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In recent years, the issue of structure-borne noise caused by steel bridges has become increasingly significant. The periodic ribbed plate not only serves as a fundamental component of steel bridges but also represents the primary source of noise. This paper integrates the advanced statistical energy analysis (ASEA) method with acoustic radiation theory to propose a method for predicting the noise generated by periodic ribbed plates. Simultaneously, sample experiments were conducted to validate the accuracy and reliability of the proposed method. A comparative analysis between the ASEA method and the traditional statistical energy analysis (SEA) method reveals a substantial underestimation by the SEA method for the acoustic response of plates located far from the excitation. At high frequencies, the prediction error of the SEA method reaches up to 30dB. At the end of the paper, the effects of base plate thickness, rib height, and rib thickness on the transmission coefficient and difference of sound power level (DSWL) of periodic ribbed plates were investigated. It was found that increasing the base plate thickness and rib height can respectively weaken and enhance the energy attenuation capability of periodic ribbed plates, while the effect of rib plate thickness on the energy attenuation capability is weak.

Acoustic radiation from double composite laminated cylindrical shells with cyclic rectangular rib-plates is analytically investigated by using the Sommerfeld-Watson transform. High-frequency acoustic model of double composite cylindrical shells with rectangular rib-plates is established in terms of creeping waves, geometrical acoustic waves and sound pressure asymptotic integrals. One kind of bending wave boundary layers for the shear deformable rectangular rib-plate is shown. Each set of creeping wave poles for the composite cylindrical shells with rectangular rib-plates is uniformly distributed by the cyclic period. This characteristic still holds for the cyclic structures with the smallest period. Creeping wave poles of the stiffened composite cylindrical shells appear in the entire complex circumferential wavenumber plane. The asymptotic integrals with Airy function are proposed to fast calculate acoustic pressure in the shadow and penumbra regions without making use of creeping wave poles.

Acoustic black hole (ABH), as a new wave manipulation technique, shows excellent applications in vibration and noise reduction of structures. Nowadays, most ABHs use materials with a fixed elastic modulus, limiting their low-frequency performance. Herein ABH plates with variable elastic modulus (VM-ABH) is designed, and its vibration and acoustic radiation characteristics are investigated by using numerical analysis. The results show that the vibration response of VM-ABH has a decrease of 5–13.2dB relative to that of the uniform texture ABH (UT-ABH) in the frequency range of 10–5000Hz, and the degree of energy aggregation is significantly improved. Moreover, the sound pressure level was reduced by 3.6 dB. Meanwhile, by linearly varying the elastic modulus in the center region of the VM-ABH, the effects of gradient index and terminal elastic modulus on the damping characteristics and dynamic response are revealed. The research results provide new objects for the study of vibration and noise reduction of ABH.

Predicting the response of a complex structural-acoustic system across a broad frequency range presents a number of challenges to an analyst. It is quite common to find that the uncertainty associated with the local dynamic properties of various subsystems of a system can vary greatly across the system. It is also common to find that the modal density and wavenumber content of the various subsystems can vary greatly across the system. Typically, this results in a mixture of strongly phase correlated (long wavelength) motion which spans many subsystems, superimposed with weakly phase correlated local motion that is confined to individual subsystems. This mismatch in the local statistical and dynamic properties of a system is often referred to as the mid-frequency problem. This paper provides a qualitative definition of the mid-frequency problem and suggests that a statistical description of the local dynamic properties of a system is an essential element of any mid-frequency prediction method. A hybrid approach to the mid-frequency problem is then described which employs a statistical description of the local modal properties of various subsystems in a system. The spatial statistics of the local modes are of particular interest and the way in which these statistics are encompassed in the hybrid analysis is discussed. Experimental investigations of the spatial statistics of a frame-panel structure are then presented and measurements of the acoustic power radiated by the structure are compared with numerical predictions.

A modal method is developed for solving, analyzing, and controlling vibration and sound radiation of coupled fluid-structure systems. The method recasts the coupled equation of a coupled fluid-structure system in the classical matrix structural dynamic equation by modeling the acoustic load vector as direct linear function of the acceleration, velocity, and displacement vector. With the Rayleigh damping assumption of the coupled fluid-structure system the resulting equation can be uncoupled via a transformation to modal coordinates and analyzed by solving independent equations of single degree of freedom system. The modal radiation efficiencies, effect of modal interaction on sound radiation, mode shapes, and modal control of the coupled fluid-structure system are presented and discussed. Numerical example of the vibration and sound radiation of a fluid-loaded stiffened plate is presented solely as a vehicle to demonstrate the method. The comparisons in terms of computed sound power of the present method with the standard coupling method and available published results show a very good agreement. The mode shapes and the self- and mutual-radiation efficiencies of modes of the fluid-loaded stiffened plate are given and discussed. The study of the effect of modal interaction on sound power shows that the power radiated by a single mode is to increase total radiated power and the interaction of modes may lead to an increase or a decrease or no change in the total radiated power. Numerical results also show that the modal control achieves good reductions in the mean square velocity and the sound power of the fluid-loaded stiffened plate.

