3.4. Applications in Civil Engineering

Try these first

1. 1.

   What is the form of the equation for free vibration of structures?

   Hint

   Consider the components of mass, damping, and stiffness.

2. 2.

   What happens to the equation when q(x) = 0 in beam deflection?

   Hint

   Think about the implications of having no external load.

3. 3.

   What does the characteristic equation derive from?

   • Homogeneous equation
   • Non-homogeneous equation
   • Both

   Hint

   Consider the nature of the equation you start with.

4. 4.

   True or False: The damping ratio less than one indicates an overdamped system.

   • True
   • False

   Hint

   Think about the definitions of damping ratios.

5. 5.

   Derive the characteristic equation for a cantilever beam subjected to a point load at the free end and discuss the physical implications.

   Hint

   Recall the steps you've learned for deriving equations.

6. 6.

   Analyze the behavior of a damped vibrating structure when subjected to alternating loads and describe the resulting motion.

   Hint

   Consider drawing a phase space to visualize the oscillations.