Analysis of underwater decoupling properties of a locally resonant acoustic metamaterial coating

This paper presents a semi-analytical solution for the vibration and sound radiation of a semi-infinite plate covered by a decoupling layer consisting of locally resonant acoustic metamaterial. Formulations are derived based on a combination use of effective medium theory and the theory of elasticity for the decoupling material. Theoretical results show good agreements between the method developed in this paper and the conventional finite element method(FEM), but the method of this paper is more efficient than FEM. Numerical results also show that system with acoustic metamaterial decoupling layer exhibits significant noise reduction performance at the local resonance frequency of the acoustic metamaterial, and such performance can be ascribed to the vibration suppression of the base plate. It is demonstrated that the effective density of acoustic metamaterial decoupling layer has a great influence on the mechanical impedance of the system. Furthermore, the resonance frequency of locally resonant structure can be effectively predicted by a simple model, and it can be significantly affected by the material properties of the locally resonant structure.     

一种含横向圆柱形空腔的声学覆盖层的去耦机理分析

在水下结构表面敷设去耦覆盖层是降低其声辐射的有效途径. 为了深入分析一种含横向无限长空腔的覆盖层的去耦机理, 本文将其等效为均匀介质, 建立了敷设这种覆盖层的单向基体板在线激励下的声辐射模型, 验证了计算模型的有效性, 并利用计算模型对含横向空腔覆盖层的去耦机理进行了分析. 研究结果表明: 基体板-覆盖层接触面的能量流以纵波能量为主, 而横波能量很小, 因而计算覆盖层的去耦特性时可以忽略横波的作用; 和均匀覆盖层相比, 横向空腔型覆盖层在中高频段极大地增强了基体板的力阻抗, 从而更有效地抑制了基体板的振速; 此外, 和均匀覆盖层相比, 横向空腔型覆盖层和水的阻抗失配更大, 使其在中高频具有良好的振动传递损失特性. 因此, 总体而言, 含横向空腔的覆盖层相比均匀覆盖层具有更好的中高频去耦性能.     

去耦覆盖层降噪性能评价指标的理论探讨

去耦覆盖层是降低水下结构声辐射的一个重要措施。为了给工程上去耦覆盖层降噪性能评价指标的选择提供理论参考,建立了点激励力作用下敷设去耦覆盖层的四端简支撑矩形板水下振动和声辐射理论模型,定义了可能表征去耦覆盖层降噪性能的五项评价指标。研究结果表明:只有振动传递损失相对独立于基板的长度、宽度和点激励力位置,而且能较好地描述去耦覆盖层隔离基板振动向水层传递的性能;而湿面均方振速插入损失较振动传递损失则能更好地反映辐射声功率插入损失,尤其在低频。作为评价指标,振动传递损失和湿面均方振速插入损失分别有各自的优点和缺点。      

湍流激励下柔性层贴敷加筋板自噪声的特征机理

为了研究湍流激励下柔性层贴敷加筋板自噪声的特征机理,基于湍流边界层壁面脉动压力功率谱模型、周期加筋板弯曲运动方程和固体波动方程以及力平衡与位移连续边界条件,建立了湍流边界层壁面脉动压力激励下柔性层贴敷单向周期加筋板的振动及内噪声物理模型.研究发现:橡胶外贴时对湍流激励下壳板的减振降噪主要依靠橡胶的厚度模态振动.无筋时,...     

正交加筋板声透射的板梁理论模型研究

为了研究正交加筋板的声透射问题,基于经典薄板和梁振动理论,建立了正交加筋板声透射的板梁理论模型。首先通过分析加强筋的受迫弯曲和扭转运动,求得了平板和加强筋线接触之间的反力和反力矩,然后将其引入到平板振动控制方程中,得到了正交加筋板声振方程,最后采用空间谐波展开法求解该方程得到了传声损失的表达式;在此基础上,首先研究了无限大平板和单向加筋的隔声性能,通过与解析解及两种简化模型的计算结果作对比,验证了所建理论模型的有效性;并进一步研究了加筋形式对正交加筋板隔声性能的影响。结果表明:选择合适的加筋形式可以有效避开结构的隔声波谷。      

Effect of acoustical damping with a porous absorptive layer in the cavity to reduce the structure-borne sound radiation from a double-leaf structure

