Folding beam-type piezoelectric phononic crystal with low-frequency and broad band gap

A folding beam-type piezoelectric phononic crystal model is proposed to isolate vibration. Two piezoelectric bimorphs are joined by two masses as a folding structure to comprise each unit cell of the piezoelectric phononic crystal. Each bimorph is connected independently by a resistive-inductive resonant shunting circuit. The folding structure extends the propagation path of elastic waves, while its structure size remains quite small. Propagation of coupled extension-flexural elastic waves is studied by the classical laminated beam theory and transfer matrix method. The theoretical model is further verified with the finite element method(FEM). The effects of geometrical and circuit parameters on the band gaps are analyzed. With only 4 unit cells, the folding beam-type piezoelectric phononic crystal generates two Bragg band gaps of 369 Hz to1 687 Hz and 2 127 Hz to 4 000 Hz. In addition, between these two Bragg band gaps, a locally resonant band gap is induced by resonant shunting circuits. Appropriate circuit parameters are used to join these two Bragg band gaps by the locally resonant band gap.Thus, a low-frequency and broad band gap of 369 Hz to 4 000 Hz is obtained.     

Tunable low frequency band gaps and sound transmission loss of a lever-type metamaterial plate

A novel metamaterial plate with subwavelength lever-type resonators is proposed to obtain low frequency broadband band gaps and good sound insulation performance. The band structure is theoretically derived, and the validity of the theoretical method is verified by the finite element method. The formation mechanisms of the band gaps are illustrated by the analysis of the effective dynamic mass density and group velocity. The effect of the lever ratio on the band gaps is analyzed. The results indicate that as the lever ratio increases, the first band gap shifts to lower frequencies, while the bandwidth is widened. Moreover, the sound insulation performance of the proposed metamaterial plate is evaluated via examining the sound transmission loss (STL). Compared with the metamaterial plates without lever accessories, the proposed metamaterial plates with a suitable lever ratio have better sound insulation performance at low frequencies.     

圆管型局域共振声子晶体三维构型振动带隙研究

采用多重多级子结构方法计算具有一定刚度的圆管型局域共振声子晶体三维构型振动带隙特性。考察包裹方向对带隙特性的影响,并对第一带隙上下边界点的单胞振动形式进行分析。结果表明,两种包裹形式都可以得到较低较宽的第一带隙,并且带隙特性相似,因而其周期结构都可以大幅减弱带隙范围内弹性波的传播。但两种构型带隙上下边界点对应振动形式不同,此外带隙特性还受单胞尺寸的影响。通过给定评价指标得到相关材料参数与带隙特性关系的相图,由此分析包裹层材料属性对带隙特性的影响。     

Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule (GDQR) method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.     

PHONONIC BAND GAPS IN TWO-DIMENSIONAL HYBRID TRIANGULAR LATTICE

<正>Absolute phononic band gaps can be substantially improved in two-dimensional lattices by using a symmetry reduction approach.In this paper,the propagation of elastic waves in a two-dimensional hybrid triangular lattice structure consisting of stainless steel cylinders in air is investigated theoretically.The band structure is calculated with the plane wave expansion (PWE)method.The hybrid triangular Bravais lattice is formed by two kinds of triangular lattices. Different from ordinary triangular lattices,the band gap opens at low frequency(between the first and the second bands)regime because of lifting the bands degeneracy at high symmetry points of the Brillouin zone.The location and width of the band gaps can be tuned by the position of the additional rods.     

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Eul...     

Extension/Compression-Controlled Complete Band Gaps in 2D Chiral Square-Lattice-Like Structures

Achieving tunable band gaps in a structure by external stimuli is of great importance in acoustic applications. This paper aims to investigate the tunability of band gaps in square-lattice-like elastic periodic structures that are usually not featured with notable band gaps.Endowed with chirality, the periodic structures here are able to undergo imperfection-insensitive large deformation under extension or compression. The influences of geometric parameters on band gaps are discussed via the nonlinear finite element method. It is shown that the band gaps in such structures with curved beams can be very rich and, more importantly, can be efficiently and robustly tuned by applying appropriate mechanical loadings without inducing buckling. As expected, geometry plays a more significant role than material nonlinearity does in the evolution of band gaps. The dynamic tunability of band gaps through mechanical loading is further studied. Results show that closing, opening, and shifting of band gaps can be realized by exerting real-time global extension or compression on the structure. The proposed periodic structure with well-designed chiral symmetry can be useful in the design of particular acoustic devices.     

