Potential solutions to improved sound performance of volume based lightweight multi-storey timber buildings

Lightweight building systems in general suffer from poor sound insulation, especially in the low frequency region. Since no reliable mathematical models that can predict the impact sound pressure level exists, the lightweight building design is to a high extent based upon previous experience and upon measurements. A special difficulty is related to experimental measurements since the variation among identical units must not be neglected. A modern volume based lightweight wooden building concept has here been tested by numerous well controlled measurements, in laboratory as well as in more field like conditions. The volume construction technique offers new possibilities and challenges to improve sound insulation in light weight timber construction. The main purpose was to investigate how different constructional solutions in the floor, like plaster board, mineral wool, elastic glue, dividing board, floating floor etc., affect the sound insulation. Many of the tested modifications resulted in only marginally changed impact sound pressure level but parameters that substantially can improve the sound insulation were found in using elastic glue to mount the floor boards, to install extra board layers and to use floating floors.     

Non-diffuseness of vibration fields in ribbed plates

This paper presents numerical simulations of structural intensity in a rib-reinforced plate, investigating the diffuseness. Many prediction models of building and structural acoustics, such as statistical energy analysis or energy flow methods, assume the vibrational wave fields to be diffuse. However, the diffuseness assumption is not always valid. One such example is a rib-reinforced plate typically found in a lightweight floor with wooden joists. Other examples can be found in aircraft and ship structures. The structural intensity of a ribbed plate is computed at low to mid frequencies using the Fourier sine expansion of the transverse displacement of the plate. Hamilton's principle is used in combination with thin plate theory and Euler beam theory. The model takes into account interactions between components. The Fourier sine modes are re-formulated as plane waves in a radial coordinate system, which can express the structural intensity in terms of the angular component of the modes. In the simulations, ensemble averages and rain-on-the-roof excitations are used. The numerical results show that the structural intensity varies significantly as the angle of propagation changes and cannot be assumed to form a diffuse field.     

Measurement of plane wave acoustic fields in flow ducts

The response of a fluid loaded plate is derived as function of the incident pressure in the fluid. The results are compared with full scale measurements made in the aft peak tank on a ship. Propeller induced pressure and hull plate velocity were measured with flush-mounted hydrophones and accelerometers. It is found that for a typical aft body construction the boundaries of the plate elements can be assumed to be simply supported. The plate model agrees well with full scale measurements down to 40 Hz. Below this frequency global vibrations determine the response of the hull. Both theoretical and experimental results indicate that the field induced by the vibrating plate elements can be considerable. The response of a plate can be decreased if the width of the plate is decreased or the plate thickness increased.     

水下多层均匀材料的声特性

本文研究水和空气中由不同厚度的两层弹性板及消声橡胶共同组成的分层介质在斜入射时的声特性,并采用数值方法求解多层结构声场的线性方程组。得到反射,透射系数,当板的厚度远小于波长时,采用弹性薄壳振动模型和弹性波模型进行计算,它们的结果基本相同,但是薄壳振动模型更便于计算和理论分析;对系统反射系数和透射系数的计算结果表明,系统增加消声橡胶层后,极大地改变后射系数和透射系数的频率响应;频率升高,反射系数减小     

Study on sound transmission characteristics of a cylindrical shell using analytical and experimental models

A circular cylindrical cavity enclosed by a thin elastic shell is found in many practical devices such as expansion volume mufflers, hermetic compressors and aircraft cabins. Analytical and experimental studies are conducted in this work to understand the characteristics of sound transmission through the cylindrical wall of such a system. Using an infinitely long circular cylindrical shell subjected to a plane incident wave, an exact solution is obtained by solving the classical shell vibration equations and the acoustic wave equations simultaneously. Transmission losses obtained from the solution are compared to the transmission losses that are measured for a cylindrical shell of finite length and the same cross-sectional dimensions. The comparison suggests that the theoretical model can be used as an effective design tool despite considerable simplifications involved.     

