Free bar fundamental vibration relationship length to width

In summary, the conversation discusses finding the fundamental for thin bars and extending the accuracy of the approximate equation to include width. It also mentions the difference in node locations and frequency between a square and rectangle bar, and the best placement for holes on square vibraphone bars. The suggestion to search for "plate vibrations" is given as a solution.
  • #1
Ross M Mccullough
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When finding the fundamental for thin bars, the approximate equation (http://hyperphysics.phy-astr.gsu.edu/hbase/Music/barres.html) only refers to the length and thickness when calculating. I'm trying to figure out the frequency and node location along the length and width of the fundamental vibration as the width approaches the same value as the length. Basically, I want to extend the accuracy of this equation to include width. Intuitively, it seems as though a square bar will not retain the same node locations or frequency as a rectangle. As the bar's width begins to exceed the length, eventually that direction will begin to define the fundamental resonance. Trying to root out my misconception or understand the relationship of length, width, and thickness. Any resources, intuitive spews, or pure math are welcome. Imagine square vibraphone bars, where would be the best place to put holes? would the same relationship .224L still be the node point for both length and width? I look forward to this discussion.
 
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  • #2
You are looking for a plate vibration solution, a more complicated matter than a simple beam vibration. Search on the subject "plate vibrations," and I think you will find what you need.
 

1. What is the free bar fundamental vibration relationship length to width?

The free bar fundamental vibration relationship length to width is a scientific concept that describes the relationship between the length and width of a vibrating bar. It states that the fundamental frequency of vibration of a bar is inversely proportional to its length and directly proportional to its width.

2. Why is the free bar fundamental vibration relationship length to width important?

This relationship is important because it helps scientists and engineers understand the behavior of vibrating bars and how their dimensions affect their vibrations. It is also used in the design and optimization of structures and machines that rely on vibrating bars, such as musical instruments and bridges.

3. How is the free bar fundamental vibration relationship length to width calculated?

The relationship is calculated using the equation f = (1/2L) x (W/ρ)^1/2, where f is the fundamental frequency, L is the length of the bar, W is the width of the bar, and ρ is the density of the material. This equation is derived from the wave equation and the boundary conditions of a vibrating bar.

4. Does the free bar fundamental vibration relationship length to width hold true for all materials?

No, this relationship is only valid for homogenous, isotropic materials, meaning materials that have the same properties in all directions. Real-world materials may have variations in their properties, which can affect their fundamental vibration frequency.

5. How does the free bar fundamental vibration relationship length to width affect practical applications?

The relationship has many practical applications, such as in the design of musical instruments and industrial machines. For example, in the design of a guitar, the length and width of the strings and fretboard must be carefully considered to produce the desired fundamental frequency and sound. In industrial machines, such as vibrating screens, the dimensions of the vibrating bars must be optimized to achieve efficient and effective performance.

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