Abstract
Insight into phononic bandgap formation is presented using a first principles-type approach where phononic lattices are treated as coupled oscillators connected via massless tethers. The stiffness of the tethers and the mass of the oscillator are varied and their influences on the bandgap formation are deduced. This analysis is reinforced by conducting numerical simulations to examine the modes bounding the bandgap and highlighting the effect of the above parameters. The analysis presented here not only sheds light on the origins of gap formation, but also allows one to define design rules for wide phononic gaps and maximum gap-to-midgap ratios.
Highlights
Insight into phononic bandgap formation is presented using a first principles-type approach where phononic lattices are treated as coupled oscillators connected via massless tethers
The analysis presented here sheds light on the origins of gap formation, and allows one to define design rules for wide phononic gaps and maximum gap-to-midgap ratios
The thickness needed to generate the wider bandgap is considerably more than that for the square lattice.[10]. This complicates the excitement of mechanical waves in the Phononic crystals (PnCs) with surface-mounted interdigitated transducers (IDTs), which are commonly used for experimentation.[11]
Summary
Insight into phononic bandgap formation is presented using a first principles-type approach where phononic lattices are treated as coupled oscillators connected via massless tethers. (Received 7 September 2013; accepted 7 November 2013; published online 20 November 2013) Each simulation for a discrete tether length results in a pair of frequency values for the upper and lower edge of that particular bandgap, thereby defining the bandgap width.
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