Scattering and active acoustic control from a submerged piezoelectric-coupled orthotropic hollow cylinder

A general exact analysis for three-dimensional scattering of a time-harmonic plane-progressive sound wave obliquely incident upon an arbitrarily thick bilaminated circular hollow cylinder of infinite extent, which is composed of a cylindrically orthotropic axially polarized piezoelectric inner layer perfectly bonded to an orthotropic outer layer, is presented. An approximate laminate model in the context of the so-called state space formulation along with the classical T-matrix solution technique involving a system global transfer matrix is employed to solve for the unknown modal scattering and transmission coefficients. Numerical example is given for an air-filled and water-submerged two-layered elasto-piezoelectric hybrid (steel/PZT4) hollow cylinder insonified by an obliquely incident unit-amplitude plane sound wave. Following the acoustic resonance scattering theory (RST), the total form function amplitude together with the associated global scattering, the far-field inherent background, and the resonance scattering coefficients of the nth normal mode are computed as a function of dimensionless frequency for selected angles of incidence, piezoelectric layer thickness parameters, and electrical boundary conditions (i.e., open/closed circuit or active). Also, the electrical voltage coefficients required for partial or complete cancellation of the reflected sound field are calculated. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.     

Exact gravitational field of the infinitely long rotating hollow cylinder

The vacuum line element inside an infinitely long rotating hollow cylinder is the usual flat space line element. It is fitted in a most general way to the general cylindrical vacuum field outside at the singular hypersurfaceR ₀=const, representing the infinitely thin hollow cylinder. With the use of the jump conditions atR ₀=const the surface densities , of which the energy-momentum-stress tensor of the shell consists, are calculated. The physical properties of the cylinder, as derived from the eigenvalues and -vectors of , and the generated gravitational field are discussed in full detail.     

Radiative absorption in an infinitely long hollow cylinder with Fresnel surfaces

Radiation absorption in an infinitely long hollow cylinder with Fresnel surfaces is studied using the ray tracing method. It is found that the inner boundary can be modeled as a total reflective surface for the infinitely long hollow cylinder. Radiative absorption of hollow cylinders with Fresnel surfaces is compared to diffusive surfaces predicted by the finite volume method. Effects of refractive index, optical thickness and hole size on radiative absorption are studied. Abrupt changes in radiative absorption near τ_r/τ_Ro=1/n are observed for hollow cylinders with Fresnel surfaces. It is because the Fresnel relation predicts a critical angle at . This trend is not observed in diffusive surfaces. Refractive index and optical thickness are two competing factors that govern the radiative absorption. Higher refractive index drives higher absorption close to the inner surface, while higher optical thickness yields higher absorption near the outer surface. The results of this study can also serve as benchmark solutions for modeling radiative heat transfer in hollow cylinders with Fresnel surfaces. It is also found that the directional or hemispherical emittance can be calculated without solving the radiative transfer equation in the media when the temperature variation in the media is small.     

Radial vibrations of orthotropic laminated hollow spheres

The three-dimensional elasticity problem of the radial vibrations of a composite hollow spherical shell laminated of spherically orthotropic layers is considered. After formulating the equations, the exact determinantal equation from which the frequencies of vibration can be extracted is developed. Some calculated results for combinations of isotropic and orthotropic materials indicate the sensitivity of the frequencies to the geometry and material make up of the shells.     

Transient elastodynamic response of finite and infinite solid cylinders

The orthogonal eigensolutions for the vibrations of an isotropic finite solid cylinder with a traction-free lateral boundary and rigid-smooth end boundaries are provided. The transient elastodynamic response of this solid cylinder is then constructed using the method of eigenfunction expansion and further extended explicitly and concisely to that of an isotropic infinite solid cylinder. The numerically evaluated analytical solution is shown to compare favorably with that by finite element method (FEM). The effect of external forces on the excitation of each guided wave mode can be quantitatively investigated on the basis of the present solution.     

