VIBRATIONS

Question 1

What is a freedom class Muu?

Question 2

Why don’t we take into account the damping to calculate the eigenfrequencies?

Answer 2

The solution to the differential equation becomes too complex.

Question 3

How do I get the eigenfrequencies of a system? How many natural frequencies does a system have?

Answer 3

One natural frequency for each degree of freedom. At each natural frequency, the system will vibrate at a different mode shape.

Question 4

Why do we need the modal space?

Question 5

What is the physical interpretation of the modal space?

Question 6

What do we need stiffness or mass normalization for?

Question 7

Where does the frequency compliance response comes from?

Answer 7

The system receives a sinusoidal input. The graph shows the amplitude of the output in terms of the frequency, and it has a maximum in the natural frequency. Resonance

Question 8

How does the response vary if I input the response function in node 1 or in node 3?

Question 9

When do we use the lump mass matrix? And when the consistent mass matrix?

Question 10

How many natural frequencies does a system have?

Answer 10

Only one that depends on the lumped mass and the spring stiffness.

Question 11

Different types of damping:

Answer 11

1. Underdamped: regular damping, amplitude decreases with the time.
2. Overdamped: no vibration will occur. A very viscous fluid is inserted in the damper.
3. Critically damped: limit between both cases, it appears to begin vibrating, but it stops just before any vibration x=0 (middle). Just the limit value of damping enough to suppress vibrations, not so viscous.

Question 12

How do you define the damping ratio?

Answer 12

1. The ratio between the damping coefficient of the system and the coefficient that would result in a critical damping response.
   [damp_ratio=c/c_crit] underdamped: damp_ratio < 1
2. It can also be calculated from the logarithmic decrement.

Answer 13

One degree of freedom for each mass or for each moving coordinate.