On the sound fields of infinitely long strips

Exact solutions are derived for sound radiation from four kinds of infinitely-long strips: namely a rigid strip in a baffle of finite width, a resilient strip in free space, and a resilient or rigid strip in an infinite baffle. In one limit, the strip in a finite baffle becomes a rigid strip in free space and in the other, a line source in a finite baffle. Here "rigid" means that the surface velocity is uniform, whereas "resilient" means that the surface pressure is uniform, and the strip is assumed to have zero mass or stiffness, as if a force were driving the acoustic medium directly. According to the Babinet-Bouwkamp principle, radiation from a resilient strip in an infinite baffle is equivalent to diffraction of a plane wave through a slit in the same. Plots are shown for the radiation impedances, far-field directivity patterns, and on-axis pressure responses of the four kinds of strip. A simple relationship between the radiation admittance of the rigid strip in an infinite baffle and the resilient strip in free space is presented. The two-dimensional rectangular wave functions developed in this paper can be applied to related problems.     

Dictums for problem solving and approximation in mathematical acoustics: examples involving low-frequency vibration and radiation

A sequence of dictums for mathematical acoustics is given representing opinions intended to be regarded as authoritative, but not necessarily universally agreed upon. The dictums are presented in the context of the detailed solution for a class of problems involving the forced vibration of a long cylinder protruding half-way into a half-space bounded by a compliant surface (impedance boundary) characterized by a spring constant. One limiting case corresponds to a cylinder vibrating within an infinite rigid baffle, and another limiting case corresponds to a vibrating cylinder on the compliant surface of an incompressible fluid. The second limiting case is identified as analogous to that of a floating half-submerged cylinder whose vibrations cause water waves to propagate over the surface. Attention is focused on vibrations at very low frequencies. Difficulties with insuring a causal solution are pointed out and dictums are given as to how one overcomes such difficulties. Various approximation techniques are described. The derivations involve application of the theory of complex variables and the method of matched asymptotic expansions, and the results include the apparent entrained mass in the near field of the cylinder and the radiation resistance per unit length experienced by the vibrating cylinder.     

Numerical computation of the radiation impedance of a rigid annular ring vibrating in an infinite plane rigid baffle

An expression for the radiation impedance of a rigid annular ring vibrating with uniform amplitude in a close-fitting infinite plane rigid baffle is presented. An algorithm for the numerical evaluation of this expression by electronic computer is included in the form of an Algol 60 procedure. A selection of numerical results obtained is included.     

Radiation from modes of a rectangular panel into a coupled fluid layer

Modal radiation efficiencies are evaluation for a rectangular panel which is simply supported in an infinite baffle and coupled to a fluid layer. The analysis is based on the calculation of the acoustic power radiated into the layer by the panel vibrating in one of its in vacuo natural modes. At low frequencies, the efficiency is inversely proportional to the layer depth; at high frequencies, it exhibits a complex, multiple peak characteristic, associated with the acoustic field of the layer. Comparison with the modal radiation efficiencies of a panel coupled to a fluid half-space shows a similar dependence on mode order and panel dimensions.     

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.     

Stochastic finite element analysis of a vibrating string

The response of a vibrating string subjected to spatial white noise excitation is analyzed by using the finite element (Galerkin) method. The discretization is achieved by using basis functions in the spatial and random spaces. The continuous time finite element equations are then integrated in time by using the central difference algorithm. It is shown that when the string is divided into N segments, the Galerkin approach leads to N(N?1) degrees of freedom which are governed by N subsets of equations. The subsets are similar in form. Furthermore, for a uniform string, they are governed by the same operator as that which governs the system of (N?1) degrees of freedom arising from the corresponding deterministic problem. Random initial conditions can also be treated by the same method, and the analysis of strings with initial conditions described by the standard Brownian process is carried out. Numerical results are given to illustrate the stochastic response.     

Impedance of pistons on a two-layer medium in a planar infinite rigid baffle

An integral transform technique is used to develop a general solution for the impedance of rigid pistons acting on a two-layer medium. The medium consists of a semi-infinite acoustic fluid on a viscoelastic thick plate in a rigid infinite baffle. The stresses acting on the planar baffle, as a result of piston motion, are determined using theory of linear elasticity and are therefore unrestricted in terms of applicable frequency range. The special case of a circular piston is considered and expressions for the self-and mutual impedances are developed and evaluated numerically. Numerical results are compared with classical piston impedance functions and finite-element model results. At low frequencies (k(0)a<1), the self-impedances vary significantly from the classical piston impedance functions due to the shear properties of the viscoelastic medium. In the midfrequency range (1相似文献   

