Longxiang Dai

An Enhanced Plane Wave Expansion Method to Solve Piezoelectric Phononic Crystal with Resonant Shunting Circuits

An enhanced plane wave expansion (PWE) method is proposed to solve piezoelectric phononic crystal (PPC) connected with resonant shunting circuits (PPC-C), which is named as PWE-PPC-C. The resonant shunting circuits can not only bring about the locally resonant (LR) band gap for the PPC-C but also conveniently tune frequency and bandwidth of band gaps through adjusting circuit parameters. However, thus far, more than one-dimensional PPC-C has been studied just by Finite Element method. Compared with other methods, the PWE has great advantages in solving more than one-dimensional PC as well as various lattice types. Nevertheless, the conventional PWE cannot accurately solve coupling between the structure and resonant shunting circuits of the PPC-C since only taking one-way coupling from displacements to electrical parameters into consideration. A two-dimensional PPC-C model of orthorhombic lattice is established to demonstrate the whole solving process of PWE-PPC-C. The PWE-PPC-C method is validated by Transfer Matrix method as well as Finite Element method. The dependence of band gaps on circuit parameters has been investigated in detail by PWE-PPC-C. Its advantage in solving various lattice types is further illustrated by calculating the PPC-C of triangular and hexagonal lattices, respectively.

Coupling between two kinds of band gaps of a shunted tube piezoelectric phononic crystal

A tube-type piezoelectric phononic crystal model is proposed to study interaction between locally resonant and Bragg band gaps, which is arrayed periodically by metal and piezoelectric segments. Each piezoelectric segment consists of a shell with series-connected and opposite directions polarized double layers and a resonant shunting circuit. According to the interaction between Bragg scattering and local electromagnetic oscillation, three regions corresponding to the inductance can be divided as follows: quasi-short circuits region, coupling region, and quasi-open circuits region. Some interesting phenomena are found from the coupling between Bragg scattering and locally resonant of electromagnetic oscillation. (1) In the coupling region, a pass band splits a Bragg band gap into two band gaps. But the cut-off frequency of the second band gap does not change with the inductance. (2) In the quasi-open circuits region, Bragg and locally resonant band gaps exist independently. (3) The first band gap transits from Bragg scattering to local resonance when the inductance increases from quasi-short circuits region to quasi-open circuits region. (4) The cut-off frequency of the first band gap is always less than the estimated resonant frequency of inductor-capacitor oscillators. Finally, the theoretical result is validated by two kinds of finite element models based on ANSYS.

Two methods to broaden bandwidth of a nonlinear piezoelectric bimorph power harvester

Shan Jiang Department of Mechanics; Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment, Huazhong University of Science and Technology, Wuhan 430074, China; Franche-Comt e Electronique M ecanique Thermique et Optique, CNRS UMR 6174, Universit e de Bourgogne Franche-Comt e, Besançon 25030, France Hairen Wang Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, China e-mail: hairenwang@pmo.ac.cn

Two Kinds Equal Frequency Circuits to Achieve Locally Resonant Band Gap of a Circular Plate Attached Alternately by Piezoelectric Unimorphs

A circular thin plate is proposed for vibration attenuation, which is attached alternately by annular piezoelectric unimorphs with resonant shunt circuits. Two kinds of equal frequency resonant shunt circuits are designed to achieve an integrated locally resonant (LR) band gap (BG) with a much smaller transmission factor: (1) the structure is arrayed periodically while the resonant shunt circuits are aperiodic; (2) the resonant shunt circuits are periodic while the structure is aperiodic. The transmission factor curve is calculated, which is validated by the finite element method. Dependences of the LR BG performance upon the geometric and electric parameters are also analyzed.

Band gap frequencies of piezoelectric phononic crystals tuned by axial force

A theoretical model of piezoelectric phononic crystal with tuned band gaps has been proposed. The piezoelectric phononic crystal consists of a beam and periodic array of piezoelectric patches. Each pair of piezoelectric patches is connected in parallel by resonant shunting circuits independently. The effect of structure and material parameters on Bragg and locally resonant band gap has been investigated. The numerical results show Bragg band gap is tuned 34Hz by the axial force. Synchronization can be maintained spontaneously since it is not necessary to adjust parameter of every unit as the way that moving band gap by circuit parameter needs to change every shunting circuit synchronously. This property can enhance the applicability of phononic crystals.

Analysis of a micro piezoelectric vibration energy harvester by nonlocal elasticity theory

A theoretical model of a micro piezoelectric energy harvester is proposed based on the nonlocal elasticity theory, which is operated in the flexural mode for scavenging ambient vibration energy. A nonlocal scale is defined as the product of internal characteristic length and a constant related to the material. The dependences of performance of the harvester upon the nonlocal scale and the scale ratio of the nonlocal scale to the external characteristic parameter are investigated in detail. Numerical results show that output power of the harvester decreases, and resonance frequency reduces gradually at first then increases rapidly when nonlocal scale increases. The results of nonlocal elasticity theory are compared with that of classic beam theory. All the results are helpful for material and structure design of the micro piezoelectric energy harvester.

Interaction between band gaps of beam piezoelectric phononic crystal

Theoretical models of beam piezoelectric phononic crystal have been proposed, where piezoelectric patches and other elastic structure are arrayed periodically. Each piezoelectric patch is connected by a resonant shunting circuit independently. Three kinds of piezoelectric patches, i.e., bimorph in series and in parallel, and unimorph, are taken into consideration. The coupling interaction between Bragg and locally resonant band gaps is investigated. The numerical results have demonstrates that it is feasible to obtain specific band gaps through adjusting the interaction between band gaps by inductance. This characteristic can enhance the applicability of phononic crystals.

Transmission of radial vibration along piezoelectric tubular phononic crystal in parallel with resonant shunting circuits

A tube phononic crystal (PC) model arrayed periodically by metal and piezoelectric segments is proposed. Each piezoelectric segment consists of two piezoelectric layers connected in parallel independently by a resonant shunting circuit. The inductor and a piezoelectric equivalent capacitor form an inductor-capacitor oscillator. Coupling vibration of extension and flexure of the thin periodic tube structure is studied by the classical shell theory and linear piezoelectric theory. Precise electric field method and transfer matrix method are applied to solve band gap structures and transmission factor curves. Two locally resonant band gaps and one Bragg band gap are distinguished. Some interesting phenomena of interaction between two locally resonant bands are found. The effects of circuit inductance, material parameters of the tube PC on these three band gaps are investigated.