Wave Dynamics And Tunability In One-Dimensional Phononic Crystals

Research of phononic crystals(PCs)is flouring in both fundamental physics and emerging applications,because of their extraordinary abilities of tailoring acoustic and elastic waves.Particularly,the properties of band gaps,defect localized modes and negative refraction provide a flexible way for the PCs to design novel devices for vibration filtering,acoustic imaging and sound stealth.Typically,PCs are composed of those passive materials with continuum linear elasticity,and the wave dynamics is demonstrated to be hardly tunable,resulting in limited options for PCs to be used in harsh and various engineering enviroments.Recently,some advanced topics have been figured out for achieving more flexible tuning degrees of freedom(DOFs)in PCs.One of them is the developments of granular media and granular crystals(GCs)that go beyond the regime of linear continuum elasticity,in which the presence of nonlinearity enables complex wave dynamics and a dramatical tunability of the system.Tunability of the properties in PCs,i.e.,the band structures,can also be achieved by constitutive media with multiple physics such as acousto-electric or acousto-magnetic fields.However,it is still difficult to analyse and predict some particular wave behaviours in PCs due to the inherent complexities of the nonlinearity and the multiple physics couplings.Therefore,this paper aims to achieve the tunability by introducing alternative ways of nonlinearity,external force and electric fields,and further to explore the wave dynamics among different configurations of PCs.At the beginning,we theoretically study the longitudinal wave propagation in onedimensional(1D)weakly nonlinear monatomic and diatomic GCs.The self-action nonlinearity of the longitudinal wave leads to the wave behaviors including second harmonic generations,and subsequently their nonlinear beating and nonlinear resonances in GCs.The tunability of the system comes from the changings of nonlinear strength,and particularly,of the mass ratio for diatomic GCs.Further,we extend the single longitudinal wave work to the coupled waves one by taking the shear and rotational DOFs into account in 1D GCs.Ulike the self-action nonlinearity of the longitudinal wave,the coupled transverse-rotational waves have the inter-action nonlinearity,thus generating the combined frequency(i.e.,the sum frequency and the difference frequency)wave components when they propagate along the GCs.Based on the tunability of the contact characteristics,the GCs may show some nonlinear resonances under which the energy of the system flows from the fundamental frequency into combined frequencies.In order to induce more flexible DOFs of tuning wave dynamics,external stimulus including tangential force and torsional torque are applied to a V-shaped rail-GC system that possesses 6 DOFs of motion.The shear and torsional stiffness characteristics between the granular particles and the V-shaped rail depend on the external force and the torque,respectively,which yields more complex coupled wave dynamics such as zero group velocity mode,accidental degeneracy and mode hybridizations.Furthermore,the presence of the V-shaped rail couples different types of motion and provides yet another alternative strategy for tuning the wave dispersion of the system.Finally,based on the electro-mechanical couplings between the acoustical vibration and electric fields,we developed an analytical model of 1D tunable PC with both active piezoelectric elements and passive elements.Both the low-frequency active band gaps and passive Bragg band gaps are found in this type of PCs,and the former can be tuned by optimizing the voltages that are applied to the piezoelectric elements.Above all,the wave dynamics and tunability in several configurations of 1D PCs are investigated by means of theoretical calculation and numerical validition.The findings of this paper are expected to provide a theoretical basis for understanding the complex wave process in GCs,as well as to inspire the design of acoustic functional devices for tunable selective vibration filtering,sound frequency converting and energy transferring.