基于波传播法的周期复合板振动带隙衰减特性研究

运用波传播法对有限和无限周期对边简支复合板的振动带隙衰减特性进行了研究.在建立相邻板结构边界连续方程的基础上, 分别运用传递矩阵和Bloch定理建立了有限和无限周期复合板的耦合运动方程, 并详细对比分析了有限和无限周期复合板带隙衰减特性的关联关系.研究表明: 周期板结构的振动带隙频率范围与激励方式和激励位置是相关的, 若周期复合板在宽度方向按某阶模态进行线激励, 则该激励下的振动带隙与无限周期复合板在该阶模态下的振动带隙是一致的; 若周期板在点激励作用, 则该点激励下的振动带隙是参与振动的各阶模态振动带隙的交集. 此外, 还进一步研究了结构阻尼对振动衰减带隙的影响. 关键词： 周期复合板 带隙衰减特性 波传播法 结构阻尼     

Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures

The complete flexural vibration band gaps are studied in the thin plates with two-dimensional binary locally resonant structures, i.e. the composite plate consisting of soft rubber cylindrical inclusions periodically placed in a host material. Numerical simulations show that the low-frequency gaps of flexural wave exist in the thin plates. The width of the first gap decreases monotonically as the matrix density increases. The frequency response of the finite periodic thin plates is simulated by the finite element method, which provides attenuations of over 20dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.     

一种多频局域共振型声子晶体板的低频带隙与减振特性

设计了一种多频局域共振型声子晶体板结构, 该结构由一薄板上附加周期性排列的多个双悬臂梁式子结构而构成. 由于多个双悬臂梁式子结构的低频振动与薄板振动的相互耦合作用, 这种局域共振型板结构可产生多个低频弯曲波带隙(禁带); 带隙频率范围内的板弯曲波会被禁止传播, 利用带隙可以实现对薄板的多个目标频率处低频减振. 本文针对这种局域共振型板结构进行了简化, 并基于平面波展开法建立了其弯曲波带隙计算理论模型; 基于该模型, 结合具体算例进行了带隙特性理论分析. 设计、制备了一种存在两个低频弯曲波带隙的局域共振型板结构样件, 通过激光扫描测振仪测试证实该结构存在两个低频带隙, 在带隙频率范围的板弯曲振动被显著衰减.     

Complete flexural vibration band gaps in membrane-like lattice structures

The propagation of flexural vibration in the periodical membrane-like lattice structure is studied. The band structure calculated with the plane wave expansion method indicates the existence of complete gaps. The frequency response function of a finite periodic structure is simulated with finite element method. Frequency ranges with vibration attenuation are in good agreement with the gaps found in the band structure. Much larger attenuations are found in the complete gaps comparing to those directional ones. The existence of complete flexural vibration gaps in such a lattice structure provides a new idea for vibration control of thin plates.     

多振子梁弯曲振动中的局域共振带隙

从梁的弯曲振动方程出发,利用传递矩阵法,给出了无限周期结构的一维多振子声子晶体梁的弯曲振动能带结构,并利用有限元方法计算了有限周期结构梁的弯曲振动频率响应.建立了多振子声子晶体梁的简化模型,推导出带隙起始截止频率公式.结果表明:一维多振子声子晶体梁具有比单振子声子晶体梁更宽更丰富的振动带隙,可应用于呈倍频关系的减振降噪中;振动在带隙频率范围内频率响应具有明显的衰减;所建立的简化模型与理论模型结果符合较好.研究工作为梁类结构的减振提供一种新的思路.     

局域共振型声学超材料机理探讨

本文以二维固体薄板中的弹性波传播为例, 对基于共振子结构的声学超材料带隙机理进行了探讨, 证明在声学超材料中带隙形成既与共振子对波的散射相位有关, 也与波在共振体之间的几何传播相位有关. 通过调节散射相位和几何传播相位均能实现对色散关系的调控. 基于这一理解, 探究了弹性波超材料中的次波长缺陷态和负折射现象的实现条件.     

