Size effects on a one-dimensional defective phononic crystal sensor

Abstract

The influence of size effects on one-dimensional defective phononic crystal sensors based on simplified strain gradient elasticity theory is studied in this paper. Phononic crystals have been widely used in high-sensitivity gas and liquid sensors by introducing defects to disrupt the perfect phononic crystal modes. In comparison with classical elasticity theory, the simplified strain gradient elasticity theory includes two microstructure-related material parameters that can accurately reflect the size effects of the structure. In this paper, the stiffness matrix method was used to calculate the transmission coefficients of the proposed model, avoiding the numerical instability of the transfer matrix method. The results show that the size effects at the microscale affect the perfect phononic crystal bandgap's frequency range, and the microstructure constants impress the resonant frequency while detecting liquids. Consequently, the accuracy of the sensor is reduced. These findings provide a theoretical basis for designing microscale phononic crystal sensors.