Energy distribution and radiation loading of a cylindrical source suspended within a nonconcentric fluid cylinder

Acoustic radiation from a cylindrical source undergoing angularly periodic and axially-dependent harmonic surface vibrations while eccentrically suspended within a fluid cylinder, which is submerged in an infinite fluid medium, is analyzed in an exact manner. This configuration, which is a realistic idealization of a cylindrical liquid-filled acoustic lens with focal point inside the lens when used as a sound projector, is of practical importance with applications in underwater and biomedical ultrasonics. The formulation utilizes the appropriate wave-field expansions along with the pertinent translational addition theorem to develop an infinite series solution. The analytical results are illustrated with a numerical example in which the basic acoustic quantities, such as the modal acoustic radiation impedance load on the source, on-axis pressure magnitude, radiated far-field pressure directivity patterns, and the radiation intensity distribution are evaluated for representative values of the parameters characterizing the system. Numerical results clearly illustrate that, in addition to source frequency and surface velocity distribution, its position (eccentricity) can be of great significance in sound radiation.     

Use of constant,linear and quadratic boundary elements in 3D wave diffraction analysis

The performance of the Boundary Element Method (BEM) depends on the size of the elements and the interpolation function used. However, improvements in accuracy and efficiency obtained with both expansion and grid refinement increases demand on the computational effort. This paper evaluates the performance of constant, linear and quadratic elements in the analysis of the three-dimensional scattering caused by a cylindrical cavity buried in an infinite homogeneous elastic medium subjected to a point load. A circular cylindrical cavity for which analytical solutions are known is used in the simulation analysis. First, the dominant BEM errors are identified in the frequency domain and related to the natural vibration modes of the inclusion. Comparisons of BEM errors are then made for different types of boundary elements, maintaining similar computational costs. Finally, the accuracy of the BEM solution is evaluated when the nodal points are moved inside linear and quadratic discontinuous elements.     

Transient response of a submerged cylindrical foam core sandwich panel subjected to shock loading

Predicting the dynamic response of submerged vehicles subjected to hydrostatic pressure and underwater shock loading is of great interest to many structural designers and engineers for improving material and configuration design in recent years. In this paper, the finite element method is used to evaluate the dynamic response of a submerged cylindrical foam core sandwich panel subjected to shock loading. The sandwich panel consists of a foam core surrounded by fiber-reinforced laminates. The effect of fluid–structure coupling is included in the finite element analysis whereas the fluid is assumed to be compressible and inviscid. Time histories of circumferential stress for different composite plies are presented in graphical form and the effects of core type on circumferential stress and velocity of stand-off point are also investigated. Additionally, the distribution of pressure in fluid domain and the deformation of cylindrical foam core sandwich panel are estimated. To the best of the authors’ knowledge, the specialized literature addressing the dynamic response of submerged cylindrical foam core sandwich panel to underwater shock loading is rather scanty. This work is likely to fill a gap in the specialized literature on this topic.     

Diffraction of elastic sphericalP waves by a cylindrical cavity

Summary This paper deals with the three dimensional diffraction of impulsive compressional waves by a cylindrical cavity. The cavity is embedded in an unbounded, isotropic, homogeneous elastic medium. The compressional point source, generating the incident pulse, is supposed to be situated outside the cavity. The formal solution to the problem is obtained in integral form. The integrals are evaluated asymptotically for the early time motion by the residue-Cagniard method.With 6 Figures     

Magnetothermoelastic interaction in an infinite elastic continuum with a cylindrical hole subjected to ramp-type heating

A solution is given for the induced temperature and stress fields in an infinite transversely isotropic solid continuum with a cylindrical hole. The solid medium is considered to be exposed to a magnetic field and the cavity surface is assumed to be subjected to a ramp-type heating. Green and Lindsay model has been used to account for finite velocity of heat conduction. Magnetic field induced within the cavity is also determined. The problem is solved analytically by using integral transform technique.     

