Resonances of Cylindrical Shells with uniform radial pressure

In summary, the conversation discusses the problem of calculating the compliance and modal pattern of a uniform cylindrical shell under uniform radial pressure and offers suggestions for resources that may provide solutions to this problem.
  • #1
thadman
27
0
I have picked up "Roark's Formulas for Stress and Strain" and "Mechanical Vibrations" and have been unable to reach resolution on a particular problem.

I am interested in the behavior of a uniform cylindrical shell (cylinder diameter >> wall thickness) rigidly clamped at both ends wherein uniform radial pressure is applied over the surface area of the cylinder.

How can I calculate the compliance and modal pattern of such an arrangement?

Thanks,
Thadman
 
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  • #2
you're trying to build a cylindrical ESL speaker aren't you ?

i was actually thinking of making a spherical one but it's probably not worth the trouble ...
 
  • #3
Try:

Soedel, W., Vibrations of Shells and Plates, CRC Press (2004)

Timoshenko, S., Theory of Plates and Shells, McGraw Hill (1959)

Both of those have solutions for thin walled cylinders if memory serves correctly.
 

1. What is the significance of studying resonances of cylindrical shells with uniform radial pressure?

The study of resonances of cylindrical shells with uniform radial pressure is important in understanding the vibrations and acoustic behavior of cylindrical structures, such as pipes, tanks, and musical instruments. It can also have practical applications in engineering and design of such structures.

2. How do resonances occur in cylindrical shells with uniform radial pressure?

Resonances in cylindrical shells with uniform radial pressure occur when the natural frequency of the shell matches the frequency of the external excitation. This results in a build-up of vibrations and can lead to amplification of sound or structural failure if not properly controlled.

3. What factors affect the resonances of cylindrical shells with uniform radial pressure?

The resonances of cylindrical shells with uniform radial pressure are influenced by several factors, including the material properties of the shell, the thickness and geometry of the shell, the nature of the external pressure, and any internal or external damping present.

4. How are resonances of cylindrical shells with uniform radial pressure calculated?

The resonances of cylindrical shells with uniform radial pressure can be calculated using analytical methods, such as the Rayleigh-Ritz method, or numerical techniques, such as finite element analysis. These methods take into account the shell's properties and boundary conditions to determine the natural frequencies and corresponding mode shapes.

5. How can resonances of cylindrical shells with uniform radial pressure be controlled?

Resonances of cylindrical shells with uniform radial pressure can be controlled through various methods, including changing the material properties, altering the geometry or thickness of the shell, adding damping materials, or applying external forces or constraints. These methods can shift the natural frequencies of the shell away from the excitation frequency and reduce the amplitude of vibrations.

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