Application Of The Piezoelectric Material For The Design Of Tunable Phononic Crystals

In this paper,we investigate the dispersion properties of the one-dimensional piezoelectric phononic crystals with shunted external circuit.The mechanism of how the position and width of band gap can be influenced by the shunting circuit is investigated.Based on the results,we suggest a new way for the design of tunable phononic crystals.The main conclusions including:(1)We theoretically investigate the propagating properties of elastic wave inside the one-dimensional piezoelectric phononic crystals.The transfer matrix method is extended according to the piezoelectric equation and the elastic equation(2)According to the transfer matrix and the Bloch theorem,we calculate the dispersion characteristic with open-circuit,short-circuit,capacitance(C)-circuit,inductance(L)-circuit and LC-circuit.Result shows that the position and width of the band gap vary with the shunting circuits.By tuning the electrical elements in the shunting circuit,the band gap can be tuned easily.(3)By serially connecting the piezoelectric segments into supercells by wire,which introduces an inter-coupling effect among the vibration of piezoelectric segments,we construct a new kind of tunable piezoelectric phononic crystals.We point out that there are two kinds of boundary condition that the elastic wave should satisfy.One is the elastic boundary caused by the elastic mismatch between the piezoelectric and non-piezoelectric material.The other is the electrical boundary caused by the inter-coupling effect.Since the length of a supercell is n times original period,the position of the band gap caused by electrical boundary can be put into lower frequency range easily by changing the length of the supercell.