Nearfield acoustic holography (NAH) is an indirect technique for identifying noise sources and visualizing acoustic field. Recently, several different methods, such as the spatial Fourier transform method, the boundary element method (BEM) and the Helmholtz equation-least squares (HELS) method, have been used to realize the NAH successfully. In the paper, a novel numerical method, the distributed source boundary point method (DSBPM), is proposed to realize the NAH. In the method, the transfer matrices from the reconstructed surface to the hologram surface are constructed indirectly by a set of particular solution sources located inside the vibrating structure, and their inverses are carried out by singular value decomposition (SVD) technique. Additionally, considering the high sensitivity of the reconstructed solution to measurement errors, the Tikhonov regularization method is implemented to stabilize the reconstruction procedure and the regularization parameter is determined by L-curve criterion. Compared with the BEM-based NAH, the variable interpolation, the numerical quadrature, and the treatments of singular integral and nonuniqueness of solution are all avoided in the proposed method. Two numerical examples and an experiment are investigated to validate the feasibility and correctness of the proposed method.

Algorithms for an alternative integral-formulation method (AIM) are developed for predicting acoustic radiation from an arbitrary source in a free field. The main advantages of these algorithms are that the solution is always unique and the efficiency in numerical computations is very high. The input data to these algorithms consist of the normal and tangential components of the particle velocities that are specified on a hypothetical surface enclosing the source, and output data are the acoustic quantities that include the acoustic pressure, particle velocity, and acoustic intensity on and beyond the enclosure. To speed up the numerical computations, the Dijistra algorithm is adopted that searches automatically the shortest path between two neighboring nodes in carrying out line integral. Experiments in both interior and exterior regions are conducted, and the predicted acoustic pressure is checked against the benchmark value measured at the same location. The efficiency of AIM is examined and compared with that of conventional boundary element method (BEM) based Helmholtz integral formulations.

Acoustic radiation from a spherical source, vibrating with an arbitrary, axisymmetric, time-harmonic surface velocity distribution, while immersed near a thermoviscous fluid sphere suspended in an unbounded viscous thermally conducting fluid medium is computed. The formulation utilizes the appropriate wave field expansions and boundary conditions along with the translational addition theorem for spherical wave functions to develop a closed-form solution in form of infinite series. The prime objective is to investigate the thermoviscous loss effects on acoustic radiation and its associated field quantities. The analytical results are illustrated with a numerical example in which the spherical source, that may vibrate either in a monopole-like or a dipole-like mode, is suspended in a thermoviscous fluid medium near an equal-sized viscous thermally conducting fluid sphere. To avoid numerical difficulties normally arising in process of solving thermoviscous radiation/scattering problems in the frequency range of interest, a basic multiple precision FORTRAN computation package was utilized in developing specialized codes for computing special mathematical functions including spherical Bessel functions of complex argument and performing large complex matrix manipulations on floating point numbers of arbitrarily high precision. The essential acoustic field quantities such as the modal acoustic radiation impedance load on the source, the radiated far-field pressure directivity pattern and the radiated on-axis pressure are evaluated and discussed for representative values of the parameters characterizing the system. Limiting cases are examined and excellent agreements with well known solutions are attained.

A numerical study on the active control of a machine suspension system supported on a cylindrical shell aiming to reduce the sound radiation is presented in this paper. In this system, a rigid-body machine is supported on a simply-supported elastic cylindrical shell through four active isolators. A theoretical model is employed and four types of active control strategies including kinetic energy minimization strategy, power flow minimization strategy, squared acceleration minimization strategy and acoustic power minimization strategy are considered, with corresponding active control force obtained by linear quadratic optimal method. Numerical simulations are conducted and detailed results were presented. Active control performance under these four control strategies is compared and analyzed in terms of radiated sound power, and the effect of the number of active actuators is discussed by numerical analysis. The results show that acoustic power minimization strategy has the best performance to reduce the sound power radiated from supporting shell in general. Through numerical simulations, some comprehensive design principles of active control system are discussed at the end.

