Study On Periodicity Of One - Dimensional Phononic Crystal Bandgap Structure

Elastic wave transmission in the dielectric periodic structures, interaction with the media, is similar to light waves propagation in photonic crystal band gap is existing, development opened up a new field for the application of the theory of sound wave, such as noise filtering, acoustic waveguide, shock absorption, noise reduction, etc., have become an important research hotspot.In this paper, based on the theory of elastic wave, starting from the Bloch theorem, with the help of transfer matrix and the eigenvalue equation of sound wave propagation in one dimension phononic crystal, study the corresponding dispersion relation, band gap structure. Through a finite number of transfer matrix multiplication, research acoustic transmission characteristics in limited period phononic crystal, discuss the transmittance and reflectance.With different structure of phononic crystal as samples, this paper discusses the initial frequency, the terminate frequency and the center frequency of all kinds of phononic crystal band gap, to research the center frequency of one-dimensional phononic crystal interval distribution;Through numerical calculation method, discuss the center frequency of adjacent band gap center frequency interval distribution;Against influence the parameters of the one-dimensional phononic crystal band gap structure, with first band gap of one dimension phononic crystal as the research object, investigate factors of the band gap range,such as material composition ratio, lattice size etc. phononic crystal structure parameters,elastic modulus and density etc. material parameters;Design experiments, in view of the phononic crystal which composed of water and plastic sample, study appears band gap then produce the phenomenon of inhibition when the sound waves transmission in one dimension phononic crystal.Through theoretical and experimental studies have found that in cycle medium, after the center frequency of the second band gap of ultrasonic transmission successively is n times to the center frequency of the first band gap, that is, set the first band gap center frequency is f1, then the back of the center frequency is2f1,3f1,4f1,..., nf1,... in turn.With the lattice constant increases gradually, the band gap gradually narrowed;With material composition ratio increases gradually, the narrow band gap will widen before gradually;As A young’s modulus of the material increases gradually, the band gap of the initial frequency less affected, termination of A greater influence on the frequency, band gap widened gradually at the same time;As the young’s modulus of materials B increases gradually, the band gap of the starting frequency, termination of frequency is affected, the band gap gradually narrowed;As the density of A material increases gradually, band gap widened gradually;With the density of material B increases gradually, the band gap widened gradually.The experimental results agree well with the transfer matrix theory.