基于Timoshenko梁模型的周期充液管路弯曲振动带隙特性和传输特性

充液管路的固液耦合振动广泛存在于各种工程领域中,对其弯曲振动控制进行研究具有重要意义.将声子晶体的周期性思想引入到管路结构设计中,将管壁设计成沿轴向交替排列的周期性复合结构.基于Timoshenko梁模型,采用传递矩阵法计算了固液耦合条件下周期管路结构的弯曲振动能带结构及其传输特性,同时分析了材料阻尼系数、周期和非周期支撑对带隙特性的影响.充液周期管路结构的弯曲振动带隙特性为管路的振动控制提供了一条新的技术途径. 关键词： 声子晶体 充液管路 振动带隙     

Interplay of local resonances and Bragg band gaps in acoustic waveguides with periodic detuned resonators

This letter is concerned with acoustic wave propagation and transmission in acoustic waveguides with periodically grafted detuned Helmholtz resonators. The interplay of local resonances and Bragg band gaps in such periodic systems is examined. It is shown that, when the resonant frequencies of the resonators are tuned close to a Bragg band gap, the behavior of the Bragg band gap can be affected dramatically. Particularly, by introducing appropriately tuned resonators, the bandwidth of a Bragg band gap can be reduced to zero, leading to a very narrow pass band with great wave attenuation performance near both band edges. The band formation mechanisms of such periodic waveguides are further examined, providing explicit formulae to locate the band edge frequencies of all the band gaps, as well as the conditions to achieve very narrow pass bands in such periodic waveguides.     

Design and optimization of periodic structure mechanical filter in suppression of foundation resonances

The paper describes the development of periodic structure mechanical filter (PSMF) that has the potential to reduce vibration transmission and sound radiation at resonances of the foundation in a two-degree-of-freedom (2dof) vibration isolation system by using the band gaps of the periodic structure. The transmission matrix method is used to model vibration transmission of the 2dof system and an analytical expression of sound radiation from the foundation plate is derived. The multi-layer PSMF composed of rigid plates and curved beams is represented by an equivalent m-k-c (viscous damping) model. The propagation/attenuation zones and attenuation ability of PSMF are expressed in the propagation scenario and the iso-attenuation curves by exploiting the unit cell transfer matrix invariant. Influence of the number of unit cells, viscous damping on the mobility of PSMF and vibro-acoustic behavior of the 2dof system is extensively studied. And under the constraints of installation space and stability of the whole system, the more the number of the unit cells, the better attenuation ability in the band gap can be obtained. The interaction between PSMF and the 2dof system is analyzed by the substructure method and contribution of frequency component from different substructures is identified by setting different level of damping for each substructure. Factors influencing the first mounting frequency of the 2dof system with PSMF are discussed and three styles of installing PSMF are studied. The performance of piecewise periodic PSMF and quasi-periodic PSMF is also studied in an attempt to eliminate new-born resonances by PSMF. An optimization scheme involving sensitivity analysis is applied to obtain the optimal values of m and k. And the optimization is effective. The experiment of detecting the band gap of PSMF and the comparative trial of a 2dof system with a flexible plate as the foundation with/without PSMF are carried out. Both numerical and experimental simulation results have demonstrated that by use of PSMF, the vibration transmission at resonances is reduced and the radiation of the foundation at resonances is suppressed.     

Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid

Flexural vibration in a pipe system conveying fluid is studied. The pipe is designed using the idea of the phononic crystals. Using the transfer matrix method, the complex band structure of the flexural wave is calculated to investigate the gap frequency range and the vibration reduction in band gap. Gaps with Bragg scattering mechanism and locally resonant mechanism can exist in a piping system with fluid loading. The effects of various parameters on the gaps are considered. The existence of flexural vibration gaps in a periodic pipe with fluid loading lends new insight into the vibration control of pipe system.     