Active control of flexural waves in a phononic crystal beam with staggered periodic properties

The band gaps of a phononic crystal beam with staggered periodic structure are investigated. The periodic system consists of a pure elastic (i.e. PMMA) matrix beam and some piezoelectric (i.e. PZT) patches with coupling between the mechanical–electrical components. The PZT patches connected by negative capacitance circuits are applied to function as the active control system. Based on the condition at the interface between adjacent unit cells, the transfer matrix and localization factor are derived. The influence of the degree of interlacing and negative capacitance circuits are discussed. The numerical results show that another band gap can be generated by the staggered periodic structure of PZT patches. The widths and locations of the band gaps can be changed by the degree of interlacing.     

Bandgap characteristics of the two-dimensional missing rib lattice structure

In this paper, the bandgap characteristics of a missing rib lattice structure composed of beam elements are investigated by using the Floquet-Bloch theorem. The tuning of the width and position of the bandgap is achieved by changing the local structural parameters, i.e., the rotation angle, the short beam length, and the beam thickness. In order to expand the regulation of the bandgap, the influence of the material parameters of the crossed long beams inside the structure on the bandgap is analyzed. The results show that the mass density and stiffness of the structure have significant effects on the bandgap, while Poisson's ratio has no effect on the bandgap. By analyzing the first ten bands of the reference unit cell, it can be found that the missing rib lattice structure generates multiple local resonance bandgaps for vibration reduction, and these bandgap widths are wider. The modal analysis reveals that the formation of the bandgap is due to the dipole resonance of the lattice structure, and this dipole resonance originates from the coupling of the bending deformation of the beam elements. In the band structure, the vibrational mode of the 9th band with a negative slope corresponds to a rotational resonance, which is different from that with the conventional negative slope formed by the coupling of two resonance modes. This study can provide a theoretical reference for the design of simple and lightweight elastic metamaterials, as well as for the regulation of bandgaps and the suppression of elastic waves.     

Complete band gaps in two-dimensional piezoelectric phononic crystals with {1–3} connectivity family

In this paper, we present results of full band structures for two-dimensional piezoelectric phononic crystals with {1–3} connectivity family. The plane-wave-expansion (PWE) method is applied to the theoretical derivation of secular equations of the two polarization modes: a transverse polarization mode and a mixed (longitudinal-transverse) polarization mode. And the band structures of the two modes for both the case of piezoelectric rods embedded in a polymer matrix and the case of polymer rods embedded in a piezoelectric matrix are calculated for two different cross-sections of the rods, i.e., circular and square, considering the practical fabrication of phononic crystals. We reveal the existence of several very large complete band gaps in a material of practical interest such as PZT rods reinforced polythene composite. The effects of shapes and filling fraction of the rods on band gaps are discussed in detail. The existence of these gaps in relation to the physical parameters of the constituent materials involved is studied. Understanding the band structures of piezoelectric phononic crystals can give some information for improvements in the design of acoustic transducers.     

一维磁电弹准周期结构带隙特性的研究

采用传递矩阵方法,研究了横波(SV波)垂直入射时压电/（弹性/压磁）和（压电/弹性）/压磁两种Fibonacci准周期结构的频带特性,通过计算局部化因子和位移透射系数,数值揭示了此两种Fibonacci准周期结构频带特性的差异以及与相应理想周期结构频带特性的不同,而且表明（压电/弹性）/压磁Fibonacci准周期结构的频带特性与纯弹性材料Fibonacci准周期结构的频带特性是相似的。     

Multi-resonator coupled metamaterials for broadband vibration suppression

In this study,multi-resonator coupled metamaterials(MRCMs)with local resonators are proposed to obtain the multiple and wide band gaps.Kinetic models of the MRCMs are established,and the boundary conditions of the unit cell are obtained with Bloch's theorem.The effects of structural parameters,including the mass of the resonator and the spring stiffness,on the distributions of the band gaps are studied.Furthermore,the frequency domain responses and the time domain responses are calculated for analyzing the structural vibration characteristics and the effects of damping on structural vibration.The results show that the frequency domain response can accurately express the distributions of the band gaps of the MRCMs,and we can increase the number and the width of the band gaps by using the MRCMs for the superior vibration suppression capability.     

