Band Gap Regulation Mechanism and Rule of Locally Resonant Thermo-Magneto-Mechanical Phononic Crystal Double-Layer Nanobeam Based on Symmetric and Antisymmetric Vibration Modes

A locally resonant (LR) thermo-magneto-mechanical (TMM) phononic crystal (PC) double-layer nanobeam is presented, which is achieved by periodically attaching "vertical spring-precompressed horizontal spring-additional spring-mass" resonators onto the surface of lower and upper nanobeams. The band structure is calculated with surface elastic theory and TMM coupling constitutive Euler beam model, which are applied to the plane wave expansion (PWE) method. Three unabridged band gaps can be effectively exposed under 10 GHz. Vibration modal analysis improves that all the bands can be divided into symmetry bands and antisymmetry bands. Precompressed horizontal springs and extra springs can aid in further widening band gaps based on such a creation mechanism. Besides, with the growth of stiffness of horizontal and additional springs, the widths of band gaps increase. The unique symmetric and antisymmetric regulation mechanism and rule of double-layer nanobeam is unpossessed of single-layer nanobeam. It is envisaged that all of these studies will be applied to active vibration control in nano TMM systems.