Free bar fundamental vibration relationship length to width

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SUMMARY

The discussion focuses on the fundamental vibration relationship of thin bars, particularly how to extend the existing equation to account for width alongside length and thickness. The user seeks to understand the frequency and node locations as the width approaches the length, noting that a square bar may exhibit different resonance characteristics than a rectangular one. The conversation highlights the complexity of plate vibrations compared to simple beam vibrations, emphasizing the need for a deeper exploration of these concepts.

PREREQUISITES
  • Understanding of fundamental vibration theory
  • Familiarity with the properties of thin bars and their dimensions
  • Knowledge of resonance and node locations in vibrating systems
  • Basic grasp of plate vibration concepts
NEXT STEPS
  • Research "plate vibrations" to explore more complex vibration behaviors
  • Investigate the mathematical modeling of frequency in relation to length and width
  • Examine the impact of geometry on node placement in vibrating bars
  • Study the design considerations for vibraphone bars, including optimal hole placement
USEFUL FOR

Engineers, physicists, and musicians interested in the acoustics of vibrating bars, as well as anyone involved in the design and optimization of musical instruments like vibraphones.

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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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.
 

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