Multi-frequency calculation is usually very time-consuming due to the repeated numerical integration for numerous frequencies in acoustic scattering or radiation problems. A series expansion method has been proposed to speed up this process just by taking the frequency-dependent terms out of the integral sign. However, this method, constrained by the number of truncation terms, is only applicable to low and medium frequencies and/or small-size structures. This paper develops an improved series expansion method that can be employed in a wider frequency band and larger-scale problems but with less computing expense. In the present method, the frequency-dependent term kr in the integral kernel is firstly transformed into the range from -π to π due to the periodicity of sine and cosine functions. Afterwards, truncation error would be kept reasonably small while the number of expansion terms would not increase with kr. Test cases of acoustic radiation from a pulsating sphere and a cat's eye structure are conducted and numerical results show significant reduction of computational time but suffering little accuracy loss for multi-frequency problems with this approach.

This paper investigates the efficiency of the wave finite element (WFE) method to assess the vibroacoustic behavior of finite baffled axisymmetric elastic pipes interacting with internal and external acoustic fluids. The pipes, of either homogeneous or multi-layered cross-sections, are surrounded by an external fluid of infinite extent, which can be light or heavy. The Sommerfeld radiation condition is taken into account by considering a perfectly matched layer (PML) around the external fluid. The method involves the computation of waves traveling along an axisymmetric multi-physics waveguide that incorporates a pipe, internal and external fluids, as well as a PML. Numerical experiments are carried out which highlight the relevance of the WFE method in terms of accuracy and CPU time savings, in comparison with the conventional finite element analysis.

This paper reviews the equivalent source method (ESM), an attractive alternative to the standard boundary element method (BEM). The ESM has been developed under different names: method of fundamental solutions, wave superposition method, equivalent source method, etc. However, regardless of the method name, the basic concept is very similar; that is to use auxiliary points called equivalent sources to reconstruct the acoustic pressure for radiation or scattering problems. The strength of the equivalent sources are then determined via various approaches such that the boundary conditions on the boundary surface are satisfied. This paper reviews several frequency-domain and time-domain ESMs. There are several distinct advantages in these types of methods: (1) the method is a meshless approach so that it is easy and simple to implement; (2) it does not have a numerical singularity problem that occurs in the BEM; (3) the number of equivalent sources can be fewer than the number of surface collocation points so that the matrix size is reduced and a fast computation is achieved for large problems. The main issue of the ESM is that there is no rule to find out the optimal number and position of equivalent sources. In addition, the ESM suffers from the numerical instability that is associated with the ill-conditioned matrix. Some guidelines have been suggested in terms of finding the number and position of the sources, and several numerical techniques have been developed to resolve the numerical instability. This paper reviews the common theories, numerical issues and challenges of the ESM, and it summarizes recent developments and applications of the ESM to aircraft noise.

The vibration and acoustic behaviors of both glass fiber laminated plates and carbon/glass fiber hybrid laminated plates are investigated by numerical simulation. The free vibration, forced vibration and acoustic radiation of laminated plates including glass fiber laminates and carbon/glass fiber hybrid laminates in air and water are calculated by the coupled finite element and boundary element method and compared with the corresponding test results. It was demonstrated that results obtained by the coupled finite element and boundary element method are in good agreement with the experimental ones. The effects of dispersion, outer fiber types and fiber hybrid ratio on the vibration and sound radiation of the laminates plates are also discussed.

In this work, the smoothed finite element method using four-node quadrilateral elements (SFEM-Q4) is employed to resolve underwater acoustic radiation problems. The SFEM-Q4 can be regarded as a combination of the standard finite element method (FEM) and the gradient smoothing technique (GST) from the meshfree methods. In the SFEM-Q4, only the values of shape functions (not the derivatives) at the quadrature points are needed and the traditional requirement of coordinate transformation procedure is not necessary to implement the numerical integration. Consequently, no additional degrees of freedom are required as compared with the original FEM. In addition, the original “overly-stiff” FEM model for acoustic problems (governed by the Helmholtz equation) is properly softened due to the gradient smoothing operations implemented over the smoothing domains and the present SFEM-Q4 possesses a relatively appropriate stiffness of the continuous system. Therefore, the well-known numerical dispersion error for Helmholtz equation is decreased significantly and very accurate numerical solutions can be obtained by using relatively coarse meshes. In order to truncate the unbounded domains and employ the domain-based numerical method to tackle the acoustic radiation in unbounded domains, the Dirichlet-to-Neumann (DtN) map is used to ensure that there are no spurious reflections from the far field. The numerical results from several numerical examples demonstrate that the present SFEM-Q4 is quite effective to handle acoustic radiation problems and can produce more accurate numerical results than the standard FEM.