一种超材料梁对机械波振动吸收的模拟研究

本文设计了一种能够对机械波进行吸收的超材料梁,超材料梁由若干质量-弹簧微结构系统和一根各向同性梁构成.通过对两种不同结构的质量-弹簧系统的分析,从理论上解释了"负有效质量"和"负有效刚度".根据Hamilton原理,导出了超材料梁的代表性胞元的控制方程.通过数值模拟分析了两种不同结构的有限超材料梁对机械波的吸收性能,一种是弹性系数线性变化的质量-弹簧系统在有限梁内均匀分布,另一种是由固有频率线性变化的弹簧-阻尼器子系统构成四个相同吸收器子群在有限梁内均匀分布.模拟结果表明,进入梁中的机械波与质量-弹簧振子 关键词： 超材料梁 负有效质量 负有效刚度 机械波     

Attenuation of flexural vibration for floating floor and floating box induced by ground vibration

This paper investigates the vibration isolation performance of floating floor and floating box structures to control rail vibration transmission. Simple theoretical and experimental methods are developed to analyze the effects of stiffener beam, mass and arrangement of isolator on the fundamental natural frequency of the flexural vibration of floating floor and box structure.The vibration reduction performances of floating floor and box structure are found to be degraded by flexural vibration of the floor or supporting stiffener beam. From the results of vibration measurements; stiffener beams increase the fundamental natural frequency of flexural vibration of floating floor and enhance vibration isolation. Also they can further alleviate the effect of flexural vibration using optimum isolator arrangement effectively. The proposed floating box design achieved a vibration reduction of 15-30 dB in frequency region of critical rail vibration (30-200 Hz).     

Reliability assessment of different plate theories for elastic wave propagation analysis in functionally graded plates

The importance of elastic wave propagation problem in plates arises from the application of ultrasonic elastic waves in non-destructive evaluation of plate-like structures. However, precise study and analysis of acoustic guided waves especially in non-homogeneous waveguides such as functionally graded plates are so complicated that exact elastodynamic methods are rarely employed in practical applications. Thus, the simple approximate plate theories have attracted much interest for the calculation of wave fields in FGM plates. Therefore, in the current research, the classical plate theory (CPT), first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT) are used to obtain the transient responses of flexural waves in FGM plates subjected to transverse impulsive loadings. Moreover, comparing the results with those based on a well recognized hybrid numerical method (HNM), we examine the accuracy of the plate theories for several plates of various thicknesses under excitations of different frequencies. The material properties of the plate are assumed to vary across the plate thickness according to a simple power-law distribution in terms of volume fractions of constituents. In all analyses, spatial Fourier transform together with modal analysis are applied to compute displacement responses of the plates. A comparison of the results demonstrates the reliability ranges of the approximate plate theories for elastic wave propagation analysis in FGM plates. Furthermore, based on various examples, it is shown that whenever the plate theories are used within the appropriate ranges of plate thickness and frequency content, solution process in wave number-time domain based on modal analysis approach is not only sufficient but also efficient for finding the transient waveforms in FGM plates.     

船舶典型结构损耗因子试验及应用研究

损耗因子是衡量系统阻尼特性并决定其振动能量耗散能力的重要参数,对船舶水下噪声预报分析具有重要影响。针对船舶结构特点,选取内底板、舱壁板和甲板等典型结构建立试验模型,基于瞬态衰减法,对船舶典型结构损耗因子进行测试,分析、掌握其特性规律。在此基础上,开展船舶典型结构损耗因子水下噪声预报应用研究,结果表明,损耗因子对船舶水下噪声具有较大影响,进行船舶水下噪声预报时需开展相关损耗因子测试。     

Flexural wave baffling by use of a viscoelastic material

The effectiveness of baffles against flexural wave noise is discussed. A plane layer model is considered, consisting of an infinite elastic plate excited by a line force, a viscoelastic layer representing the baffle, and an outer plate which separates the baffle layer from the semi-infinite fluid medium. The effectiveness of the baffle is characterized by its insertion loss.     

