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.

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 ...

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.

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.

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.

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.

Sound radiation attenuation by circular total-reflection elastic metasurface composed of subunits with cubic profiles

Utilizing metamaterials or acoustic black holes(ABHs)to control wave propagation and then to realize vibration control and sound radiation attenuation is a hot topic in recent years.However,using elastic metasurfaces that possess similar wave manipulation abilities with metamaterials and ABHs to attenuate sound radiation has not been reported yet.In this paper,a circular total-reflection elastic metasurface(CTREM)composed of subunits with cubic profiles similar with ABHs is proposed to realize vibration isolation and achieve broadband sound radiation attenuation of a plate below the cut-on frequency of the ABH.Compared with the corresponding bare plate and the plate containing a single ABH with a conventional design,the sound radiation efficiencies of the CTREM plate within and outside the vibration isolation band are both substantially attenuated.This phenomenon can be attributed to two distinct mechanisms:the total reflection of flexural waves caused by vibration isolation,and the local resonances of subunits.Analyses of the wavenumber spectra obtained from normal vibration velocities of the CTREM plate,both experimentally and numerically,along with the supersonic intensity patterns,reveal that the confined vibration energies are subsonic components localized within ineffective sound radiation areas.This,in turn,reduces the coupling strength of sound and vibration,thereby significantly attenuating sound radiation efficiency.The proposed CTREM provides a lossless and lightweight method for sound radiation attenuation.

Precision Improvement of the Discrete Calculation Method for Sound Radiation Research

Sound radiation of thin plates is a common problem in engineering. Hashimoto proposed the discrete calculation method(DCM) to deal with the problem. The calculation of the radiation impedance of the rectangular element is more cumbersome than that of the circular one, so the discrete rectangular radiation element is approximated by the circular one. However, error is also introduced. The formula developed by Sha has been employed to get self- and mutual-radiation impedances of rectangular radiation element. Numerical study was performed to verify error introduced by the approximation Hashimoto adopted. Experimental researches on sound radiation of a 2 mm-thick and a 4 mm-thick magnesium alloy plates were also carried out to evaluate the errors introduced by the approximation. The experimental results indicate that the circular approximation Hashimoto adopted overestimates the sound radiation efficiency. The maximum error levels of the radiation efficiencies of the2 mm-thick and 4 mm-thick magnesium alloy plates are up to 0.15 and 0.12, respectively. The effect of element aspect ratio on the sound radiation efficiency is also remarkable.

VIBRATION AND SOUND RADIATION OF AN ASYMMETRIC LAMINATED PLATE IN THERMAL ENVIRONMENTS

Analytical studies on the vibration and sound radiation characteristics of an asymmetric laminated rectangular plate are carried out in this paper. Theoretical formulations, in which the effects of thermal environments are taken into account, are derived for the vibration and sound radiation based on both first-order shear deformation plate theory and Rayleigh integral. It is found that the natural frequencies, the resonant amplitudes of vibration response and the sound pressure level decrease with the temperature rising. The natural frequencies of asym- metric plates are smaller than those of symmetric plates and the velocity responses of asymmetric plates are larger than those of symmetric plates.

A SEMI-ANALYTICAL METHOD FOR THE VIBRATION OF AND SOUND RADIATION FROM A TWO-DIMENTIONAL BEAM-STIFFENED PLATE

A semi-analytical method based on space harmonics to investigate the vibration of and sound radiation from an infinite, fluid-loaded plate is presented. The plate is reinforced with two sets of orthogonally and equally spaced beam stiffeners, which are assumed to be line forces. The response of the stiffened plate to a convected harmonic pressure in the wave-number space is obtained by adopting the Green＇s function and Fourier transform methods. Using the boundary conditions and space harmonic method, we establish the relationship between the stiffener forces and the vibration displacement of the plate. In this paper, the stiffener forces are expressed in terms of harmonic amplitudes of the plate displacement, which are calculated by using a numerical reduction technique. Finally, the Fourier inverse transform is employed to find expressions of the vibration and sound radiation in physical space. Agreements with existing results prove the validity of this approach and more numerical results are presented to show that this method converges rapidly.

Active feedback control of sound radiation in elastic wave metamaterials immersed in water with fluid-solid coupling

Due to their potential properties unlike traditional materials and structures,elastic wave metamaterials have received significant interests in recent years.With the coupling between the acoustic and vibration,their mechanical characteristics can be tuned by the active feedback control system at low frequency ranges in which the traditional passive control is limited.This work illustrates that the superior performances of the effective mass density and sound pressure level(SPL)of an elastic wave metamaterial can be significantly changed by the active control,in which the periodic array of local resonators and orthogonal stiffeners are included.Significantly,based on the locally resonant mechanism,the negative density occurs over a frequency range.Due to the effects of lattice constant,structural damping and other parameters,the SPL with the function of fluid-solid coupling are illustrated and discussed.

Sound radiation of parallelly stiffened plates under convected harmonic pressure excitation

The radiation of noise from a parallelly rib-stiffened skin plate of aircraft cabin fuselage in the presence of external mean flow is theoretically investigated.An aero-acoustic-elastic model is developed and used to calculate the radiated sound pressure level(SPL) versus frequency curves with reference to sound radiation of a bare plate immersed in a steady fluid.The flexural and rotational motions of the rib stiffeners are described by applying the Euler-Bernoulli beam theory and torsional wave equation,respectively.Therefore,the coupling forces and moments between the ribs and the face-panel,caused separately by flexural and rotational motion of the ribs,are both taken into account.Given the periodicity of the structure,the Fourier transform technique is employed to solve panel vibration equations and acoustic equations.Systematic parametric investigation demonstrates that the presence of mean flow as well as rib spacings play significant roles in the sound radiation behavior of parallelly rib-stiffened plates.The proposed model provides a convenient and efficient tool for the factual engineering design of this kind of periodic structures with acoustic requirements.

Time-domain analysis for vibration and sound radiation of submerged spherical shell excited by force

The vibration and sound radiation of a submerged spherical shell are studied in the time-domain by Laplace transform method, where a CW pulse force acts at the apex of the shell. The numerical results for the case of long pulse show that the different vibrational modes and the resonant or beat radiated sound are excited for different carrier-frequencies, but litle sound is radiated for some vibrational modes. For the case of short pulse the waveforms of the pulse become widened and deformed, when the pulse propagates between apexes of the shell. Then, the Doubly Asymptotic Approximations (DAA2) and Kirchhoff's Retarded Potential Formulate (KRPF)are used to solve the same problem. It is shown that the results of DAA2 and KRPF method have a good agreement with the results of Laplace transform method.