Structure-borne sound radiation from a double-leaf structure with a porous absorptive layer in the cavity is studied theoretically as well as experimentally. The study is for establishing a countermeasure to reduce the structure-borne noise radiated from an interior leaf into rooms and for clarifying its reduction effect. The sound field radiated from a double-leaf elastic plate with layers of arbitrary media in the cavity set into vibration by a point force excitation is theoretically analyzed. The effect of the bulk vibration of an absorptive layer is also considered by a simple model into the present theory. Radiation reduction of an inner-layer derived from the theory is experimentally validated. Parametric studies reveal that increasing the ratio of an absorptive layer thickness to the cavity depth is effective to reduce the structure-borne sound radiation but high flow resistivity of the absorbent material is not necessarily required. A practical equation to predict the mass-air-mass resonance frequency for absorbent cavity case is given in a simple form.     

双层加筋板低频声的隔离与有源控制

为探讨加筋对双层结构低频隔声及有源控制的影响,分析了筋条数目及布放位置对双层加筋结构低频隔声性能、有源控制策略选取及有源隔声性能的影响。首先利用模态叠加与声-振耦合理论对双层加筋结构建模,然后采用数值算例对上述问题展开探讨。研究发现,筋条数目增多或筋条靠近基板的中间位置布放,将有利于双层加筋结构低频隔声性能的提高。对于有源控制措施,声控制策略与力控制策略相比,前者的控制效率较高且降噪效果较好。由于筋复杂的耦合影响,添加多条筋或筋条靠基板中间布置时有源控制效果减弱,需施加多个点源才能获得较好的降噪效果。      

Influence of stiffeners on plate vibration and radiated noise excited by turbulent boundary layers

The influence of stiffeners on plate vibration and noise radiation induced by turbulent boundary layers is investigated by wind tunnel measurements. Plates with and without stiffeners are tested under the flow speed of 60 m/s, 71 m/s and 86 m/s, respectively. The stiffeners are set either perpendicular or parallel to the direction of the free stream. Measured vibration and noise levels are compared with theoretical calculations, where wall pressure cross-spectra are described by the Corcos model. For the plates tested, it is evident that stiffeners perpendicular to the direction of the free stream could increase noise radiation, but have almost no influence on vibration level of plates.     

降低加肋双层圆柱壳辐射噪声线谱的结构声学设计

为降低双层圆柱壳辐射噪声线谱,从控制内壳振动响应和衰减壳间振动传递率进行结构声学设计。采用机械阻抗理论分析了环肋圆柱壳模态响应控制机理;由环肋振动方程推导分析了环肋径向机械阻抗特性;基于阻抗失配、波形转换原理提出一种阻抗加强环肋,分析了振动波阻抑特性;利用阻尼减振技术,综合考虑肋板的刚度、阻尼特性,设计了金属橡胶层叠肋板;结合数值计算实例,分析了设计双层壳模型的声辐射性能。结果表明:设计的双层加肋圆柱壳结构能有效降低辐射噪声线谱,在分析频段内辐射声压线谱平均降低约6.6 dB。研究结果对研制低噪声水下航行器具有良好的工程价值和应用前景。      

含损伤黏弹性阻尼加筋层合板声功率和指向性变异*

该文旨在研究损伤位置和程度对自由阻尼加筋层合板声辐射功率和指向性的影响。基于Mindlin和Timoshenko梁理论,建立了自由阻尼层合板-梁组合结构有限元模型。数值求解四边简支边界条件自由阻尼加筋层合板振动响应,继而通过Rayleigh积分计算加筋层合板辐射声功率和指向性。将计算得到的前4阶模态固有频率、声辐射功率与指向性与已有文献进行了对比基本一致,验证了数值模型的正确性。最后,详细讨论了损伤位置和程度对自由阻尼加筋层合板固有频率、振型、声辐射功率和指向性的影响,结果表明：随着结构损伤程度的增大,声辐射功率峰值向低频移动,在更多角度上出现明显的指向性;声辐射功率和指向性对损伤位置比损伤程度更加敏感。     

Three-dimensional elasticity model for a decoupling coating on a rectangular plate immersed in a heavy fluid.