基于集中质量法的一维声子晶体弹性波带隙计算

通过将一维声子晶体中的原胞简化为有限多个自由度的弹簧振子结构，引入了一种基于集中 质量法的一维声子晶体弹性波带隙计算方法.与传统平面波展开法相比，该方法的计算结果 与之相符合，而且在收敛性方面较之有很大改善.通过使用集中质量法，可在得到同样计算 精度的条件下，显著降低计算量，提高计算速度. 关键词： 声子晶体 弹性波带隙 集中质量法 平面波展开法     

Flexural vibration insulation with an elastic layer for a plate under nonuniform vibratory action

A method is proposed for calculating the vibration insulation of an elastic layer positioned between a finite-size plate with free edges and a vibrationally active base. The elastic layer consists of a discrete set of springs. In the case of an out-of-phase vibration of the base surface, the mean dynamic action on the plate decreases, which leads to an increase in vibration insulation. By contrast, the resonances of flexural plate vibrations reduce the vibration insulation at resonance frequencies. For different cases, the system parameters that correspond to a positive effect of vibration insulation are estimated. The simplest mass-spring system possessing a single degree of freedom is discussed.     

Prediction of airborne sound transmission across a timber–concrete composite floor using Statistical Energy Analysis

This paper concerns the development and experimental validation of prediction models using Statistical Energy Analysis (SEA) to calculate the airborne sound insulation of a timber–concrete composite floor. The complexity in modelling this floor is due to it having (1) a multilayer upper plate formed from concrete and Oriented Strand Board (OSB), (2) multiple types of rigid connector between the upper plate and the timber joists and (3) a resiliently suspended ceiling. A six-subsystem model treats the concrete–OSB plate as a single subsystem and three different five-subsystem models treat the combination of concrete, OSB and timber joists as a single orthotropic plate subsystem. For the orthotropic plate it is suggested that bending stiffnesses predicted using the theories of Huffington and Troitsky provide a more suitable and flexible approach than that of Kimura and Inoue. All SEA models are able to predict the weighted sound reduction index to within 2 dB of the measurement. The average difference (magnitude) between measurements and predictions in one-third octave bands is up to 4 dB. These results confirm that SEA can be used to model direct transmission across relatively complex floor constructions. However, this requires the inclusion of measured data in the SEA model, namely the dynamic stiffness of the resilient isolators and the cavity reverberation time.     

Flexural and transversal wave motion in homogeneous isotropic thermoelastic plates by using asymptotic method

The present investigation is concerned with the flexural and transversal wave motion in an infinite, transversely isotropic, thermoelastic plate by asymptotic method. The governing equations for the flexural and transversal motions have been derived from the system of three-dimensional dynamical equations of linear theory of coupled thermoelasticity. The asymptotic operator plate model for free vibrations; both flexural and transversal, in a homogenous thermoelastic plate leads to fifth degree and cubic polynomial secular equations, respectively, that governs frequency and phase velocity of various possible modes of wave propagation at all wavelengths. All the coefficients of differential operator have been expressed as explicit functions of the material parameters. The velocity dispersion equations for the flexural and transversal wave motion have been deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate waves. The approximations for long and short waves and expression for group velocity have also been derived. The thermoelastic Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations whose equivalence is established with that of asymptotic method. The dispersion curves for phase velocity, group velocity and attenuation coefficient of various flexural and transversal wave modes are shown graphically for aluminum-epoxy material elastic and thermoelastic plates.     

A finite difference analysis of the field present behind an acoustically impenetrable two-layer barrier

The interaction of an incident sound wave with an acoustically impenetrable two-layer barrier is considered. Of particular interest is the presence of several acoustic wave components in the shadow region of this barrier. A finite difference model capable of simulating this geometry is validated by comparison to the analytical solution for an idealized, hard-soft barrier. A panel comprising a high air-content closed cell foam backed with an elastic (metal) back plate is then examined. The insertion loss of this panel was found to exceed the dynamic range of the measurement system and was thus acoustically impenetrable. Experimental results from such a panel are shown to contain artifacts not present in the diffraction solution, when acoustic waves are incident upon the soft surface. A finite difference analysis of this experimental configuration replicates the presence of the additional field components. Furthermore, the simulated results allow the additional components to be identified as arising from the S(0) and A(0) Lamb modes traveling in the elastic plate. These Lamb mode artifacts are not found to be present in the shadow region when the acoustic waves are incident upon the elastic surface.     

