Enhanced ultrasonic wave generation using energy-localized behaviors of phononic crystals

Abstract

This paper aims to bridge the energy-localized behaviors of a phononic crystal (PnC) and an ultrasonic-wave-generation (UWG) system. A defective PnC manifests an intriguing phenomenon in which input ultrasonic-wave energy is confined near the defect in several defect-band frequencies that appear in the phononic band-gap range. Using the inverse of this energy localization, remarkably amplified ultrasonic waves can be generated compared to a UWG system without the PnC. This work proposes an analytical model that predicts the UWG system's sensitivities and electrical admittance. The mechanical equation of motions and the electrical circuit equation of the piezoelectric-patch-bonded defect are derived using the Rayleigh-Love rod theory and the extended Hamilton's principle. Through the use of Green's functions, these electroelastically coupled equations are solved. With two assumptions, specifically, (i) continuity conditions throughout the PnC and (ii) no incident waves toward the UWG system, the S-parameter-method-based analytical approach presents the system performances explicitly. Furthermore, the modified analytical model for application to engineering situations with finite boundary conditions is also proposed. The predicted results of the proposed analytical model match well with those of the finite element model and show that the UWG performances are amplified to several times their prior value. The main contributions of this work are as follows: (i) this is the first attempt to utilize a defective PnC as UWG systems, (ii) the analytical model is newly proposed and dramatically shortens the computational time compared to the finite-element-method, and (iii) the proposed defective-PnC-incorporated UWG system and its analytical model are effective, regardless of the boundary conditions.