The influence of reflections from the train body and the ground on the sound radiation from a railway rail

Purpose – The vibration of the rails is a significant source of railway rolling noise, often forming the dominantcomponent of noise in the important frequency region between 400 and 2000 Hz. The purpose of the paper is toinvestigate the influence of the ground profile and the presence of the train body on the sound radiation fromthe rail.Design/methodology/approach – Two-dimensional boundary element calculations are used, in which therail vibration is the source. The ground profile and various different shapes of train body are introduced in themodel, and results are observed in terms of sound power and sound pressure. Comparisons are also made withvibro-acoustic measurements performed with and without a train present.Findings – The sound radiated by the rail in the absence of the train body is strongly attenuated by shieldingdue to the ballast shoulder. When the train body is present, the sound from the vertical rail motion is reflectedback down toward the track where it is partly absorbed by the ballast. Nevertheless, the sound pressure at thetrackside is increased by typically 0–5 dB. For the lateral vibration of the rail, the effects are much smaller. Oncethe sound power is known, the sound pressure with the train present can be approximated reasonably well withsimple line source directivities.Originality/value – Numerical models used to predict the sound radiation from railway rails have generallyneglected the influence of the ground profile and reflections from the underside of the train body on the soundpower and directivity of the rail. These effects are studied in a systematic way including comparisons with measurements.

Vibration and Sound Radiation of Cylindrical Shell Covered with a Skin Made of Micro Floating Raft Arrays Excited by Turbulence

To reduce the vibration and sound radiation of underwater cylindrical shells,a skin composed of micro floating raft arrays and a compliant wall is proposed in this paper.A vibroacoustic coupling model of a finite cylindrical shell covered with this skin for the case of turbulence excitation is established based on the shell theories of Donnell.The model is solved with the modal superposition method to investigate the effects of the structural parameters of micro floating raft elements on the performance of reducing vibration and sound radiation of the cylindrical shell of this skin.The results indicate that increasing the stiffness ratio,damping ratio,mass ratio,or decreasing the interval betweenmicro floating raft elements can improve the vibration and sound radiation reduction performance of this skin over the frequency range 0∼2000 Hz.Moreover,the mean quadratic velocity level and sound radiation power level of the finite cylindrical shell with this skin can be reduced by 12.00 dB and 9.65 dB respectively compared to the finite cylindrical shell with homogeneous viscoelastic coating in the frequency range from0∼2000Hz,implying a favorable performance of this skin for reducing the vibration and sound radiation of cylindrical shells.

Extension of sound field reconstruction based on element radiation superposition method in a sparsity framework

Nearfield acoustic holography(NAH)is a powerful tool for realizing source identification and sound field reconstruction.The wave superposition(WS)-based NAH is appropriate for the spatially extended sources and does not require the complex numerical integrals.Equivalent source method(ESM),as a classical WS approach,is widely used due to its simplicity and efficiency.In the ESM,a virtual source surface is introduced,on which the virtual point sources are taken as the assumed sources,and an optimal retreat distance needs to be considered.A newly proposed WS-based approach,the element radiation superposition method(ERSM),uses piston surface source as the assumed source with no need to choose a virtual source surface.To satisfy the application conditions of piston pressure formula,the sizes of pistons are assumed to be as small as possible,which results in a large number of pistons and sampling points.In this paper,transfer matrix modes(TMMs),which are composed of the singular vectors of the vibro-acoustic transfer matrix,are used as the sparse basis of piston normal velocities.Then,the compressive ERSM based on TMMs is proposed.Compared with the conventional ERSM,the proposed method maintains a good pressure reconstruction when the number of sampling points and pistons are both reduced.Besides,the proposed method is compared with the compressive ESM in a mathematical sense.Both simulations and experiments for a rectangular plate demonstrate the advantage of the proposed method over the existing methods.

Active control of structural sound radiation in an acoustic enclosure consisting of flexible structure

The active control of structural sound radiation in an acoustic enclosure is studied by using distributed point force actuators as the secondary control force, and the control mechanisms for the radiated noise in the cavity are analyzed. A rectangular enclosure involving two simply supported flexible plates is created for this investigation. The characteristics of the primary and secondary sound field and the structural-acoustic coupled system are analyzed, and the optimal control objective for reducing the sound pressure level （SPL） in the cavity is derived. The response of the SPL in the cavity is analyzed and compared when the secondary point force actuators with different locations and parameters are applied to the two flexible plates. The results indicate that the noise in the cavity can be better controlled when some point force actuators are applied to two flexible plates for cooperative control rather than the point force actuators being only applied to the excited flexible plate.