To improve the accuracy of the standard finite element (FE) solutions for acoustic radiation computation, this work presents the coupling of a radial point interpolation method (RPIM) with the standard FEM based on triangular (T3) mesh to give a coupled “FE-Meshfree” Trig3-RPIM element for two-dimensional acoustic radiation problems. In this coupled Trig3-RPIM element, the local approximation (LA) is represented by the polynomial-radial basis functions and the partition of unity (PU) concept is satisfied using the standard FEM shape functions. Incorporating the present coupled Trig3-RPIM element with the appropriate non-reflecting boundary condition, the two-dimensional acoustic radiation problems in exterior unbounded domain can be successfully solved. The numerical results demonstrate that the present coupled Trig3-RPIM have significant superiorities over the standard FEM and can be regarded as a competitive numerical techniques for exterior acoustic computation.

A study on vibration and acoustic radiation characters of an isotropic rectangular thin plate under thermal environments is presented in this paper. It is assumed that thermal loads caused by thermal environments just change the structure stress state. Thermal stresses induced by uniform temperature rise of the plate are determined with the thermo-elastic theory. Then the stress state is used in the following dynamic analysis as a pre-stressed factor. It is observed that thermal loads influence the natural frequencies evidently, especially the fundamental natural frequency. The order of mode shapes stays the same. Dynamic response peaks float to lower frequency range with the increment of structure temperature. Acoustic radiation efficiency of the plate subjected to thermal loads decreases in the mid-frequency band. For validation, numerical simulations are also carried out. It can be found that the combined approach of finite element method (FEM) and boundary element method (BEM) is more appropriate for radiation problems.

The vibration and acoustic radiation for an orthotropic composite conical shell in a hygroscopic environment are explored through the wave propagation approach and Galerkin method. Theoretical results of the natural vibration and far field sound pressure are presented with incremental moisture content. The effects of incremental stiffness and different semi-vertex angle on the acoustic radiation characteristics are studied too. It is found that the natural frequencies decrease with incremental moisture content. The wavenumbers associated with the lowest frequency mode reaches the modal indices corresponding to the lowest buckling mode near the critical buckling moisture content. With the increasing moisture content, a shifting of natural frequencies toward lower frequency band could be observed in lower frequency band of the modal density in constant frequency band. The overall sound pressure level (SPL) decreases generally with the moisture content, but shows a marginal increase near the critical buckling moisture content. The modal density and overall SPL decrease with the incremental stiffness generally, which increases with the decrease of the semi-vertex angle.

A hybrid computational method is proposed for three-dimensional structural-acoustic radiation in shallow water, which combines the wave superposition method (WSM) with the adjustable Green function and the multi-physical-coupled finite element method (FEM). A low-frequency acoustic model in the near field is established by the FEM to discretize the continuous and arbitrary-shaped radiator, and the normal vibration velocity on the wetted surface is used as the input in the WSM to calculate the strengths of simple sources enclosed within the radiator. Finally, the sound propagation in the far field of the elastic structure is efficiently computed by superimposing the sound field of each simple source. The numerical examples of the pulsating sphere and elastic spherical shell in the shallow water are developed to verify the high accuracy and efficiency of the presented method, respectively. Moreover, the regularization algorithms are employed as the complementary approaches to improve the stability of this method in engineering practices, it is found that the algorithms can significantly hold the calculation accuracy in case the velocity data contain noise, and the least-squares QR is an efficient and accurate method with a few iteration numbers and better stability effect as compared with other algorithms.

This paper presents the thermo-acoustic frequency response of an un-baffled rectangular panel subjected to an external excitation load. A boundary element method BEM has been employed taking into account the Kirchhoff-Helmholtz K-H integral equation for the acoustic pressure and with the fluid-plate interface boundary condition the acoustic pressure jump over the panel is calculated. The thermal effects are considered regarding in the form of a uniform increment of temperature of the panel and are analysed in order to prevent the buckling phenomena. The excitation force considered is in the form of a concentrated load at some point of the panel and the deformation modes correspond to the vacuum case. Applying a collocation method for the panel equation, a frequency transfer function is obtained that relates the deflexion of the panel with the applied load. The effect of several geometric parameters, different thermal loads and location of the load applied on the acoustic radiated power and the acoustic efficiency spectrum are evaluated. Furthermore, the influence of the excitation frequency on the sound directivity is evaluated. The verification of the method is proven with other works.

In this paper, the sound directionality patterns produced by a nonseparable source located on a rigid cylinder of infinite length have been investigated for the case in which the source strength may be represented as a sum of separable sources by use of addition theorems. The result shows that the patterns of amplitude and phase distribution over the whole farfield space for the source are dependent of the frequencies of sound waves, circumference of the cylinder, and the strength of the source piston. It reveals that the observation points and the frequencies are important to the techniques of the boiler tube leak trace. This result can be applied to the technique of acoustic leak detection.