Eccentricity effects on acoustic radiation from a spherical source suspended within a thermoviscous fluid sphere

Acoustic radiation from a spherical source undergoing angularly periodic axisymmetric harmonic surface vibrations while eccentrically suspended within a thermoviscous fluid sphere, which is immersed in a viscous thermally conducting unbounded fluid medium, is analyzed in an exact fashion. The formulation uses the appropriate wave-harmonic field expansions along with the translational addition theorem for spherical wave functions and the relevant boundary conditions to develop a closed-form solution in form of infinite series. The analytical results are illustrated with a numerical example in which the vibrating source is eccentrically positioned within a chemical fluid sphere submerged in water. The modal acoustic radiation impedance load on the source and the radiated far-field pressure are evaluated and discussed for representative values of the parameters characterizing the system. The proposed model can lead to a better understanding of dynamic response of an underwater acoustic lens. It is equally applicable in miniature transducer analysis and design with applications in medical ultrasonics.     

Transmitting boundaries for time-harmonic elastodynamics on infinite domains

A finite element method with transmitting boundary is developed for time-harmonic elastodynamics on infinite domains. Only a finite inner domain needs to be discretized into conventional finite elements, while the effect of the exterior domain is simulated by introducing the transmitting boundary stiffness matrix on the degrees-of-freedom of the transmitting boundary nodes. In order to incorporate the Sommerfeld radiation condition, the reciprocity relation, on the transmitting boundary for the radiating elastodynamic state under consideration and the one which is induced by a finite number of point source is used to calculate the transmitting boundary stiffness matrix. The effectiveness of the transmitting boundary technique has been demonstrated by solving the stress concentration problems of a homogeneous isotropic full space with a circular cylindrical cavity and of the one with a spherical cavity, which are subjected to plane incident waves, and the results are compared with the ones of the conventional FEM and the exact data.     

2.5D coupled BEM–FEM used to model fluid and solid scattering wave

We describe a hybrid method to study fluid and solid interaction problems in the frequency domain. The numerical method is based on subdomain decomposition. The BEM is used to model unbounded solid mediums, whereas the confined subdomains, both fluid and solid, are represented by the FEM. The analysis is carried out by superposing two‐and‐a‐half dimension (2.5D) problems for different longitudinal wave numbers. A novel 2.5D FEM formulation for inviscid fluids is proposed, which include the energy lost at the fluid boundary enclosure. The fluid and solid subdomains are coupled, and appropriate boundary conditions are imposed at the interfaces. The proposed technique is verified from analytical solutions. A cylindrical cavity located in an unbounded solid medium excited by a dilatational point source is studied. Computed results are in good agreement with the analytical solution. Later, noise and vibration in a concrete tunnel due to an internal pressure load is analysed with the proposed methodology. Results show that tunnel and soil displacements increase with the load speed, as did the air pressure inside the tunnel, according with the travelling ranges defined by the wave propagation velocities in each medium. Copyright © 2014 John Wiley & Sons, Ltd.     

Sudden twisting of an external circular crack in an infinite medium with a cylindrical inclusion

In this paper the torsional impact response of an external circular crack in an infinite medium bonded to a cylindrical inclusion has been investigated. The infinite medium and cylindrical inclusion are assumed to be of different homogeneous isotropie elastic materials. Laplace and Hankel transforms are used to reduce the problem to the solution of a pair of dual integral equations. These equations are solved by using an integral transform technique and the results are expressed in terms of a Fredhol integral equation of the second kind. By solving Fredholm integral equation of the second kind the numerical results for the dynamic stress-intensity factor are obtained which measure the load transmission on the crack.     

The circulation produced within embedded liquid drops

A circular cylindrical or spherical subregion of an incompressible homogeneous infinite viscous fluid undergoing any mathematically definable Stokes type slow motion is composed of a liquid immiscible with the surrounding medium. Assuming that the circulation pattern for the homogeneous infinite fluid is known, a sequence of mathematical operations are derived which enable the circulation patterns for the drop and the matrix to be evaluated directly from the corresponding particular result for the homogeneous infinite fluid. The importance of these operations derives from their simplicity and generality-diversity of separate and unconnected flow fields are brought under the same roof.     