X形超阻尼局域共振声子晶体梁弯曲振动带隙特性

以声子晶体理论为基础,设计了一种具有超阻尼特性的X形局域共振结构,分析了周期性附加X形局域共振的梁弯曲振动传播特性.利用拉格朗日方程分析了X形局域共振结构动力学等效特性,揭示了该结构的阻尼放大的机理,分析了几何结构参数对于带隙特性的影响,并利用有限元法验证了X形局域共振结构的超阻尼特性.研究结果表明,周期性附加X形局域结构能够有效地抑制低频弯曲振动在梁中的传播,产生超阻尼特性,实现低频、宽带的减振效果,为结构的低频减振提供了一个新的设计方案.     

Temperature-controlled tunable acoustic metamaterial with active band gap and negative bulk modulus

The local resonant band gap and the negative bulk modulus of the acoustic metamaterial with Helmholtz resonators are strongly affected by the temperature of water. In this paper, the acoustic transmission line method (ATLM) is introduced to investigate the influences of the temperature of water on the local resonant band gap and the negative bulk modulus of the acoustic metamaterial. Results show that the relative variations of the local resonant band gap and the negative effective bulk modulus suffering from the change of the temperature of water are approximately equivalent and are up to about 11%. The reason is that the local resonant frequency is proportional to the sound speed of fluid which is strongly effects by the temperature of water. By achieving the unambiguous relationships between these unusual properties of the acoustic metamaterial and the temperature of water, we find that the temperature-controlled acoustic metamaterial with the active band gap and the active negative bulk modulus can be realized in theory. This idea opens a new avenue for the design of the tunable acoustic metamaterial that can modulate the acoustic wave propagation.     

Broadband locally resonant beams containing multiple periodic arrays of attached resonators

The plane wave expansion method is extended to study the flexural wave propagation in locally resonant beams with multiple periodic arrays of attached spring-mass resonators. Complex Bloch wave vectors are calculated to quantify the wave attenuation performance of band gaps. It is shown that a locally resonant beam with multiple arrays of damped resonators can achieve much broader band gaps, at frequencies both below and around the Bragg condition, than a locally resonant beam with only a single array of resonators, although the two systems have the same total resonator masses.     

Propagation of flexural wave in periodic beam on elastic foundations

The propagation properties of flexural wave in the periodic beam on elastic foundations are studied theoretically. The wavenumbers and traveling wave characteristics in the beam on elastic foundations are analyzed. Basing on the equations of motion, the complex band structures and frequency response function are calculated by the transfer matrix method. And the Bragg and locally resonant gaps properties and the effects are researched. A gap with low frequency and wide range can exist in a beam on elastic foundations.     

Flexural vibration band gaps in a thin plate containing a periodic array of hemmed discs

Using a periodic expansion by means of the Bloch theorem, the flexural vibration band gaps are studied in a thin plate with two-dimensional ternary locally resonant structures, i.e. a thin epoxy plate containing a periodic square array of lead discs hemmed around by rubber. The full band gaps of flexural vibration in the thin plate are obtained within which sound and vibration will be forbidden. The numerical results are used to show how the width of the first full band gap depends on the radius ratio of lead disc to hemmed disc, filling fraction, lattice constant (distance between the centers of the nearest lead discs) and thickness of the thin plate. It is observed that the gap width can be changed a lot by modulating these physical parameters.     

Low band gap frequencies and multiplexing properties in 1D and 2D mass spring structures

This study reports on the propagation of elastic waves in 1D and 2D mass spring structures.An analytical and computation model is presented for the 1D and 2D mass spring systems with different examples.An enhancement in the band gap values was obtained by modeling the structures to obtain low frequency band gaps at small dimensions.Additionally,the evolution of the band gap as a function of mass value is discussed.Special attention is devoted to the local resonance property in frequency ranges within the gaps in the band structure for the corresponding infinite periodic lattice in the 1D and 2D mass spring system.A linear defect formed of a row of specific masses produces an elastic waveguide that transmits at the narrow pass band frequency.The frequency of the waveguides can be selected by adjusting the mass and stiffness coefficients of the materials constituting the waveguide.Moreover,we pay more attention to analyze the wave multiplexer and DE-multiplexer in the 2D mass spring system.We show that two of these tunable waveguides with alternating materials can be employed to filter and separate specific frequencies from a broad band input signal.The presented simulation data is validated through comparison with the published research,and can be extended in the development of resonators and MEMS verification.     

Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures

The vibrational response of finite periodic lattice structures subjected to periodic loading is investigated. Special attention is devoted to the response in frequency ranges with gaps in the band structure for the corresponding infinite periodic lattice. The effects of boundaries, viscous damping, and imperfections are studied by analyzing two examples; a 1-D filter and a 2-D wave guide. In 1-D the structural response in the band gap is shown to be insensitive to damping and small imperfections. In 2-D the similar effect of damping is noted for one type of periodic structure, whereas for another type the band gap effect is nearly eliminated by damping. In both 1-D and 2-D it is demonstrated how the free structural boundaries affect the response in the band gap due to local resonances. Finally, 2-D wave guides are considered by replacing the periodic structure with a homogeneous structure in a straight and a 90° bent path, and it is shown how the vibrational response is confined to the paths in the band gap frequency ranges.     

Ultrawide low frequency band gap of phononic crystal in nacreous composite material

The band structure of a nacreous composite material is studied by two proposed models, where an ultrawide low frequency band gap is observed. The first model (tension-shear chain model) with two phases including brick and mortar is investigated to describe the wave propagation in the nacreous composite material, and the dispersion relation is calculated by transfer matrix method and Bloch theorem. The results show that the frequency ranges of the pass bands are quite narrow, because a special tension-shear chain motion in the nacreous composite material is formed by some very slow modes. Furthermore, the second model (two-dimensional finite element model) is presented to investigate its band gap by a multi-level substructure scheme. Our findings will be of great value to the design and synthesis of vibration isolation materials in a wide and low frequency range. Finally, the transmission characteristics are calculated to verify the results.     

Modulating lamb wave band gaps using an elastic metamaterial plate

Modulating band gaps (extending the bandwidths or shifting into a lower frequency range) is a challenging task in phononic crystals. In this paper, elastic metamaterial plates composed of a square array of “hard” stubs or “soft” stubs on both sides of a 2D binary locally resonant plate are proposed, and their band structures are studied. The dispersion relationships and the displacement fields of the eigenmodes are calculated using finite element methods. Numerical results show that the band gaps are shifted to lower frequencies and the bandwidths are enlarged compared to classic elastic metamaterial plates. A conceptual “analogousrigid mode” that includes an “out-of-plane analogous-rigid mode” and an “in-plane analogous-rigid mode” is developed to explain these phenomena. The “out-of-plane analogous-rigid mode” mainly adjusts the band gaps into the lower frequency range, and the “in-plane analogous-rigid mode” mainly enlarges the bandwidth. Furthermore, the band gap effects of composite “hard” stubs and “soft” stubs are investigated. The results show that the location of the band gaps can be modulated into a relatively lower frequency and the bandwidth can be extended by the use of different composite stubs. These elastic wave properties in the proposed structure can be used to optimize band gaps and possibly produce low-frequency filters and waveguides.     

LCR分流电路下压电声子晶体智能材料的带隙

将带有LCR分流电路的压电陶瓷片对贴在铝和环氧树脂组成的声子晶体结构中.使智能材料的机械振动与压电陶瓷的压电效应耦合起来,推导出机械振动在压电陶瓷片上的等效附加应力;使LCR分流电路中的电磁振荡效应和声子晶体的能带特性有机结合,计算了在分流电路作用下智能材料扭转和弯曲振动的带隙特性,研究了电阻、电感、电容元件的改变对压电声子晶体智能材料带隙的影响.研究结果表明:在合理尺寸下,随着分流电路中电阻值的增大,带隙的频率范围变宽,但衰减幅值有所降低;电感和电容值的增大都可以使带隙向低频移动,带隙的衰减幅值随着电感值的增大而升高,但随着电容值的增大而降低.从而给压电声子晶体智能材料减震降噪的控制提供了一种新思路.