Radial Vibrations of Thick‐Walled Hollow Cylinders

Approximate formulas are given for the natural wavelengths associated with the free radial vibration of a thick‐walled, infinitely long, hollow cylinder. For the radial extensional mode, the wavelength is nearly proportional to the nth‐order mean radius, where n depends on Poisson's ratio. For the thickness modes, a correction factor is derived which may be applied to the plane‐wave solution. The extensional solution is also applied to the case of a thin, flat washer.