Nonlinear band gap characteristics of piezo-electro-magnetic phononic crystal micro and nanobeams based on size-dependent continuum mechanics models

This paper presents size-dependent continuum mechanics models for the nonlinear band gap (BG) characteristics of a piezo-electro-magnetic phononic crystal (PC) micro and nanobeam under voltage-based control (VBC) and negative capacitance-based control (CBC) methods. Taking various size-dependent effects into account, the BG properties of a piezo-electro-magnetic PC micro/nanobeam are analyzed based on Rayleigh beam theory (RBT), plane wave expansion (PWE), Bloch theorem, and nonlinear von-Karman method. The effects of electro-magneto-mechanical coupling fields, geometric parameters, and micro/nanobeam dimensions on BG properties are discussed. It is found that all BGs frequencies can be controlled by the applied physical fields and elastic medium.