Rigid piston approximation for computing the transfer function and angular response of a fiber-optic hydrophone

The transfer function of a fiber-optic hydrophone (FOH) is computed for various fiber core radii. The hydrophone is modeled as a rigid disk, with plane waves impinging at normal or oblique incidence. The total sound field is written as the sum of the incident field and the field diffracted from the hydrophone. The diffracted field is approximated by the field generated by a vibrating planar piston in an infinite rigid baffle. For normal incidence and a pointlike fiber core, an analytical solution is presented. For finite fiber core radii, and for oblique incidence, the transfer functions are computed numerically. The calculated transfer functions exhibit an oscillatory frequency dependency that is most pronounced for small fiber cores. The solution for a core radius of 2.5 microm can be very well approximated by the analytical solution for a pointlike core at frequencies of up to 30 MHz. The results for normal incidence can be directly employed to deconvolute ultrasonic pressure signals measured with an FOH. From the transfer functions for oblique incidence, the angular response of the hydrophone is calculated. The angular response obtained here differs significantly from the model commonly used for piezoelectric hydrophones. The effective hydrophone radius derived from the angular response shows a strong frequency dependency. For low frequencies, it is found to be larger than the outer fiber radius, whereas it generally lies between the outer radius and the fiber core radius for frequencies above 10 MHz.     

Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains

This paper presents an analysis of unsteady flow of incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal time-dependent shear stress and the outer cylinder that is moving at a constant velocity. The velocity field and shear stress are determined using the Laplace and finite Hankel transforms. Obtained solutions are presented in terms of the generalized G and R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of generalized solutions. The influence of different parameters on the velocity field and shear stress is also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.     

Acoustic behavior of circular dual-chamber mufflers

The acoustic behavior of a circular dual-chamber muffler is investigated in detail by: (1) a two-dimensional (2-D) axisymmetric analytical approach based on the mode-matching technique for the concentric configurations; (2) the finite element method; and (3) experimental work. A number of effects is studied, including (1) the presence of a rigid baffle in the chamber; (2) the inner radius of the baffle; (3) the position of the baffle along the axial direction; and (4) the extended inlet/outlet and baffle ducts. Some of these effects are shown to modify the acoustic behavior drastically, suggesting potential means to improve the acoustic performance.     

无障板圆形活塞换能器波束特性建模

针对ka<π时无障板活塞声源波束特性不能用无限平面障板活塞换能器理论进行描述的问题,提出一种基于有限元方法结合曲线拟合的简便数学建模方法.模型采用了无限平面障板活塞换能器理论的基本函数表达,通过增加修正因子函数来改变模型的细节部分,用曲线拟合方法给出了较准确的两个修正因子函数的数学表达式。最终建立了无障板圆形活塞换能器波束特性经验公式模型,模型在ka为0.03~5.2范围内与有限元方法给出的波束曲线相一致,并且在ka取更大值时与无限平面障板活塞换能器理论公式等效.      

R-C系统外遮光罩挡光环的程序化设计及锥状内遮光罩的改进

基于几何作图法推导出R-C系统外遮光罩内挡光环顶点的坐标公式,利用C语言编程实现程序化设计挡光环.在中心遮光比确定的情况下,推导出内遮光罩的顶点坐标公式,并将通常使用的主镜一级锥状遮光罩改进为二级锥状遮光罩,以高速摄影系统的R-C型折反式主物镜为例,对其主镜和次镜内遮光罩进行设计,并给出设计结果.当轴角为70°,遮光罩为二级和一级时,到达像面的杂散光照度分别为1.082 3×10-12 W/m2和1.661 4×10-10 W/m2,相差二个数量级,证明改进的二级遮光罩优于一级遮光罩,能有效抑制杂散光.最后,设计了主、次镜间镜筒内壁上等高挡光环,进一步抑制了R-C系统的杂散光.     

Analysis and improvement of sound radiation performance of spherical cap radiator

A spherical cap radiator is one of the important parts of an underwater wide-beam imaging system. The back radiation of a traditional spherical cap radiator, which is composed of a vibrating cap and a rigid baffle, is strong and its far-field directivity function may fluctuate in big amplitude in the vicinity of the polar axis. These shortcomings complicate the processing of the reflective waves received for imaging the targets. In this study, the back radiation is weakened by adding an acoustic soft material belt between the vibrating cap and the rigid baffle. And the fluctuation mentioned above is lowered remarkably by dividing the spherical cap radiator into many annuluses and a relatively smaller spherical cap, and by controlling the phase retardations of all elements appropriately. Furthermore, the numerical experiments are carried out by the finite element method (FEM) to prove the validity of the above methods.     