Broadband elastic metamaterial with single negativity by mimicking lattice systems

The narrow bandwidth is a significant limitation of elastic metamaterials for practical engineering applications. In this paper, a broadband elastic metamaterial with single negativity (negative mass density or Young's modulus) is proposed by mimicking lattice systems. It has two stop bands and the bandwidth of the second one is infinite theoretically. The effect of the relevant parameters on band gaps is discussed. A continuum model is proposed and the selection of materials is discussed in detail. It shows that continuum metamaterials can be described accurately by using the lattice model, and the second stopband can be ultra-broad but not infinite. This discrepancy is investigated and a method is provided to calculate the upper limit of the second stopband for a continuum metamaterial. As a verification, the proposed metamaterial is used for wave mitigation over broadband frequency ranges. Moreover, the present method is extended to design 2D anisotropic elastic metamaterials, and a device to control the direction of elastic wave transmission is proposed as an example.     

ELASTIC WAVE LOCALIZATION IN TWO-DIMENSIONAL PHONONIC CRYSTALS WITH ONE-DIMENSIONAL QUASI-PERIODICITY AND RANDOM DISORDER

The band structures of both in-plane and anti-plane elastic waves propagating in two-dimensional ordered and disordered （in one direction） phononic crystals are studied in this paper. The localization of wave propagation due to random disorder is discussed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method. By treating the quasi-periodicity as the deviation from the periodicity in a special way, two kinds of quasi phononic crystal that has quasi-periodicity （Fibonacci sequence） in one direction and translational symmetry in the other direction are considered and the band structures are characterized by using localization factors. The results show that the localization factor is an effective parameter in characterizing the band gaps of two-dimensional perfect, randomly disordered and quasi-periodic phononic crystals. Band structures of the phononic crystals can be tuned by different random disorder or changing quasi-periodic parameters. The quasi phononic crystals exhibit more band gaps with narrower width than the ordered and randomly disordered systems.     

一种新的结构损伤识别试验方法研究

提出在构件上增设附加质量来模拟结构损伤的试验方法,证明了质量增加与刚度降低的等价关系.以简支梁为例,给出了采用附加沙袋法、悬挂质量法两种附加质量方式模拟结构损伤的具体试验方案,完成了多工况下简支梁附加质量模拟结构损伤的动测试验.通过试验验证了本文所提方法的正确性,得出了在梁构件上采用附加沙袋法可准确模拟出不同损伤位置、...     

钝圆头质量块对简支梁的多次弹塑性撞击

考虑多次局部弹塑性接触变形行为、多次撞击和多次分离过程,提出了1种采用有限差分方法研究柔性结构多次弹塑性撞击问题的MCIS方法,研究了钝圆柱头刚性质量块水平撞击简支梁的过程。研究结果表明,该撞击过程实际上是1个复杂的多次弹塑性撞击过程,一般存在2个以上的明显撞击区,每个撞击区包含了形式多样的复杂的次生撞击过程。其他撞击区的冲量值与第1个撞击区的冲量值相当,其他撞击过程中损失的撞击动能的总和与首次撞击过程中损失的撞击动能相当,因此,多个撞击区和多次撞击过程将对梁的撞击物理行为产生重要影响。研究还发现,小质量块刚性体撞击时,首次撞击过程的撞击动能损失明显。在大质量刚性体撞击时,后续的多次撞击过程的撞击动能损失明显。 更多还原     

A brief review of metamaterials for opening low-frequency band gaps

Metamaterials are an emerging type of man-made material capable of obtaining some extraordinary properties that cannot be realized by naturally occurring materials. Due to tremendous application foregrounds in wave manipulations, metamaterials have gained more and more attraction. Especially, developing research interest of low-frequency vibration attenuation using metamaterials has emerged in the past decades. To better understand the fundamental principle of opening low-frequency (below 100 Hz) band gaps, a general view on the existing literature related to low-frequency band gaps is presented. In this review, some methods for fulfilling low-frequency band gaps are firstly categorized and detailed, and then several strategies for tuning the low-frequency band gaps are summarized. Finally, the potential applications of this type of metamaterial are briefly listed. This review is expected to provide some inspirations for realizing and tuning the low-frequency band gaps by means of summarizing the related literature.