Effect of Wheel Load on Wheel Vibration and Sound Radiation

The current researches of wheel vibration and sound radiation mainly focus on the low noise damped wheel. Compared with the traditional research, the relationship between the sound and wheel/rail contact is difficulty and worth studying. However, there are few studies on the effect of wheel load on wheel vibration and sound radiation. In this paper, laboratory test carried out in a semi-anechoic room investigates the effect of wheel load on wheel natural frequencies, damping ratios, wheel vibration and its sound radiation, The laboratory test results show that the vibration of the wheel and total sound radiation decrease significantly with the increase of the wheel load from 0 t to 1 t. The sound energy level of the wheel decreases by 3.7 dB. When the wheel load exceeds 1 t. the attenuation trend of the vibration and sound radiation of the wheel becomes slow. And the increase of the wheel load causes the growth of the wheel natural frequencies and the mode damping ratios. Based on the finite element method （FEM） and boundary element method （BEM）, a rolling noise prediction model is developed to calculate the influence of wheel load on the wheel vibration and sound radiation. In the calculation, the used wheel/rail excitation is the measured wheel/rail roughness. The calculated results show that the sound power level of the wheel decreases by about 0.4 dB when the wheel load increases by 0.5 t. The sound radiation of the wheel decreases slowly with wheel load increase, and this conclusion is verified by the field test. This research systematically studies the cffcct of wheel load on wheel vibration and sound radiation, gives the relationship between the sound and wheel/rail contact and analyzes the reasons, therefore, it provides a reference for further research.

ANALYSIS OF SOUND RADIATION FROM THE RING-STIFFENED CYLINDRICAL SHELL COATED WITH VISCOELASTIC LAYER IN FLUID MEDIUM

The Donnell theory of shell is applied to describe shell motion and layer motion is described by means of three-dimensional Navier equations.Using deformation harmonious condi- tions of the interface,the effects of stiffeners and layer are treated as reverse forces and moments acting on the cylindrical shell.In studying the acoustic field produced by vibration of the sub- merged ring-stiffened cylindrical coated shell,the structure dynamic equation,Helmholtz equation in the fluid field and the continuous conditions of the fluid-structure interface compose the cou- pling vibration equation of the sound-fluid-structure.The extract of sound pressure comes down to the extract of coupling vibration equation.By use of the solution of the equation,the influ- ences of hydrostatic pressure,physical characters and geometric parameters of the layer on sound radiation are discussed.

NUMERICAL SIMULATION OF SOUND RADIATION ON GEARBOX'S HOUSING

The fluid-structure coupling finite element model and the boundary element model of a complex gearbox＇s housing are built based on the theory of fluid-structure coupling finite element method and boundary element method. At the same time, the exciting forces of the housing are analyzed and applied to the finite element models. Firstly, vibration of the housing is calculated by the fluid-structure coupling finite element model; secondly, the calculated result is verified by the experiment; finally, sound radiation of the housing is calculated by the boundary element. According to the calculated results, the housing adds some ribs not only to increase the strength, but also to reduce the sound radiation of the housing. At last, the sound radiation of the modified housing is calculated, which shows that the sound radiation of the modified housing with ribs is lower.

Sound radiation of a functionally graded material cylindrical shell in water by mobility method

Based on the fundamental dynamic equations of functionally graded material (FGM) cylindrical shell, this paper investigates the sound radiation of vibrational FGM shell in water by mobility method. This model takes into account the exterior fluid loading due to the sound press radiated by the FGM shell. The FGM cylindrical shell was excited by a harmonic line radial force uniformly distributing along the generator. The FGM shell equations of motion, the Helmholtz equation in the exterior fluid medium and the continuity equation at fluid-shell interface are used in this vibroacoustic problem. The expressions of sound radiation efficiency and sound field of the FGM shell have been derived by mobility method. Radiation efficiency, modal mobility and the directivity pattern of the sound field are solved numerically. In particular, radiation efficiency and directivity pattern with various power law index are analyzed.

Acoustic design sensitivity analysis of structural sound radiation

This paper presents an acoustic design sensitivity(ADS)analysis on sound radiation of structures by using the boundary element method(BEM).We calculated the velocity distribution of the thin plate by analytical method and the surface sound pressure by Rayleigh integral,and expressed the sound radiation power of the structure in a positive definite quadratic form of the Hermitian with an impedance matrix.The ADS analysis of the plate was thus translated into the analysis of structure dynamic sensitivity and ...