On the sound field of a resilient disk in free space

Radiation characteristics are calculated for a circular planar sound source in free space with a uniform surface pressure distribution, which can be regarded as a freely suspended membrane with zero mass and stiffness. This idealized dipole source is shown to have closed form solutions for its far-field pressure response and radiation admittance. The latter is found to have a simple mathematical relationship with the radiation impedance of a rigid piston in an infinite baffle. Also, a single expansion is derived for the near-field pressure field, which degenerates to a closed form solution on the axis of symmetry. From the normal gradient of the surface pressure, the surface velocity is calculated. The near-field expression is then generalized to an arbitrary surface pressure distribution. It is shown how this can be used as a simplified solution for a rigid disk in free space or a more realistic sound source such as pre-tensioned membrane in free space with non-zero mass and a clamped rim.     

An efficient finite volume method for electric field–space charge coupled problems

The goal of this paper is to introduce some recently developed finite volume schemes to enable numerical simulation of electric field–space charge coupled problems. The key features of this methodology are the possibility of handling problems with complex geometries and accurately capturing the charge density distribution. The total variation diminishing (TVD) scheme and the improved deferred correction (IDC) scheme are used to compute the convective and diffusive fluxes respectively. Our technique is firstly verified with the computation of hydrostatic solutions in a two coaxial cylinders configuration. The homogeneous and autonomous injection from the inner or outer electrode is considered. Comparison has been made with the analytical solution. The numerical technique is also applied to the problem of corona discharge in a blade-plane configuration. The good agreement between our numerical solution and the one obtained with a combination approach of Finite Element Method (FEM) and Method of Characteristics (MoC) is shown.     

Scattering of sound by an elastic plate with flow

An elastic plate, set in an infinite baffle and immersed in a fluid moving with a uniform subsonic velocity, is excited by an acoustic source. The scattered sound field is analyzed when fluid-plate coupling is large, and a solution is found by the use of matched asymptotic expansions. The far field is found to approximate to the solution obtained when the elastic plate is absent. At a plate resonance, however, the outer field must include eigensolutions with singularities at the plate edges, and close to the plate the dominant terms are travelling plate waves. These plate waves are found to have a wavelength independent of the frequency of the source. It is also shown that a plate resonance corresponds to a divergence instability of aerodynamic flutter theory and that the stability results found in this paper are in agreement with those obtained by using modal expansions. The limit as the Mach number goes to zero is found to be singular, suggesting an analysis of the model for small flow velocity. This calculation is performed and the results match smoothly to the respective solutions for a stationary fluid and for a large subsonic flow.     

A numerical study of the effects of the vertical baffle on liquid sloshing in two-dimensional rectangular tank

The liquid sloshing in a moving partially filled rectangular tank with a vertical baffle is investigated. A numerical algorithm based on the volume of fluid (VOF) technique is used to study the nonlinear behavior of liquid sloshing. The numerical model solves the complete Navier–Stokes equations in primitive variables by using of finite difference approximations with the moving coordinate system. The ratio of baffle height to the initial liquid depth has been changed in the range of 0≤h_B/h≤1.2. The critical baffle height to reach the roof of the tank and the baffle height beyond the liquid does not get over the baffle anymore have been investigated. The vortex originated by the flow separation from the baffle tip became weaker with increasing the baffle height. In order to assess the accuracy of the method used, some results with baffle height are compared with the experimental results. Comparisons show good agreement for slosh loads in the cases investigated. The free surface elevation and the time variations of pressures have been also presented.     

Application of the FEM and the BEM to compute the field of a transducer mounted in a rigid baffle (3D case)

A three-dimensional finite element model has been developed which allows the harmonic analysis of a piezoelectric structure mounted on a rigid baffle and radiating into water. The solution of this problem consists of coupling a finite element method to a boundary element method. The first one enables the modelling of the vibrating structure and the second one the modelling of propagating waves in the semi-infinite fluid medium surrounding the structure. In this way, the near-field and the far-field pressures are calculated as well as the displacement field of the piezoelectric structure taking into account the acoustical interaction. Numerical and experimental results are provided which validate the numerical procedure. The good agreement obtained indicates that this three-dimensional model is a very useful tool to optimise the design of transducer arrays used in medical imaging.     

The radiation impedance of a baffled piston source

The problem of a vibrating disk set in a finite, rigid, concentric baffle is reduced to the solution of a Fredholm integral equation of the second kind. The acoustic radiation impedance is computed from the numerical solution of this equation and results tabulated for values of (wavenumber × disk radius) between 0·2 and 2·0.