Actively Tunable Wave Propagation In Beam-type And Membrane-type Metamaterials

By creating artificial materials with micro-structures on a sub-wavelength or deep sub-wavelength scale,resonator arrays are purposely engineered into the materials to dramatically change their dynamic response properties,giving rise to subdiffraction-limited resolution and a few other myriad novel properties that are not observed in nature,such as negative mass density,negative moduli and negative refraction ratio,etc.These state-of-art,artificially engineered materials that have abnormal features are named as metamaterials.The acoustic(or elastic)metamaterials can break the mass density law,and thus can open low-frequency band gaps without significantly increasing the mass or the volume.However,the band gaps generated by the local resonance mechanism are always narrow,and thus the broadening of band gaps or extension of working frequency intervals becomes a topical issue.The active metamaterials have the wonderful capacity of changing band gaps at will,conferring the possible extension of operation intervals and possessing highly flexible adaption to environment.Hence,this thesis will focus on the active tunability of wave propagation in beam-type and membrane-type metamaterials by taking various control approaches into consideration,such as piezo-spring under active electric control action(ACEA),shunted piezoelectric patches,finite deformation and nonlinearity.The present work can provide guidance for either designs of active metamaterials or estimation of their dynamic performance.The piezo-spring under ACEA and the axial pre-stress are simultaneously applied to tune the flexural wave band gaps in beam-type metamaterials,and their influences on the bandgap ranges and formation mechanisms are investigated based on both theoretical analysis and numerical simulation.The broadband quasi-gap formed by two extremely adjacent band gaps is observed in this active beam-type metamaterials,and its existence condition can be expressed explicitly in terms of pre-stress and the ACEA parameter.Furthermore,such quasi-gap can be actively controlled by adjusting the pre-stress and the ACEA parameter simultaneously,in a way satisfying the existence condition.The shunted piezoelectric patches have the ability to open both Bragg scattering and local resonance band gaps in the controlled structures.However.the local resonance band gap generated in this way is always narrow and in a relatively high range.Instead of generating band gaps directly by the shunted piezoelectric patches,this technology is applied to actively adjust the dynamic performance of initially engineered resonators in the system,so that the generated local resonance band gaps can be wide and arbitrarily low,together with the advantage of being easy to control.The numerical simulations demonstrate that the negative capacitance shunting circuit can sensitively control the local resonance band gaps.In particular,the adjustment of the capacitance value through the instable interval,which is actually easy to realize,can achieve fast and wide-range control of band gaps.A new soft membrane-type metamaterial is designed in the present thesis by spraying fine metal particles onto a homogeneous elastic membrane,in a locally homogeneous but globally periodic way.A density-heterogeneous membrane model is proposed to simplify the description of such complex membrane structure,whose validity is demonstrated by comparing with the finite element analysis.The propagation of transverse waves in such pre-stretched membrane-type metamaterial is theoretically and numerically investigated for the first time,and various interesting wave performances are observed,such as broadband quasi-gap that can be tuned by a single parameter,tunable complete band gap,exchange of gap natures and high robust to large deformation,etc.Both the perturbation method and the spectral-spatial analysis method are applied to investigate the performances of harmonic waves and transient wave packets in the weakly nonlinear metamaterials.The perturbation method can accurately predict the dispersion relation of harmonic waves,but fails to capture the wave packet propagation properties.A lot of peculiar phenomena are observed with the help of the spectral-spatial analysis,such as the inhomogeneous distribution of solitons in the spectral space,novel frequency conversion which is completely different from the traditional way and the existence of pseudo-gap,etc.The cause of the inhomogeneous distribution of solitons is revealed theoretically by strict mathematical derivations.Based on the abnormal frequency conversion phenomenon and the pseudo-gap,a high-performance direction-biased waveguide is designed.