Laser-induced circumferential waves on hollow cylinder and their interaction with defects by finite element method

A three dimensional (3-D) finite element model for simulating laser induced circumferential wave on a hollow cylinder is developed based on the thermoelastical mechanism, which can take any laser source into account and simulate the interactions between circumferential wave and defects in the hollow cylinder. The model is verified by a control calculation. The results show that the waveforms of circumferential wave are in very good agreement with those available in literature, not only on the arrival time and shape but also on the amplitudes of A ₀, S ₀ and A₁ modes. Using the model, circumferential waves on the surfaces of two series hollow cylinders are simulated, one with same thickness but different outer radius, and the other with the same outer radius but different thickness. The results show that a new mode appears in circumferential wave, compared with Lamb wave in plate. With increase of thickness or radius, the amplitude of the new mode reduces. Another conclusion is that with increase of the thickness of the hollow cylinder, the circumferential wave evolves gradually to the cylindrical Rayleigh waveform, which results from the attenuation of the coupling effect between the outer and inner surface. Moreover, the circumferential waves generated on a hollow cylinder with a surface defect are also simulated, and the results indicate that in the circumferential waves obtained at the point beyond the defect, the amplitude of A ₀ mode decreases and its dispersion enhances. More importantly, a new bipolar waveform corresponding to the interaction of S ₀ mode with the defect appears, its amplitude is larger than three times of that of S ₀ mode. As a result, we consider that the new bipolar waveform will be the optimal feature to nondestructively detect the surface defect on the hollow cylinder.     

Example of a rigorous solution for the gravitational field of a hollow,rotating cylinder

A class of exact solutions-depending upon two dimensionless parameters-to the gravitational field equations is obtained, where the source of the field is a rotating, hollow cylinder of infinite length. The material properties, although highly idealised, nevertheless are not unrealistic and chosen in such a way as to allow elementary integration. The solutions show how the inertial frame inside the cylinder is dragged by the rotating material, and also how the drag continues inside the material and in the outside region. They are exact examples for the Lense-Thirring effect.     

中空圆柱形边界条件下非线性介质中的晶格孤子

本文采用自相似方法求解中空圆柱形边界贝塞尔晶格中变系数非线性薛定谔方程, 得到了与数值模拟解一致的解析解, 表明由非衍射贝塞尔光束诱导的光子晶格可支持稳定的自相似孤子簇. 精确解ψ_mn是n+2层, 2m极的多极孤立波, 其形状及大小在传播过程中保持不变. 关键词： 空间光孤子 贝塞尔晶格 边界 自相似     

Vibroacoustic response of an eccentric hollow cylinder

The linear 3D elasticity theory in conjunction with the classical method of separation of variables and the translational addition theorem for cylindrical wave functions are employed to investigate the three-dimensional steady-state sound radiation characteristics of an arbitrarily thick eccentric hollow cylinder of infinite length, submerged in an unbounded ideal acoustic medium, and subjected to arbitrary time-harmonic on-surface mechanical drives. The spatial Fourier transform along the shell axis and Fourier series expansion in the circumferential direction are utilized to obtain a formal integral expression for the radiated pressure field in the frequency domain. The method of stationary phase is subsequently implemented to evaluate the integral for an observation point in the far field. The analytical results are illustrated with numerical examples in which air-filled water-submerged concentric and eccentric steel cylinders are driven by harmonic concentrated radial and transverse surface loads. Effects of excitation and cylinder eccentricity on the far-field radiated pressure amplitudes/directivities are discussed and contributions from pseudo-Rayleigh, whispering gallery, and axially guided waves are examined through selected spatial dispersion patterns. Limiting cases are considered and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature.     

圆柱体相对转动动力学方程的积分解

针对圆柱体任意两个横截面间的相对转动动力学方程，运用解耦方法获得方程的解析解，由于方程的特殊性，利用Jordan标准形求得可逆矩阵.从而得到了圆柱体相对转动动力学方程的积分形式的解.根据工程应用，给出了冲击性和周期性两类典型载荷作用下的解析解. 关键词： 相对转动 相似模拟 动力学方程 解析解     

An analytical discrete-ordinates solution for dual-mode heat transfer in a cylinder

A modern analytical version of the discrete-ordinates method is used along with Hermite cubic splines and Newton's method to solve a class of coupled nonlinear radiation-conduction heat-transfer problems in a solid cylinder. Computational details of the solution are discussed, and the algorithm is implemented to establish high-quality results for various data sets which include some difficult cases.     