Multi-objective Optimization of Non-uniform Beam for Minimum Weight and Sound Radiation

A multi-objective optimization of non-uniform beams is presented for minimum radiated sound power and weight. The transfer matrix method is used to compute the structural and acoustic responses of a non-uniform beam accurately and efficiently. The multi-objective particle swarm optimization technique is applied to search the Pareto optimal solutions that represent various compromises between weight and sound radiation. Several constraints are imposed, which substantially reduce the volume fraction of feasible solutions in the design space. Two non-uniform beams with different boundary conditions are studied to demonstrate the multi-objective optimal designs of the structure. © 2017, Tianjin University and Springer-Verlag Berlin Heidelberg.

A General Model for Analysis of Sound Radiation from Orthogonally Stiffened Laminated Composite Plates

A general theoretical model is developed to investigate the sound radiation from an infinite orthogonally stiffened plate under point excitation force. The plate can be metallic or composite, and fluid loading is also considered in the research. The first order shear deformation theory is used to account for the transverse shear deformation. The motion of the equally spaced stiffeners is examined by considering their bending vibrations and torsional movements. Based on the periodic structure theory and the concepts of the equivalent dynamic flexibility of the plate, the generalized vibro-acoustic equation of the model is obtained by applying the Fourier transform method. The generalized model that can be solved numerically is validated by comparing model predictions with the existing results. Numerical calculations are performed to investigate the effects of the location of the excitation, the spacing of the stiffeners, the plate thickness, the strengthening form and the fiber orientation on the sound radiation characteristic of the orthogonaUy stiffened plate, and some practical conclusions are drawn from these parameter studies.

SOUND RADIATION FROM PLATES ON ELASTIC FOUNDATION UNDER ACTION OF MOVING LINE FORCES

An analysis is made of the problem of sound radiation from infinite one-dimensional plateson elastic foundation, when the plates are subjected to the action of harmonic line forces movingat subsonic speeds (M 【 1). The expressions of nondimensional sound power are formulated andthe asymptotic forms of sound power in the low frequency regions are derived. The radiatedsound power is shown as a function of the stiffness of elastic foundation, in terms of stiffness fac-torψ, the moving speed of line force, in terms of Math number M, and the frequency, in termsof wavenumber ratio γ . The effects of the parameter ψ in conjunction with the parameters Mand γ on the radiated sound power level and the phenomenon of coincidence radiation are alsoinvestigated in detail.

A General Method to Study the Sound Radiation of a Finite Cylindrical Shell Based on Elastic Theory

A general method was proposed to study the sound and vibration of a finite cylindrical shell with elastic theory. This method was developed through comprehensive analysis of the uncoupled Helmholtz equation obtained by the decomposition of elastic equations and the structure of the solution of a finite cylindrical shell analyzed by thin shell theory. The proposed method is theoretically suitable for arbitrary thickness of the shell and any frequency. Also, the results obtained through the method can be used to determine the range of application of the thin shell theory. Furthermore, the proposed method can deal with the problems limited by the thin shell theory. Additionally, the method can be suitable for several types of complex cylindrical shell such as the ring-stiffened cylindrical shell, damped cylindrical shell, and double cylindrical shell.

Sound Radiation Analysis of Damping Structure Based on Response Surface Method

The methods of modifying dimension and shape of structure, or covering damping material are effective to reduce structure-borne noise, while these methods are based on the knowledge of qualitative and quantitative relationship between sound radiation and design parameters. In order to decrease the complexity of the problem, response surface method(RSM) was utilized to analyze and optimize the vibro-acoustic properties of the damping structure. A simple case was illustrated to demonstrate the capabilities of the developed procedure. A structure-born noise problem was approximated by a series of polynomials using RSM. Three main performances were considered, i.e. sound radiation power, first order modal frequency and total mass. Consequently, the response surface model not only gives the direction of design modification, it also leads to an optimal design of complex systems.

Research on vibration and near-field sound radiation of ring-ribbed cylindrical shell coated deadening and decoupling materials

The research on structural vibration and sound radiation of underwater ring-ribbed cylindrical shell, which is coated with a kind of deadening and decoupling materials, becomes a focus in recent years. This paper analyzes the problem on two aspects: model experiment and numerical calculation. The model experiment is carried out including three cases firstly, in which the structural vibration response and radiating acoustic field are measured respectively, and the results gained in these three cases are analyzed to discuss the effect of reducing structural vibration and radiating noise of the deadening and decoupling materials. The coupling FEM/BEM and the SEA methods are both used in numerical calculation, i.e. the arithmetic of the coupling FEM/BEM method is adopted to calculate the low frequency characteristics and the SEA method is adopted to calculate the medium-high frequencies characteristics of the model. By comparing experimental results with numerical calculation results, it is proved that the algorithm adopted in this paper is reasonable.

