and a spring constant of 500 N/m. Derive the equation of motion if subjected to a ground motion described as an acceleration function $u_g(t) = 0.05sin(2 t)$. What will be the implications this has on the system's response?

   Hint

   Try substituting values into the equation and consider the effects of each term.

6. 6.

   In a building designed to withstand seismic forces, the parameters $k$ and $c$ were determined to be 1000 N/m and 50 Ns/m. How would altering these values affect the resulting equation of motion and the structure's ability to resist base excitation?

   Hint

   Think about how the terms of the equation are interrelated to influence the structure's response.