Discussion Forum

Dear all,
I am researching on using the Bloch-Floquet Wave Propagation method to seek the effective modulus matrix of one unit cell (7*7*7 mm), made of built-in isotropic carbonate material. The shape of the unit cell is overall isotropic, like a simple 12-frame cubic model with uniform shape of wall. The cross section of the wall is 0.7 mm, with shape of square.

As for the B-F Wave Propagation Method, I set Floquet Period conditions on all three directions (x, y and z). A B-F wave is propagated through the unit cell in the x-direction. When the wave number is parametric swept and approaching zero, I get the first three eignefrequencies of the unit cell. The first two refer to the shear wave and the last refers to the polarized wave. When getting the slope of each eigenfrequencies to the wave number, I derive the phase velocities of shear waves and polarized wave. As the model is isotropic geometrically, the first two phase velocities should be the same.

By using these three phase velocities, I can figure out the effective modulus matrix of the unit cell.

For the Floquet periodic condition setting, I sweep a parameter, kx , referring to the wave number of the B-F wave in the x-direciotn. The B-F wave propagates along the x-direction, I put kx on the x-direction wave number definition of all the three periodic conditions, while set 0 on y- and z-directions.

I mesh the entire model with Free-Triangle on all the boundaries and Free-Tetrahedral on the remaining, with the Finer size.

For comparison, I also run a static test on the unit cell so I can derive moduli. However, when I compare the value of effective modulus matrices in two ways, I find that result of the B-F Wave Propagation Method is far from the reality. The x-direction Young's modulus is okay, meaning that the polarized B-F wave in the x-direction is perfectly simulated. However, the Young's moduli on the other two directions are just 7-8% of the theoretical value, pointing out that the phase velocities of two shear waves, as well as the first two eigenfrequencies of the unit cell under B-F wave propagation method, are much lower than the real value.

In one word, the simulated phase velocity of the polarized B-F wave is great, but that of the two shear waves are much lower than the supposed value. I cannot upload images onto my thread so this thread is not that understandable. Does anyone have any idea that which part may go wrong?

Thanks.