2018/03/02 by Andrea Bacigalupoa, Bacigalupoa, Andrea, Marco Lepidi +1 · 1 citation
Engineering · #Acoustic Wave Phenomena Research #Numerical methods in engineering #Vibration and Dynamic Analysis
paper · pdf · doi:10.48550/arxiv.1803.08132
The free propagation of acoustic plane waves through cellular periodic\nmaterials is generally accompanied by a flow of mechanical energy across the\nadjacent cells. The paper focuses on the energy transport related to dispersive\nwaves propagating through nondissipative microstructured materials. The generic\nmicrostructure of the periodic cell is described by a beam lattice model,\nsuitably reduced to the minimal space of dynamic degrees-of-freedom. The linear\neigenproblem governing the wave propagation is stated and the complete\neigensolution is considered to study both the real-valued dispersion functions\nand the complex-valued waveforms of the propagating elastic waves. First, a\ncomplete family of nondimensional quantities (polarization factors) is proposed\nto quantify the linear polarization or quasi-polarization, according to a\nproper energetic criterion. Second, a vector variable related to the periodic\ncell is introduced to assess the directional flux of mechanical energy, in\nanalogy to the Umov-Poynting vector related to the material point in solid\nmechanics. The physical-mathematical relation between the energy flux and the\nvelocity of the energy transport is recognized. The formal equivalence between\nthe energy and the group velocity is pointed out, according to the mechanical\nassumptions. Finally, all the theoretical developments are successfully applied\nto the prototypical beam lattice material characterized by a periodic\ntetrachiral microstructure.\n