Resumen:

He will present a general result concerning flexural wave propagation in periodic layered beams (waveguides), valid for any number of layers in the unit cell, no matter either the material properties or the cross-section geometry.

Beginning with propagation of longitudinal waves in 1D layered media, the connection between spectral analysis of transfer matrices and the possible regimes of wave propagation will be established. The similarities and differences between longitudinal and flexural wave propagation will be highlighted.

For Euler-Bernoulli beams, the symplectic mathematical structure along with positivity of the associated transfer matrix is enough to show that, despite there being two possible propagation modes, one of them is always evanescent (decays exponentially), while the other one can either propagate without decay or decay exponentially.

I will show how this result breaks down in Timoshenko’s beam model, leading to a larger set of possible flexural wave propagation regimes. The implication derived from this fact for the design of bandgaps in layered flexural metamaterials will be addressed.