Vibrational eigenmodes of an isotropic cylinder

This page enables you to calculate the frequencies of the vibrations of a free homogeneous isotropic infinite cylinder.

Disclaimer: use at your own risk, in particular for calculations with q≠0 which have not been thoroughly tested.


The results section is updated each time a parameter is modified.

Material , ,

Mode , -1, n=





Reduced frequencies:

With a more recent web browser you would see a plot of the deformation of the cylinder here.


The calculation is carried out by your web browser (javascript). The required parameters are the longitudinal (vL) and transverse (vT) sound speeds and the diameter of the cylinder. You also have to choose the angular momentum (m), the overtone index (n) and the wavevector along z (q).

The displacement corresponding to the vibration is also displayed using the <canvas> element. Only the displacement of the points of the cylinder in the z=0 plane are represented. The equilibrium position is represented by a black dashed circle. The displacement along z are represented varying the opacity (or transparency) of the lines. For q=0, the motion of all the points is either in the z=0 plane or along z. For m≠0, the degeneracy of the mode is 2 and the second mode is obtained by rotating by π/2m.

The displacements can be visualized in 3D using one of the anisotropic calculators. The parameters are filled with the parameters above when following one of the following links:

If you use this calculator, you might be interested in the following papers: L. Saviot, Phys. Rev. B 97, 155420 (2018) and H. Portalès et al., ACS Nano 14, 4395 (2020).