Defect State And Energy Recovery Of Novel Patch Piezoelectric Phononic Crystals

Phononic crystals are a new material with artificially designed periodic functions.Because of their periodic mass density and elastic constants,acoustic waves and elastic waves produce extraordinary physical properties such as self-collimation,acoustic focusing,negative refraction and cloaking when elastic waves propagate in phononic crystals.When the local periodic structure is disrupted,defective energy bands appear in the band gap.The vibrational mode at the frequency of the defective energy band indicates that the acoustic or elastic wave energy is confined at the defective structure,thus being able to amplify the elastic or acoustic waves in the vicinity of the defect.As a new type of intelligent material,piezoelectric materials are widely used in the field of controlling structural vibrations.Piezoelectric materials have both positive and inverse piezoelectric effects,which generally allow them to be used as sensing elements and inverse piezoelectric effects as actuating elements.Introducing them into phononic crystals is expected to achieve active modulation of band gap and defect states.Therefore,in this paper,a coupling theory framework for the band gap and defect state properties of patch-type piezoelectric phononic crystals is developed,and a transfer matrix and finite element quantitative analysis method for the regulation of the local propagation behaviour of elastic waves are developed,taking into account the electromechanical coupling properties of piezoelectric materials.The influence of the external negative capacitance circuit,open circuit and short circuit on the voltage is revealed.In the first part of this dissertation,the force-electric coupling characteristics of piezoelectric materials are considered,and a composite phononic crystal beam that can actively manipulate bending wave propagation is designed,which introduces defect states into the phononic crystal beam by adjusting the external negative capacitance circuit’s so that the bending wave is efficiently localised at the point defect.The transfer matrix method is used to analyse the bending wave transmission characteristics in the beam,taking into account inertia and stiffness effects,while solving the mechanical equations of motion and the piezoelectric equations to derive the electromechanical coupling transfer matrix.The results obtained by this numerical analysis method for predicting the energy band structure of phononic crystal beams are compared with those obtained by the finite element method.By analysing the effect of different external capacitance parameters on the band gap width,an optimum wide band gap is obtained and the vibration energy localised at the defect location is recovered using an external rectifier circuit.In the second part of this dissertation,changing the electric boundary conditions applied on the upper and lower surfaces of the piezoelectric scatterers or the negative capacitance circuit parameters in series on the piezoelectric scatterers,controlling the electromechanical coupling characteristics of independent units,introducing line defects to generate tunable composite waveguides,and constructing different waveguide paths by changing the geometric parameters or the applied loads.For example,changing the geometric parameters of the scatterer on the specified path,applying different electric boundary conditions to the scatterer,or changing the negative capacitance circuit parameters in series in the piezoelectric scatterer.The transmission efficiency of waveguide structures constructed by various external conditions is studied,and the most efficient method is selected to realize the directional transmission of elastic wave energy.In the third part of this dissertation,inspired by the concept of topology in physics,topological phonon crystals are proposed to study the acoustical topological protection interface mode,which is confined to the boundary of two pseudo-spin states and does not propagate into its phonon medium.These structures,called topological insulators,only allow waves to be transmitted at the boundary and do not support body wave transmission within a specific frequency range.Therefore,topological boundary states protected by topology are robust to structural defects,which is better than cavity mode for energy capture.A kind of topological phonon crystal beam with local resonance structure is proposed.The topological phase transformation of the structure is realized by changing the capacitance parameters of the external circuit of the piezoelectric material.The low frequency elastic wave is localized at the boundary by utilizing the high efficiency local energy at the boundary,and the vibration energy recovery circuit is used to convert the vibration energy into electric energy.