A simple formula for the longitudinal modes in a cylinder

Area of Science:

• Acoustics
• Solid Mechanics
• Wave Propagation

Background:

• The Pochhammer dispersion relation accurately describes wave propagation in cylindrical shells but is complex to solve.
• Understanding wave modes in cylindrical structures is crucial for various engineering applications.

Purpose of the Study:

• To develop a simplified, solvable equation for wave number in cylindrical thin shells.
• To compare the derived modes with Lamb modes in plates and analyze their relationship.

Main Methods:

• Approximation of the Pochhammer dispersion relation for cylindrical thin shells (CT
• Solving the approximate equation to obtain an explicit function for the dimensionless wave number.
• Comparison of the obtained cylinder modes with Lamb modes in plates.

Main Results:

• An approximate equation for cylindrical thin shells was derived, analogous to Lamb modes in plates.
• The dimensionless wave number was obtained explicitly as a function of phase velocity.
• A clear interlacing pattern was observed between longitudinal cylinder modes and Lamb plate modes.

Conclusions:

• The simplified equation provides a practical method for analyzing wave propagation in cylindrical thin shells.
• The interlacing of modes highlights a fundamental connection between wave phenomena in cylindrical and plate structures.
• This research offers a new perspective on the modal analysis of thin shells and plates.