Related Experiment Video
Updated: Apr 12, 2026

Ultrasonic Fatigue Testing in the Tension-Compression Mode
Published on: March 7, 2018
Free and forced vibrations of hollow elastic cylinders of finite length
D D Ebenezer1, K Ravichandran1, Chandramouli Padmanabhan2
1Naval Physical and Oceanographic Laboratory, Thrikkakara, Kochi 682021, India.
Abstract:
An analytical model of axisymmetric vibrations of hollow elastic circular cylinders with arbitrary boundary conditions is presented. Free vibrations of cylinders with free or fixed boundaries and forced vibrations of cylinders with specified non-uniform displacement or stress on the boundaries are considered. Three series solutions are used and each term in each series is an exact solution to the exact governing equations of motion. The terms in the expressions for components of displacement and stress are products of Bessel and sinusoidal functions and are orthogonal to each other. Complete sets of functions in the radial and axial directions are formed by terms in the first series and the other two, respectively. It is therefore possible to satisfy arbitrary boundary conditions. It is shown that just two terms in each series are sufficient to determine several resonance frequencies of cylinders with certain specified boundary conditions. The error is less than 1%. Numerical results are also presented for forced vibration of hollow steel cylinders of length 10 mm and outer diameter 10 mm with specified normal displacement or stress. Excellent agreement with finite element results is obtained at all frequencies up to 1 MHz. Convergence of the series is also discussed.
Related Concept Videos
Forced Oscillations
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
Thin-Walled Hollow Shafts
Simple Harmonic Motion
Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving
Sound as Pressure Waves
The pressure fluctuation depends on the difference in displacements between the successive points in the...