This paper presents an analysis of the vibroacoustic response of a finite, simply supported rectangular plate covered by a layer of decoupling material and immersed in a heavy fluid. An exact formulation using the three-dimensional theory of elasticity for the decoupling material is derived for this problem, thereby extending previous studies that were limited to infinite plates. The paper details the constitutive equations of the problem and the analytical method of solution. Numerical results show that shear waves in the decoupling material generally have little influence on the sound radiation in the heavy fluid. Comparisons with a locally reacting model of the decoupling material and with the simple model of House [Proc. I.O.A. 13(3), 166-173 (1991)] are also presented.     

高效半解析方法分析周期正交加筋板的振动-声辐射特性

为了对水下无穷大双周期正交加筋板结构模型在简谐面力激励下的振动响应及声辐射特性进行更为合理的理论预测与分析,建立了加筋板结构的数学模型。结合傅里叶变换、泊松迭加公式及空间波数法,将周期加筋板的振动响应及辐射声压表达为关于结构位移谐波分量的函数方程,对加筋板模型提出了高效分析求解方法并进行了谐波分量截断求解。验证了方法的正确性,并分析了结构的振动特性以及加强筋周期间距和扭矩对辐射声压的影响。结果表明,加强筋的扭转作用影响加筋板结构的振动模态频率,对于较高精度要求的工程应用,加强筋的扭转作用不能忽略。通过调节加强筋周期间距及横截面尺寸,可以降低薄板在较低频域区间的远场辐射声压。      

Analysis of absorption performances of anechoic layers with steel plate backing

Rubber layers with air-filled cavities or local resonance scatters can be used as anechoic coatings. A lot of researches have focused on the absorption mechanism of the anechoic coatings. As the anechoic coatings are bonded to the hull of submarine, the vibration of the hull should not be neglected when the analysis of the absorption characters is carried out. Therefore, it is more reasonable to treat the anechoic coating and the backing as a whole when the acoustic performance is analyzed. Considering the effects of the steel plate backing, the sound absorption performances on different models of anechoic coatings are investigated in this paper. The Finite Element Method is used to illustrate the vibrational behaviors of the anechoic coatings under the steel backings by which the displacement contours is obtained for analysis. The theoretical results show that an absorption peak is induced by the resonance of the steel slab and rubber layer. At the frequency of this absorption peak, the steel plate and the coating vibrates longitudinally like a mass-spring system in which the steel slab serves for mass and the coating layer is the spring. To illuminate the effects of the steel slab backing on the acoustic absorption, the thicknesses of the steel slab and the anechoic layer are discussed. Finally, an experiment is performed and the results show a good agreement with the theoretical analysis.     

Radiation efficiency of submerged rectangular plates

The average radiation efficiency of point-excited submerged rectangular plates is investigated in two methods, deterministic analysis and statistical approach, respectively. In the deterministic analysis, the effect of mutual impedance by water loading on the velocity of the plate is illustrated analytically by using a modal summation method. The cross-modal contributions to the average radiation efficiency are averaged to zero by averaging over all possible excitation positions on the plate. In the statistical approach, by analyzing the engineering formulae of the average radiation efficiency in air, this paper modifies the formulae to be applicable in water. The numerical comparisons show that the modified formulae reflect the average level in the frequency region controlled by corner modes and are accurate enough in the region controlled by monopole and edge modes. On this basis, approximate expressions for predicting the average radiation efficiency of the submerged beam-stiffened rectangular plates are proposed. The main differences between air loading and water loading are considered. Firstly, as dry modes taken in analysis instead of real vibration modes in water, the vibration of the stiffened plate is not only determined by the first mode but by several modes simultaneously at low frequencies. Secondly, the “corner mode region” becomes inappropriate as the plate is stiffened. The proposed formulae are validated numerically in different size, thickness, and stiffener amount of the stiffened plate.     

Use of decoupling to reduce the radiated noise generated by panels

Four types of sources that induce on a panel four different responses are considered. The differences show up also in the way the responses radiate to the far field. A decoupling device in a form of a layer is placed adjacent to the top surface of the panel. The decoupling layer modifies the radiated fields that the sources generate. The modifications in terms of radiation reduction factors and levels are defined. These factors and levels are analyzed for two kinds of decoupling layers. The first is a compliant coating and the second is a layer of a mixture of gas and fluid. The compliant coating may induce on the fluid a velocity field that is different from that of the panel. The mixture of gas and fluid introduces a surface impedance discontinuity between the top surface of the panel and the top surface of the layer, the top surface being in contact with the semi-infinite fluid above the panel.     