一种新型声学超材料平板对机械波吸收性能的模拟与实验研究

基于质量-弹簧微结构通过光学振动模式对机械波进行选择性吸收的原理, 本文设计了一个由集中质量与弹性薄膜构成的二维声学超材料等效平板结构. 利用有限元法对等效平板代表性胞元的振动特性模拟结果表明, 二维超材料平板结构表现出与质量-弹簧微结构相同的振动模式. 基于模拟结果, 制作加工了一个正方形超材料平板, 并通过Polytec扫描式激光测振仪(PSV)对其振动特性进行了试验测试, 结果表明, 本文设计制作的超材料平板可以对频率157.5 Hz的机械波进行选择吸收.     

Elastic waves propagation in thin plate metamaterials and evidence of low frequency pseudo and local resonance bandgaps

A comprehensive numerical simulation study on elastic wave propagation for a novel engineered thin plate metamaterial structural system is presented. To enhance the accuracy of model, a mesh convergence study is validated. The wave dispersion spectra with bandgaps for three types of structures are presented. Based on local resonance phenomena, the low frequency pseudo and local resonance bandgaps are reported. Highlights are also included for the Bragg scattering induced directional bandgaps. The effects of material and geometric parameters on bandgaps are discussed. The finite element based frequency response study further validates the reported bandgaps. The conclusions provide a new perspective for designs and applications of thin plate metamaterials for subwavelength wave manipulation including seismic shielding of civil infrastructures.     

Vibration isolation on floating floors

An analysis is presented of the noise problem produced when the application of standard acoustic treatment to a roof-mounted diesel generator failed to meet the design criterion. The problem was diagnosed as excessive vibration reaching the building due to the excitation of a resonance of the supporting structure. The resonance responsible was identified as a flexural mode of the partial floating floor installed below the generator set in order to provide a high transmission loss acoustic barrier. A solution to the problem was provided by converting the existing vibration isolation into a compound system. The reasons for the failure of the existing system are analysed. A simple theory is developed which illustrates that the ratio of machine mass to floating floor mass is the important parameter determining the severity of excitation of floating floor resonance. It is concluded that machines can be safely mounted via vibration isolators onto continuous floating floors provided they ahve a low mass compared with the floating floor mass and are provided with a low mounted resonant frequency compared with the floating floor resonant frequency.     

The effect of boundary conditions on guided wave propagation in two-dimensional models of healing bone

Guided wave propagation has recently drawn significant interest in the ultrasonic characterization of bone. In this work, we present a two-dimensional computational study of ultrasound propagation in healing bones aiming at monitoring the fracture healing process. In particular, we address the effect of fluid loading boundary conditions on the characteristics of guided wave propagation, using both time and time-frequency (t-f) signal analysis techniques, for three study cases. In the first case, the bone was assumed immersed in blood which occupied the semi-infinite spaces of the upper and lower surfaces of the plate. In the second case, the bone model was assumed to have the upper surface loaded by a 2mm thick layer of blood and the lower surface loaded by a semi-infinite fluid with properties close to those of bone marrow. The third case, involves a three-layer model in which the upper surface of the plate was again loaded by a layer of blood, whereas the lower surface was loaded by a 2mm layer of a fluid which simulated bone marrow. The callus tissue was modeled as an inhomogeneous material and fracture healing was simulated as a three-stage process. The results clearly indicate that the application of realistic boundary conditions has a significant effect on the dispersion of guided waves when compared to simplified models in which the bone's surfaces are assumed free.     

透射边界条件在点声源海底地震波数值计算中的应用

航行舰船在海底岩土层中引起的弹性波被称为舰船地震波,主要由舰船低频辐射噪声引起,可用于识别舰船目标。本文采用大型有限元软件ANSYS中的流固耦合计算模块,结合多次透射公式(MTF)人工边界条件,对较为简单的水平分层海洋环境下低频点声源海底地震波进行了数值计算,并为了分析数值计算方法的精度,将数值计算结果与波数积分方法结果进行了比较。频率较低时两种方法的声传播损失曲线符合较好,频率较高时结果存在一定差别;两种计算方法所得声传播频率特性曲线的形式有所不同,但曲线总体变化趋势基本一致;而海底表面竖直位移、水平位移、竖直加速度和水平加速度的频率特性曲线基本符合。由此认为,基于多次透射公式人工边界,采用大型有限元软件ANSYS中的流固耦合模块,对较复杂环境下低频点声源海底地震波问题进行数值计算是基本可行的。