Babak Rostami Dogolsara - Faculty of Electrical and Computer Engineering, Tarbiat Modares University, P O Box ۱۴۱۱۵-۱۹۴
Ali Abdollahi
Mohammad Kazem Moravvej-Farshi

Two-dimensional phononic crystals (PnCs) are composite materials made of periodic distributions of infinitely long bars of mass density ρA embedded in a matrix of mass density ρB. Allmechanical properties of such PnCs follow the lattice periodicity. Mechanical waves propagatethroughout these periodic structures as elastic or acoustic waves. For a given crystal structure, theremay exists a phononic bandgap over a frequency range in which normally incident mechanicalwaves cannot propagate. Existence and the size of this phononic bandgap depend on the densitycontrast Δρ=(ρB−ρA), sound velocity contrast, lattice fill factor and topology. Employing plane wave expansion (PWE) method, we have studied the filtering properties 2D PnCs made of periodic arraysof solid cylindrical rods of radius ro in a solid background arranged in both square and triangularlattices. In order to see how lattice topology would affect the filter property, we have replaced the solid cylindrical rods by hollow cylinders of the same outer radii and various inner radii 0.1 ro≤ri≤0.75. The range of operating frequency bandwidth for the PnC filters with square lattice of constants amade of solid rods of epoxy with ρA=1142 kg/m3and radii 0.43a≤ro≤0.49a embedded in tungsten with ρB=19250 kg/m3 is found to be 0.066×(πcT/a)≤Δω≤0.27×(πcT/a) operating within the frequencyrange of 0.85×(πcT/a)≤ω≤1.16×(πcT/a), wherein cT is the transverse sound velocity. It isworth noting that when the solid rods are replaced by hollow cylinders of the same outer radii and the inner radius of ri=0.5ro, dependencies of the filter’s bandwidth and center frequency on the innerradii are both nonlinear. Simulations show that as ri increases Δω and ω first increase until the innerradii reaches to half of the outer radii for which the filter bandwidth is Δω=0.383×(πcT/a) centered about ω=1.22×(πcT/a). Then as the inner radii increase further, the filter bandwidth becomes narrower until the filter stops functioning for ri≥0.75ro.

Acoustic Filter, Phononic Bandgap (PnBG), Phononic Crystal (PnC