Vibration related: Rigid body modes

In summary, the conversation revolves around completing an open ended analysis of a problem related to determining the spring stiffness and natural frequencies of a rigid body. The speaker is not asking for a solution, but rather assistance in understanding the significance of a forcing frequency being greater than the second rigid mode frequency and how it helps in determining the spring stiffness or natural frequency of the lumped model. It is clarified that the system has two degrees of freedom and involves both linear and angular displacements. The speaker also expresses gratitude in advance for any help provided.
  • #1
Doctor_Doom
14
0
Hi, everyone. I'm required to complete an open ended analysis of the following problem:

http://imagefrog.net/show.php/146581_image.png http://imagefrog.net/show.php/146581_image.png I'm not requesting a solution, I'm only looking for assistance in relation to determining the spring stiffness and natural frequencies of the rigid body.

Please explain your understanding of the extract highlighted in the above image. Hence, what is significant about the forcing frequency being greater than the second rigid mode frequency? And how does this assist with determining the spring stiffness or natural frequency of the lumped model.

Please note this is a second degree freedom system, with a linear (up-down) displacement and an angular (about the center of mass) displacement.

Thanks in advance!
 
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1. What are rigid body modes?

Rigid body modes refer to the natural modes of vibration of a rigid object, in which the entire object moves as one unit without any internal deformation or relative motion between its parts. These modes are characterized by a constant displacement and rotation of the entire object, and are independent of the object's material properties.

2. How are rigid body modes different from other types of vibration modes?

Rigid body modes are different from other types of vibration modes, such as bending or torsional modes, because they involve the movement of the entire object as one unit. In other types of modes, there is relative motion between different parts of the object, leading to internal deformation and strain.

3. What factors affect the frequencies of rigid body modes?

The frequencies of rigid body modes are affected by the geometry and mass distribution of the object, as well as the stiffness of its supports or connections. The more rigid an object is and the higher its mass, the lower the frequency of its rigid body modes will be.

4. How do rigid body modes impact the design of structures?

Rigid body modes are important to consider in structural design because they can cause unwanted vibrations and potentially lead to structural failure. Designers must ensure that the natural frequencies of rigid body modes are different from the excitation frequencies of the structure, in order to prevent resonance and excessive vibrations.

5. Can rigid body modes be controlled or eliminated?

Rigid body modes cannot be completely eliminated, as they are inherent to the natural movement of any object. However, their frequencies can be shifted or controlled through design modifications, such as changing the mass or stiffness distribution of the object, or by introducing damping elements to dissipate energy and reduce the amplitude of vibrations.

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