Mode Shapes of a Beam: Exploring Unusual Patterns

In summary, the conversation discusses the confusion over mode shapes in a free vibration analysis on a vertical beam fixed at the ground. It is mentioned that the presence of a lumped mass affects the mode shape, with a vertically straight shape occurring when there is a lumped mass and a curved shape when there is not. The conversation also discusses the analysis of a water tower and the difficulty in understanding the concept of a "vertically straight" mode shape. It is concluded that the mode shape is always superimposed upon the static equilibrium position.
  • #1
roldy
237
2
I have never been able to grasp why certain mode shapes are the way they are. For example, I ran a free vibration analysis on a vertical beam fixed at the ground. The second mode shape is vertically straight. This is the same case whether or not I have a lumped mass at the top of the beam. Any thoughts on what would cause a mode shape to be vertical?
 
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  • #2
roldy said:
For example, I ran a free vibration analysis on a vertical beam fixed at the ground.

The clue might be in the two words "free" and "fixed". Your beam could be either one or the other, but it can't be both at the same time.
 
  • #3
So, are you talking about the vibrations of a flag pole column, with and/without a tip mass? Is that the situation you are trying to analyze here?
 
  • #4
I'm analyzing a water tower. I have three cases that I'm looking into no lumped mass, 20,000 lb, 40,000lb. For each case I use a solid and hollow cross section for the tower. So all together I have 6 runs. For all the runs that have a lumped mass, the second mode is vertically straight. Without a lumped mass I get a curved mode shape. I'm trying to figure out why this is.
 
  • #5
It is pretty difficult to understand what you mean by "vertically straight." What is the deformation shape then? What direction is the vibrational displacement?
 
  • #6
The vibrational displacement is to the left and right. What I mean by vertically straight is that it is perfectly vertical.
 
  • #7
If the static equilibrium position is straight up, then the lateral vibration modes will appear as displacements about this vertical position. The mode shape is always superimposed upon the static equilibrium position.
 

Related to Mode Shapes of a Beam: Exploring Unusual Patterns

1. What are mode shapes of a beam?

Mode shapes of a beam refer to the different patterns that a beam can vibrate in when excited by a force. These patterns are determined by the beam's geometry, boundary conditions, and material properties.

2. Why is it important to explore unusual patterns in mode shapes?

Exploring unusual patterns in mode shapes can provide valuable insights into the behavior of a beam and can help identify potential structural issues. Additionally, studying these patterns can lead to new discoveries and advancements in structural engineering.

3. How are mode shapes of a beam calculated?

Mode shapes of a beam are typically calculated using mathematical equations and numerical methods, such as the finite element method. These calculations take into account the beam's physical properties and boundary conditions to determine the various vibration patterns.

4. What factors can affect the mode shapes of a beam?

The mode shapes of a beam can be influenced by various factors, including the beam's length, cross-sectional shape, material properties, and boundary conditions. Changes in any of these factors can result in different mode shapes and vibrations.

5. How can engineers use knowledge of mode shapes to improve beam designs?

By understanding the mode shapes of a beam, engineers can optimize their designs to minimize unwanted vibrations and improve overall structural performance. This knowledge can also help in identifying potential weak points in a structure and finding solutions to strengthen them.

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