FORCED VIBRATION AND SOUND RADIATION OF A RECTANGULAR PLATE WITH VISCOELASTIC BOUNDARY SUPPORTS

A method for the forced vibration and sound radiation of a rectangular plate with viscoelastic boundary supports is proposed.The method is based on damped complex modes analysis method.Using the damped complex modes of the plate system,the modal equation of the plate motion becomes completely uncouped.The sound radiation pressure is obtained by numerical integration of the Rayleigh integral.Effects of the viscoelastic boundary supports on the vibration response and the radiated sound pressure of the vibrating plate are discussed by an example.

THEORETICAL PREDICTION OF SOUND RADIATION FROM A HEAVY FLUID-LOADED CYLINDRICAL COATED SHELL

A theoretical model is developed to predict the sound radiation ability of a cylindrical thin elastic shell of finite length, covered with a damp layer and terminated with infinite cylindrical rigid baffles. This shell is immersed in a heavy fluid extending up to infinity, and excited by a constant point load continuously traveling along the circumferential direction. A frequency-domain representation of the rotating load and three equations of the vibroacoustic coupling problem are given. The equations are solved by means of modal analysis method and asymptotic expansion method. Also, a mathematical expression of modal amplitude of shell radial displacement is obtained. The sound radiation ability of this kind of shell is evaluated and the corresponding numerical results are given.

Acoustic radiation force on a multilayered sphere in a Gaussian standing field

We develop a model for calculating the radiation force on spherically symmetric multilayered particles based on the acoustic scattering approach.An expression is derived for the radiation force on a multilayered sphere centered on the axis of a Gaussian standing wave propagating in an ideal fluid,The effects of the sound absorption of the materials and sound wave on acoustic radiation force of a multilayered sphere immersed in water are analyzed,with particular emphasis on the shell thickness of every layer,and the width of the Gaussian beam.The results reveal that the existence of particle trapping behavior depends on the choice of the non-dimensional frequency ka,as well as the shell thickness of each layer.This study provides a theoretical basis for the development of acoustical tweezers in a Gaussian standing wave,which may benefit the improvement and development of acoustic control technology,such as trapping,sorting,and assembling a cell,and drug delivery applications.

Fast Prediction of Acoustic Radiation from a Hemi-capped Cylindrical Shell in Waveguide

In order to predict acoustic radiation from a structure in waveguide, a method based on wave superposition is proposed, in which the free-space Green＇s function is used to match the strength of equivalent sources. In addition, in order to neglect the effect of sound reflection from boundaries, necessary treatment is conducted, which makes the method more efficient. Moreover, this method is combined with the sound propagation algorithms to predict the sound radiated from a cylindrical shell in waveguide. Numerical simulations show the effect of how reflections can be neglected if the distance between the structure and the boundary exceeds the maximum linear dimension of the structure. It also shows that the reflection from the bottom of the waveguide can be approximated by plane wave conditionally. The proposed method is more robust and efficient in computation, which can be used to predict the acoustic radiation in waveguide.

Active Control of Structurally Radiated Sound from an Elastic Cylindrical Shell

A numerical and experimental study was presented on active control of structurally radiated sound from an elastic cylindrical shell.An analytical model was developed for the active structural acoustic control (ASAC) of the cylindrical shell.Both global and local control strategies were considered.The optimal control forces corresponding to each control strategy were obtained by using the linear quadratic optimal control theory.Numerical simulations were performed to examine and analyze the control performance under different control strategies.The results show that global sound attenuation of the cylindrical shell at resonance frequencies can be achieved by using point force as the control input of the ASAC system.Better control performance can be obtained under the control strategy of minimization of the radiated sound power.However,control spillover may occur at off-resonance frequencies with the control strategy of structural kinetic energy minimization in terms of the radiated sound power.Considerable levels of global sound attenuation can also be achieved in the on-resonance cases with the local control strategy,i.e.,minimization of the mean-square velocity of finite discrete locations.An ASAC experiment using an FXLMS algorithm was implemented,agreement was observed between the numerical and experimental results,and successful attenuation of structural vibration and radiated sound was achieved.