Abstract
A new model of non-classical phononic crystal (PC) microbeam for the elastic wave bandgap generation is provided, incorporating microstructure, piezomagnetism, piezoelectricity and temperature effects. The wave equation of a general magneto–electro–elastic (MEE) phononic crystal microbeam is derived, which recovers piezoelectric- and piezomagnetic-based counterparts as special cases. The piezomagnetic and piezoelectric materials are periodically combined to construct the PC microbeam and corresponding bandgaps are obtained by using the plane wave expansion (PWE) method. The effects of the piezomagnetism, piezoelectricity, microstructure, geometrical parameters and applied multi-fields (e.g., external electric potential, external magnetic potential, temperature change) on the bandgaps are discussed. The numerical results reveal that the bandgap frequency is raised with the presence of piezo and microstructure effects. In addition, the geometry parameters play an important role on the bandgap. Furthermore, large bandgaps can be realized by adjusting the external electric and magnetic potentials at micron scale, and lower bandgap frequency can be realized through the temperature rise at all length scales.
Highlights
Phononic crystal (PC) structures, known as periodic composite structures, exhibiting bandgaps with piezoelectric/piezomagnetic/magnetoelectric phases, have been investigated in recent years, which can find important applications in harmonic signal processing, vibration reducing, noise controlling, filtering, and other MEMS/NEMS devices [1,2,3,4,5,6,7,8,9,10]
Qian et al [34] and Song et al [35] examined the effects of external electric and temperature fields on the bandgap for piezoelectric PC nanobeams and nanoplates based on the nonlocal theory
The bandgaps of 1D, 2D and 3D PCs based on the modified coupled stress theory (MCST) and the surface elasticity theory were symmetrically investigated [38,39,40,41,42,43], and Espo et al [8] extended this to a piezoelectric PC beam model
Summary
Phononic crystal (PC) structures, known as periodic composite structures, exhibiting bandgaps with piezoelectric/piezomagnetic/magnetoelectric phases, have been investigated in recent years, which can find important applications in harmonic signal processing, vibration reducing, noise controlling, filtering, and other MEMS/NEMS devices [1,2,3,4,5,6,7,8,9,10]. Many higher-order/non-classical theories have been proposed to explain this phenomenon, which describes the size effects by attaching additional material parameters, such as nonlocal theories [26,27], surface elasticity theories [28], strain gradient theories [17,29,30] and couple stress theories [31,32,33] These theories and their extended versions are widely applied to predict the bandgap at the micron and nanometer scales. The bandgaps of 1D, 2D and 3D PCs based on the modified coupled stress theory (MCST) and the surface elasticity theory were symmetrically investigated [38,39,40,41,42,43], and Espo et al [8] extended this to a piezoelectric PC beam model This MCST or its extended versions have been given a direct physical interpretation based on material microstructures [44], which can successfully describe the microstructure effects for thin structures at very small scale. The current model can be used to guide the design of resonator components, tunable filters and other functional MEMS devices
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