     

Investigation of flexural wave band gaps in a locally resonant metamaterial with plate-like resonators

This paper presents an investigation of flexural wave band gaps in locally resonant metamaterials (LRMs). An LRM is a periodic structure consisting of repeated unit cells containing a local resonator. Due to the local resonance occurring in the unit cell, the LRM induces a band gap (a frequency band in which no waves propagate). Discrete-like or beam-like resonators have generally been used to realise LRMs in previous research. By extending the beam-like resonator configuration, this paper studies LRMs with a plate-like resonator to exploit its advantages with respect to large design freedom. In order to understand flexural wave band gaps in an LRM with plate-like resonators, parametric studies are conducted with the development of a finite element model. Further, the influences of the plate-like resonator design parameters on flexural wave band gaps are investigated. Based on the parametric studies, the rules governing band gap properties are determined. Finally, tailoring flexural wave band gaps by adjusting the parameters is discussed.     

Imperfection and burial-depth sensitivity of the initiation and development of kink folds in laminated rocks

The first objective is to study the influence of the burial depth and of an imperfection, in the form of a tilt in the inclination of the otherwise straight, laminated beam, on the conditions for the initiation and the development of kink folds. The beam, typical of sedimentary rocks, is layered with weak interfaces between the competent beds, promoting the onset of kinking by their slip. The results are analytical and based on the upper bound approach of the classical limit analysis, referred to as the maximum strength theorem in the absence of any discussion of plasticity. The weak interface strength is described by the Coulomb criterion, whereas the bulk material is also cohesive and frictional but with an additional closure in the compressive stress domain to depict the action of compacting deformation mechanisms. The new twist to the methodology is to extend its application to the development of the failure mode beyond the onset, assuming that the structure finite response is well described by the least upper bound solution. The second objective is to compare in terms of upper bounds three different failure mechanisms which are the compaction band, the reverse fault and the kink fold. Their respective domain of dominance is constructed in failure-mechanism maps in the space spanned by the imperfection angle and the burial depth.Compaction bands are predicted at the deepest end of the beam and the reverse fault and the kink fold at the shallower end. These depth differences are resulting from the geometrical imperfection. It is found that the kink-band mode at its onset, with compaction band dominant conditions, resembles to a slip-enhanced compaction band due to the weak interface activation and the compaction along the two parallel hinges. This hybrid mode migrates suddenly through the competent beam from the deepest towards the shallowest region and develops as a kink fold, after a negligible amount of shortening. The kink fold development, beyond the onset, occurs in two phases, the first corresponding to the rotation of the kink band and the second, to its widening. The associated least upper bound is first decreasing during the development and then increasing, the minimum being controlled more by the increase in the potential energy of the system than by the most favorable orientation of the frictional weak interfaces. It is finally found that the continuous activation of slip over the weak interfaces and the widening of the kink band prevent the rotation of the kink towards the large angles which are necessary to induce its locking. It is proposed that the introduction of damage along the hinges could palliate these two effects and prompt the locking observed experimentally and in the field.     

包裹层结构对轻质声子晶体低频振动带隙的影响

基于局域共振机理提出新型轻质声子晶体包裹层结构设计方法。借助有限元法,计算新型声子晶体能带结构、本征模态,分析包裹层总缺口度数一定时不同包裹层缺口数量及布置位置对第一完全带隙截止频率的影响;设计包裹层与散射体连接形式为线连接与点连接两种新型声子晶体模型,分别得到起始频率为37.4Hz及19.0Hz的第一完全带隙,分析第一完全带隙起始频率处散射体本征模态,揭示新型声子晶体极低第一完全带隙起始频率产生机理;进而,与传统面连接型声子晶体通过增加散射体质量降低第一完全带隙起始频率的方法对比。研究结果表明,包裹层总缺口度数一定时,采用缺口数量更多且缺口位置距离连接短板更大的包裹层布置形式能得到更宽的第一完全带隙;提出的包裹层与散射体线连接与点连接型声子晶体在获得极低第一完全带隙起始频率的同时,显著降低了声子晶体质量,突破了传统声子晶体通过增加散射体质量降低第一完全带隙起始频率的限制,为轻质声子晶体获得极低局域共振带隙起始频率的研究设计提供了参考。