微重力环境下无限长柱体内角毛细流动解析近似解研究

应用同伦分析法研究无限长柱体内角毛细流动解析近似解问题,给出了级数解的递推公式.不同于其他解析近似方法,该方法从根本上克服了摄动理论对小参数的过分依赖,其有效性与所研究的非线性问题是否含有小参数无关,适用范围广.同伦分析法提供了选取基函数的自由,可以选取较好的基函数,更有效地逼近问题的解,通过引入辅助参数和辅助函数来调节和控制级数解的收敛区域和收敛速度,同伦分析法为内角毛细流动问题的解析近似求解开辟了一个全新的途径.通过具体算例,将同伦分析法与四阶龙格库塔方法数值解做了比较,结果表明,该方法具有很高的计算精度.     

Effect of the non-homogenity on the composite infinite cylinder of orthotropic material

In this Letter, the solution of non-homogeneous orthotropic elastic cylinder for plane strain problems is developed. The dynamical problem of an orthotropic cylinder containing: (i) an isotropic core and (ii) a rigid core are considered. The elastic constants and density are taken as a power function of the radial coordinate. Analytical expressions for the component of the displacement and the components of the stresses in different cases are obtained. The numerical calculations are carried out for the component of displacement and the components of the stresses through the radial of the cylinder. The results indicate that the effect of inhomogeneity is very pronounced. Those cases have been illustrated and discussed by figures.     

An exterior solution of the einstein field equations for a rotating infinite cylinder

We give here a new exact solution to the exterior Einstein field equations for a rotating infinite cylinder. The solution is characterized by an everywhere singular metric. In the Papapetrou canonical coordinates, the 3-force acting on a radially moving test particle is $f^\alpha = \left( {G\frac{m}{{\sqrt {\Gamma - \upsilon ^2 } }}{\text{ }}\frac{\lambda }{\rho },{\text{ 0,}} - \frac{m}{{\sqrt {\Gamma - \upsilon ^2 } }}{\text{ }}\frac{{C\upsilon }}{\rho }{\text{ }}} \right)$ where λ>0.f ¹ andf ³ are, respectively, the gravitational and Coriolis forces. The gravitational force is, therefore, repulsive.     

Power flow model of flexural waves in finite orthotropic plates

In this paper, an approximate power flow model is developed for the analysis of the flexural waves in finite orthotropic plate transversely vibrating in the medium-to-high frequency ranges. The derived energy equation for the model is expressed with time- and locally space-averaged farfield wave energy density. It could be the more general form than that of the conventional power flow analysis model seen in the isotropic plate. With the derived model, dynamic characteristics varying with the direction can be expressed. To verify the validity and accuracy of the model, numerical analyses are performed for the case where a finite rectangular plate is excited by a harmonic point force, and the calculated results expressed with the energy levels are compared with classical modal solutions by changing the frequency and the damping loss factor of the plate. The dominant power transmission paths in the plate are also predicted from the distribution of the approximate intensity fields.     

Simulation of guided waves in complex piping geometries using the elastodynamic finite integration technique

Although many technologies exist for inspecting piping systems, they are most successful on straight pipes and are often unable to accommodate the added complexities of pipe elbows, bends, twists, and branches, particularly if the region of interest is inaccessible. This paper presents a numerical technique based on the elastodynamic finite integration technique for simulating guided elastic wave propagation in piping systems. Comparisons show agreement between experimental and simulated data, and guided wave interaction with flaws, focusing, and propagation in pipe bends are presented. These examples demonstrate the ability of the simulation method to be used to study elastic wave propagation in piping systems which include three-dimensional pipe bends, and suggest its potential as a design tool for designing pipe inspection hardware and ultrasonic signal processing algorithms.