  Nanophononic materials are promising to control the transport of sound in the
GHz range and heat in the THz range. Here we are interested in the influence of
a dendritic shape of inclusion on acoustic attenuation. We investigate a Finite
Element numerical simulation of the transient propagation of an acoustic
wave-packet in 2D nanophononic materials with circular or dendritic inclusions
periodically distributed in matrix. By measuring the penetration length,
diffusivity, and instantaneous wave velocity, we find that the multi-branching
tree-like form of dendrites provides a continuous source of phonon-interface
scattering leading to an increasing acoustic attenuation. When the wavelength
is far less than the inter-inclusion distance, we report a strong attenuation
process in the dendritic case which can be fitted by a compressed exponential
function with $\beta>1$.