Finite element analysis of the thermoelastic interactions in an unbounded body with a cavity

Thermoelastic interactions in an infinite homogeneous elastic medium with a spherical or cylindrical cavity are studied. The cavity surface is subjected to a ramp-type heating of its internal boundary which is assumed to be traction free. A general finite element model is proposed to analyze transient phenomena in thermoelastic solids. Lord–Shulman and Green–Lindsay for the generalized thermoelasticity model are selected for that purpose since it allows for “second sound” effects and reduces to the classical model by appropriate choice of the parameters. The problem has been solved numerically using a finite element method (FEM). Numerical results for the temperature distribution, displacement, radial stress and hoop stress are represented graphically. A comparison is made with the results predicted by the three theories.     

Propagation of axisymmetric waves on the surface of a cylindrical cavity in elastic medium

A nondamped axisymmetric mode that propagates in an elastic cylindrical waveguide representing an extended cavity with a circular cross section in an infinite homogeneous medium is described. The wave dispersion in this system is analyzed and the similarity with and differences from other elastic media with one boundary are considered, including an infinite round rod and the surface of a half-space (Rayleigh wave). It is shown that, for axisymmetric waves in the cavity, a boundary frequency dependent on the curvature radius always exists, below which the waves are evanescent. A physical interpretation of results is given.     

Dynamic cylindrical cavity expansion in an incompressible elastoplastic medium

Summary Self-similar dynamic expansion of a pressurized circular cylindrical cavity, embedded in an infinite elastoplastic incompressible medium, is here investigated with the large strain J₂ flow theory. Assuming steady-state conditions, thus bypassing the initial loading history, it is shown that plane-strain fields are sustained with no diverging logarithmic stress appearing in the remote elastic field. Yet, even in the absence of remotely applied stress, the appearance of small stresses at infinity is unavoidable. The present solution is exact but limited to relatively low cavity expansion velocities. A closed form expression is given for the cavitation pressure with elastic/perfectly-plastic response. A fairly general result is derived for the cavitation pressure in hardening media with a definite yield point and in linear-hardening solids as a special case. Contact is made with earlier results of quasi-static cavity expansion along with a comparison to the self-similar dynamic expansion of a spherical cavity in an incompressible Mises solid. Upper and lower bounds for penetration depth tests are suggested by using the present cylindrical cavitation model and the incompressible spherical cavitation model.     

反平面冲击荷载作用下圆柱形洞室的动力响应

对无限弹性土体内圆柱形洞室在反平面冲击荷载的作用下的瞬态响应进行了探讨。用残余变量的方法结合拉普拉斯变换及其逆变换,在频域内的得到土体位移和应力一般表达式,并采用拉普拉斯逆变换的数值方法,给出了问题的数值解。在时域内分析了无限弹性土体内圆柱形孔洞在沿轴向方向的冲击荷载作用下的土体动力响应的变化规律,并将计算结果与静力情况下的作了比较：反平面荷载作用后,波向外发散传播,并沿半径方向衰减,衰减速度较静力情况下的衰减要慢,且距离波源越远二者差别越大;波到达后,该点土体的应力和位移均发生与外荷载相同的三角形变化：先增大,随后减小最后保持为零不变。     

The energy release rate for a Griffith crack in a piezoelectric material

The plane solution giving the stresses and electric fields in an infinite body around a cylindrical cavity with an elliptical cross-section is presented. The energy change in an infinite body due to the introduction of an elliptical cavity having an electric field within it is calculated. The electric field from the interior of the cavity is then used in conjunction with the energy change formula to calculate the total energy release rate per crack tip when a Griffith crack propagates. Due to a change of stored electrostatic energy within the crack, the total energy release rate is not equal to the energy release rate at the crack tips as the material separates. The implications for fracture and crack growth are discussed.     

