Wave Propagation In Nanoscaled Layered Periodic Smart-material Structures

Owing to piezoelectric and piezomagnetic effects,the propagation of elastic waves in the nanoscaled layered smart-material periodic structure can be tuned actively.It can provide some new thoughts for the designs and applications of the nanoscaled wave devices.In this thesis,taking size-effect into account based on the nonlocal theory,the equations of wave motion including the mechanical-electric-magnetic coupling effect are solved.The following problems for related to elastic waves propagating in the nanoscaled layered smart-material periodic structure are investigated.1.The propagation of the anti-plane and in-plane mode waves in the nanoscaled layered piezoelectric periodic structure is studied.Both the normal and oblique incidences are considered.The localization factors and dispersion curves are calculated by the transfer matrix method.Besides,the transmission spectra of a finite structure are also computed by the stiffness matrix method.The results show that a cut-off frequency appears during the propagation of the elastic wave in the nanoscaled layered periodic structures when taking the size-effect into account.With the increase of the ratio of the internal and external characteristic lengths,the cut-off frequency decreases.Strong localization phenomenon exists nearby the cut-off frequency.In the case of normal incidence,the in-plane mixed mode will be decoupled to a pure elastic P-wave mode and a coupling peizoelectic-shear QSV-wave mode.For the same characteristic length,P-wave's cut-off frequency is larger than that of QSV-wave.Therefore the cut-off frequency of the in-plane mixed mode is dependent on P-wave.In the case of oblique incidence,some band gaps in the low frequency range will become wider with increase of the incidence angle.The incidence angle has little influence on the high frequency ranges and has no influence on the cut-off frequency.2.The propagation of Lamb-type guided waves in the nanoscaled layered piezoelectric periodic structure is investigated.According to the general solution of the wave motion equations based on the nonlocal theory,the symmetric wave mode which is commonly applied is considered.Both the dispersion relation and the distributions of the mechanical displacements and the electrical potentials of the Lamb-type guided wave are derived.The influence of the volume fraction and size-effect on the dispersion relation and the mode conversions are analyzed in detail.The results show that a cut-off frequency also appears for the Lamb-type guided wave when taking the size-effect into account.This cut-off frequency has a good agreement with that of the in-plane wave.The cut-off frequency decreases with the increase of the ratio of the internal and external characteristic lengths.The volume fraction has no effect on the cut-off frequency.3.The propagation of the elastic wave in the nanoscaled layered piezoelectric/piezomagnetic periodic structure is investigated.Based on the nonlocal theory,considering mechanical-electric and mechanical-magnetic coupling effects,the wave motion equations are solved.Both the normal and oblique incidences are considered.The localization factors and dispersion curves are computed by the transfer matrix method,and the transmission spectra of a finite structure are obtained by the stiffness matrix method.The results show that the lower and upper boundaries together with the cenrtal frequency of the band gap in the low frequency range move up with the increase of the piezoelectric or piezomagnetic effects.The first band gap becomes wider or narrower with the increase of the piezoelectric or piezomagnetic effects.The cut-off frequency increases with the piezoelectric effect increasing,and remains first unchanged and then increases slowly with the piezomagnetic effect increasing.In the case of oblique incidence,QP-wave will be totally reflected when the incidence angle is larger than the critical angle when the size-effect is not taken into account.And there exists only QSV-wave mode.The critical angle is dependant on the frequency when the size-effect is taken into account.In this thesis,the present results show that the size-effect,piezoelectric effect and piezomagnetic effect have significant influences on the properties(including the width and position of pass and stop bands,the cut-off frequency,the mode conversion etc.)for waves propagating in the nanoscaled layered smart-material structure.So the wave propagation can be tuned by using the nanoscaled layered periodic smart-material structure.These researches will be relevant to the design and application of nanoscaled wave devices.