Calculating Vibration Modes of a Cylinder (Drum Shell)?

In summary, the conversation is about acoustic synthesis models of real world instruments and the use of Bessel Function zeros to model circular membranes. However, the sound of a drum comes from the "ring" of the cylinder shell and a method of calculating expected modes using ANSYS was proposed in a 1996 article. The speaker is not familiar with ANSYS and is wondering if there are easier ways to model the problem. They mention another article from 2016 that uses Finite Element Analysis and ask for suggestions on the best way to calculate the modes of thin cylindrical shells.
  • #1
mikejm
40
2
I am working on some acoustic synthesis models of real world instruments. The Bessel Function zeros give the vibration modes of a circular membrane, which can be used to model a drum head or even roughly a cymbal.

However, much of a drum's sound (especially snare) comes from the "ring" of the shell itself, which is a cylinder.

I found an article from 1996 which seems to propose a method of calculating expected modes of a cylinder using ANSYS. I have attached it for reference.

However, I have never used ANSYS and the math is a bit over my head.

I will learn whatever I have to, including ANSYS however, to get the answer. I am wondering how I should go about this and if there are easier ways to model this problem, now that it is 22 years later from that article.

Any suggestions?

Thanks.
 

Attachments

  • Vibrational modes of thick cylinders of finite length.pdf
    367 KB · Views: 392
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  • #2
I found another article from 2016 using Finite Element Analysis to calculate the modes of thin cylindrical shells. Again, though, the math is a bit above me and I'm not sure the best way to approach the modeling required for this problem.

What might be the best way of calculating this?

Thanks again.
 

Attachments

  • Finite Element Analysis of Thin Circular Cylindrical Shells.pdf
    707.2 KB · Views: 382

1. How do you determine the natural frequencies of a cylinder?

In order to determine the natural frequencies of a cylinder, you must first calculate its mode shapes. This can be done using mathematical equations or through finite element analysis. Once the mode shapes are determined, the natural frequencies can be calculated by plugging in the material properties and dimensions of the cylinder into the appropriate equation.

2. What factors affect the vibration modes of a cylinder?

The vibration modes of a cylinder are affected by several factors, including the material properties (such as density, Young's modulus, and Poisson's ratio), the dimensions of the cylinder (such as length and diameter), and the boundary conditions (such as fixed or free ends). Changes in any of these factors can alter the natural frequencies and mode shapes of the cylinder.

3. How do you visualize the vibration modes of a cylinder?

The vibration modes of a cylinder can be visualized through animations or diagrams, which show the deformation patterns of the cylinder at different frequencies. These can be created using software programs or through physical experiments using a strobe light to capture the motion of the cylinder at different frequencies.

4. How can the vibration modes of a cylinder be used in practical applications?

The vibration modes of a cylinder can be used in various practical applications, such as designing musical instruments (like drums), analyzing the structural integrity of cylindrical structures (like pipes or tanks), and understanding the behavior of rotating machinery (like engines or turbines). By understanding the natural frequencies and mode shapes of a cylinder, engineers can optimize designs for better performance and durability.

5. Are there any limitations to calculating the vibration modes of a cylinder?

There are some limitations to calculating the vibration modes of a cylinder. The equations used to determine the natural frequencies assume ideal conditions and may not accurately represent real-world scenarios. Additionally, the assumptions made in the analysis, such as linear behavior and uniform material properties, may not hold true for all types of cylinders. It is important to consider these limitations and validate the results through experiments or simulations.

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