Band Gap Calculation in Phononic Structures

Technical Challenge:
There is a growing demand for applications utilizing periodic band gaps structures. Optimizing the location and width of the band gap is most efficiently performed using an eigenfrequency analysis of the unit periodic cell with Floquet boundary conditions. This analysis requires a complex solver due to the nature of the Floquet boundary conditions (not due to damping). This capability was not readily available in commercial FEA software.

Veryst Solution:
Veryst developed a unit cell model of the two materials making up the phononic structure in COMSOL Multiphysics. We implemented the Floquet boundary conditions in equation form and performed a complex eigenfrequency analysis spanning all wave numbers covering the irreducible Brillouin zone. 

We used the finite element model to optimize the width and location of the band gap. The plot of the natural frequencies above shows the location of the band gap for a specific cell configuration. The figure below is an example that illustrates the effectiveness of the phononic band gap structure in isolating vibrations in its band gap frequency range.

The animation below shows the harmonic response of the structure when excited at the left end at 67.5 kHz. The vibration of the left end is effectively isolated from the rest of the structure.

Vibration isolation using band gap structures