Free vibration analysis of stiffened plates using finite difference method

Free vibration characteristics of rectangular stiffened plates having a single stiffener have been examined by using the finite difference method. A variational technique has been used to minimize the total energy of the stiffened plate and the derivatives appearing in the energy functional are replaced by finite difference equations. The energy functional is minimized with respect to discretized displacement components and natural frequencies and mode shapes of the stiffened plate have been determined as the solutions of a linear algebraic eigenvalue problem. The analysis takes into consideration inplane deformation of the plate and the stiffener and the effect of inplane inertia on the natural frequencies and mode shapes. The effect of the ratio of stiffener depth to plate thickness on the natural frequencies of the stiffened plate has also been examined.     

Experimental investigation of noise radiation from a circular plate covered by polyurethane foam

An experimental investigation of the noise reduction achieved by covering a thin circular plate is reported. The plate boundary was unconstrained. One side of the plate was covered by sound-absorbing material so that noise radiation from the other side for different configurations of foam cover was measured and compared with the noise level obtained without any foam cover. It has been shown that substantial noise reduction can be achieved if a specific foam cover is used.     

Analysis on vibration characteristics of large-size rectangular piezoelectric composite plate based on quasi-periodic phononic crystal structure

Based on the theory of composite materials and phononic crystals (PCs), a large-size rectangular piezoelectric composite plate with the quasi-periodic PC structure composed of PZT-4 and epoxy is proposed in this paper. This PC structure can suppress the transverse vibration of the piezoelectric composite plate so that the thickness mode is purer and the thickness vibration amplitude is more uniform. Firstly, the vibration of the model is analyzed theoretically, the electromechanical equivalent circuit diagram of three-dimensional coupled vibration is established, and the resonance frequency equation is derived. The effects of the length, width, and thickness of the piezoelectric composite plate at the resonant frequency are obtained by the analytical method and the finite element method, the effective electromechanical coupling coefficient is also analyzed. The results show that the resonant frequency can be changed regularly and the electromechanical conversion can be improved by adjusting the size of the rectangular piezoelectric plate. The effect of the volume fraction of the scatterer on the resonant frequency in the thickness direction is studied by the finite element method. The band gap in X and Y directions of large-size rectangular piezoelectric plate with quasi-periodic PC structures are calculated. The results show that the theoretical results are in good agreement with the simulation results. When the resonance frequency is in the band gap, the decoupling phenomenon occurs, and then the vibration mode in the thickness direction is purer.     

Structure-borne noise reduction for an infinite, elastic cylindrical shell

A theoretical model was developed to evaluate the reduction of structure-borne noise generated by an axially symmetric ring force which is applied on the interior of the cylindrical shell. The vibrating cylindrical shell is coated with a microvoided elastomer that is acoustically soft material designed for the reduction of the generated noise. The analytical model is a two-layer shell structure comprised of a cylindrical shell and an outer layer (coating) that is perfectly bonded to the cylindrical shell. The outer and inner surfaces of the coated shell are in contact with water and air, respectively. The analysis for this problem is based on the theory of elasticity, acoustic wave equations, and pertinent boundary conditions. Effects of various parameters such as coating thickness and material properties on the noise reductions are presented.     

Vibration amplitude and induced temperature limitation of high power air-borne ultrasonic transducers

The acoustic impedances of matching layers, their internal loss and vibration amplitude are the most important and influential parameters in the performance of high power airborne ultrasonic transducers. In this paper, the optimum acoustic impedances of the transducer matching layers were determined by using a genetic algorithm, the powerful tool for optimizating domain. The analytical results showed that the vibration amplitude increases significantly for low acoustic impedance matching layers. This enhancement is maximum and approximately 200 times higher for the last matching layer where it has the same interface with the air than the vibration amplitude of the source, lead zirconate titanate-pizo electric while transferring the 1 kW is desirable. This large amplitude increases both mechanical failure and temperature of the matching layers due to the internal loss of the matching layers. It has analytically shown that the temperature in last matching layer with having the maximum vibration amplitude is high enough to melt or burn the matching layers. To verify suggested approach, the effect of the amplitude of vibration on the induced temperature has been investigated experimentally. The experimental results displayed good agreement with the theoretical predictions.