浸没的圆柱壳在冲击波作用下动响应的Galerkin解法

研究了无粘、无旋和不可压缩流体中两端简支圆柱壳在给定冲击波作用下的动响应。圆柱壳的运动方程中考虑了流体动压力和冲击波压力的共同作用，通过将冲击波压力分布函数表示为Ｆｏｕｒｉｅｒ级数有限项形式，并利用Ｇａｌｅｒｋｉｎ方法对耦合方程进行数值求解，得到了圆柱壳在冲击波作用下的位移响应特性     

波传播法求解低频激励下水中加端板圆柱壳的振动

采用波传播法研究了低频下水中壳体的振动与响应。水中壳体由有限长加流体载荷的圆柱壳和两端的圆形端板组成,其中外部流体载荷用无限长模型进行近似处理。为了模拟推动系统的激励及船体上某一点激励,分别考虑了不同位置的轴向载荷和径向载荷,讨论了单个周向模态下的位移在总位移中的比重。主要研究了4种载荷,即作用在端板中心的轴对称载荷、作用在端板与圆柱连接处的轴向载荷、作用在连接处的径向载荷和作用在壳体中间的径向载荷,比较得出了轴对称和非轴对称、同一点不同方向载荷、同一方向不同位置载荷的响应位移的不同。此外,还研究了两端端板对不同载荷下水中壳体响应的影响,得出了端板主要抑制了壳体的较高阶模态下径向位移的结论。解析法结果与有限元法结果进行了比较,验证了该方法的正确性。     

Ultrasonic scattering by a fluid cylinder of elliptic cross section, including viscous effects

This paper analyzes acoustic scattering by a viscous compressible fluid cylinder of elliptic cross section submerged in an unbounded viscous nonheat-conducting compressible fluid medium. The classical method of eigenfunction expansion along with the appropriate wave field expansions and the pertinent boundary conditions are used to develop a solution in the form of infinite series involving Mathieu and modified Mathieu functions of complex arguments. The complications arising due to the nonorthogonality of angular Mathieu functions corresponding to distinct wave numbers in addition to the problems associated with the appearance of additional angular-dependent terms in the boundary conditions are all avoided in an elegant manner by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. A multiprecision code was developed for computing the Mathieu functions of complex argument in terms of complex Fourier coefficients that are themselves calculated by numerically solving appropriate sets of eigen-systems. The numerical results point to the imperative influence of fluid viscosity in notable reduction of pressure amplitudes at intermediate and high frequencies. They also reveal the central role of the cross sectional ellipticity in conjunction with the angle of incidence in altering the pressure directivities. Limiting cases are considered, and fair agreements with well-known solutions are obtained.     

Galton型高强气流声源的发声特性

文章介绍了一款带中心杆的Galton型气流声源,通过试验和数值模拟方法,研究了该声源发声特性、进气压力对声场分布的影响以及流体介质对发声特性的影响.研究发现,该声源稳定发声时,共鸣腔内压力场与流场均呈周期性变化;不同进气压力下,声场空间分布基本一致,具有较强的声指向性.共鸣腔后侧轴线处,声压级达到最大值,为153 dB...     

Modal vibrations of an infinite cylinder in an acoustic halfspace

Acoustic radiation from an infinite cylindrical surface vibrating with an arbitrary, time-harmonic surface velocity distribution while positioned near the rigid/compliant boundary of a semi-infinite ideal compressible fluid medium is determined in an exact fashion using the classical method of separation of variables. The formulation utilizes the appropriate wave-field expansions and the method of images along with the pertinent translational addition theorem to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which the cylindrical source, vibrating in the monopole and dipole-like modes, is positioned near the rigid/compliant boundary of a water-filled acoustic halfspace. Subsequently, the basic acoustic field quantities such as the modal acoustic radiation impedance load, radiated far-field pressure and the radiation intensity distribution are evaluated for representative values of the parameters characterizing the system.