Tunability of resonator with pre-compressed springs on thermo-magneto-mechanical coupling band gaps of locally resonant phononic crystal nanobeam with surface effects

Abstract

A locally resonant (LR) thermo-magneto-mechanical phononic crystal (PC) nanobeam by periodically attaching “vertical spring-precompressed spring-mass” resonators onto the surface of base nanobeam is proposed, which the corresponding band structure is calculated by extending surface elasticity theory and thermo-magneto-mechanical coupling constitutive model to plane wave expansion (PWE) method. In addition, the influencing rules of resonator, thermo-magneto-mechanical fields, surface effects and geometric parameters are discussed. Numerical results and further analysis demonstrate that more band gaps with lower starting frequency and wider frequency range can be opened by periodically adding resonators onto the surface of nanobeam. The horizontal springs with larger degree of pre-compression can obtain lower starting frequency of first band gap. The effect of operating temperature on band gaps can be regarded as the relation between operating temperature and Young’s modulus of epoxy. Moreover, a singular pre-stress is existed that makes the band gaps not easily opened, which keeps increasing by increasing operating temperature, magnetic field, the ratio between width and thickness or decreasing the ratio between lengths of Terfenol-D and epoxy. All the researches are expected to be applied to the active control of vibration propagation in the field of nano thermo-magneto-mechanical system.