Motion of a spherical heat source in a melting medium

The gravity-induced steady motion of a heat source boring through a solid medium is investigated. It is shown that the temperature of its surface is substantially nonuniform. Expressions are obtained for the maximum values of the radius and velocity of the source at which this temperature attains the assigned maximum allowable value.Moscow State University of Nature Conditioning, Moscow. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 5–6, pp. 506–512, November–December, 1994.     

BEM and FEM based numerical simulations for biomagnetic fluid flow

We investigate numerically the biomagnetic fluid flow between parallel plates imposed to a magnetic source placed below the lower plate. The biomagnetic fluid is assumed to be Newtonian, viscous, incompressible, electrically nonconducting, and has magnetization varying linearly with temperature and magnetic field intensity. Both steady and unsteady, laminar, two-dimensional biomagnetic fluid flow equations taking into care the heat transfer between the plates are solved using both finite element and dual reciprocity boundary element methods. Treatment of nonlinear terms by using only the fundamental solution of the Laplace equation, and discretization of only the boundary of the region are the advantages of dual reciprocity boundary element method giving small algebraic systems to be solved at a small expense. Finite element method is capable of giving very accurate results by discretizing the region affected by the magnetic source very finely, but it results in large sized algebraic systems requiring high computational cost. The results indicate that the flow is appreciably affected with the presence of magnetic source in terms of vortices at the magnetic source area. The lengths of the vortices, and temperature increase with an increase in the intensity of the magnetic field.     

Averaged heat transfer during periodic fluctuations of the heat transfer intensity of the surface of a plate,a cylinder,or a sphere

Processes of heat transfer with periodically varying intensity on the surface of heated bodies of three typical geometries (plate, cylinder, sphere) are considered. The true heat transfer coefficient, which varies in time by the law of a periodic step function having two free parameters — amplitude and asymmetry, is specified on the heat transfer surface. Resultant relations are obtained for calculating the experimental heat transfer coefficient, which is the quantity measured in a traditional heat transfer experiment and used in applied calculations.Moscow Power Engineering Institute. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 2, pp. 225–228, March–April, 1995.     

The influence of nonlinear fields on miniature hydrophone calibration using the planar scanning technique

Miniature polyvinylidene fluoride (PVDF) hydrophones used in determining the power and intensity output of ultrasonic fields, including those radiated from diagnostic ultrasound equipment, were calibrated under a variety of field conditions using the planar scanning technique. A diagnostic B-scan piston-type transducer was used as a source, and the output intensity (spatial-peak pulse-average, or SPPA) was varied from 2 to 30 W/cm(2) while the total power was kept constant. The higher-intensity waveforms were significantly nonlinear in the focal region of the source. When the lateral beam profiles of the source (as measured by the hydrophone to be calibrated) were determined by positive-peak-detecting the ultrasonic pulse, the calibrated pressure sensitivity of the hydrophone systematically decreased as the field became progressively more nonlinear. When the beam profiles were measured using the pulse intensity integral, no systematic dependence of the calibration on field linearity was noted. These results imply that measured values of power and intensity of ultrasound diagnostic equipment may be dependent on the methodology utilized to map the lateral beam profiles of the transducer being measured, and the extent of nonlinear effects in the field under characterization.     

宽带噪声目标声场干涉结构图的时空变换

水听器接收的运动目标宽带噪声的频率-时间I(ω,t)声场干涉结构图随着目标的运动会发生相应的变化。这个变化将引起I(ω,t)中干涉条纹的弯曲,使得I(ω,t)和频率-距离干涉结构图不再有简单的线性映射关系。在深入分析宽带噪声运动目标频率-时间I(ω,t)和相应频率-距离I(ω,r)声场干涉结构间的非线性映射关系的基础上,提出了一种从I(ω,t)到线性I(ω,r)的时空变换方法(Time-Space Linear Transformation,TSLT)。数值仿真实验结果表明,TSLT可以有效地消除目标运动的影响,从I(ω,t)中恢复出能真实反映频率-距离声场干涉结构规律的I(ω,r)。最后给出利用运动目标宽带噪声声场干涉结构估计波导不变量的应用例。     

传导薄板的非线性磁弹性振动问题

研究了磁场环境中传导薄板的非线性磁弹性振动问题。由虚功原理,给出了磁场中薄板的磁弹性耦合运动方程。并根据薄板薄壳的磁弹性基本假设及麦克斯威尔方程,得到了方程中电磁力及力矩的表达式。作为具体问题,采用多尺度法求出了横向磁场中条形板非线性振动的近似解析解。通过算例,分析了磁场环境对振动周期和幅值的影响。从而证实了,通过改变磁场因素,可达到控制该磁场环境中传导薄板振动的目的。所得的结论,对工程实际将有较大的应用参考价值。     

Heating of bone and soft tissue by ultrasound

Abstract

The absorption of ultrasound in human tissue always causes some local increase in temperature. In the case of ultrasound imaging, the power is usually much less than that used therapeutically and is unlikely to produce any significant physiological effect. However, a reliable means of calculating the maximum temperature rise to be expected in any given case will assist in both the development and the safe use of new ultrasound devices. To validate earlier work on ultrasonic tissue heating, including both experiment and finite element modelling (FEM), an analytical method is described for calculating the steady-state temperature rise along the axis of an axially symmetrical beam of ultrasound incident through water on a two-layer phantom consisting of agar gel and a bone mimic, the practical beam profile being modelled by a pair of coaxial Gaussian functions. It is shown that, in the absence of perfusion, the steady-state temperature distribution for the extended heat source generated by the ultrasound absorption can be obtained by integrating the point-source solution to the Bioheat transfer equation (BHTE). The boundary conditions associated with the difference in thermal properties of the mimic materials are satisfied by introducing images of the extended heat source in the gel/bone–mimic interface.     

含界面裂纹圆形夹杂的十二次对称二维准晶热应力分析

针对点热源作用下,无限大十二次对称二维准晶基体和圆形弹性夹杂界面之间含多条裂纹的问题进行了研究。基于复变函数分区全纯理论、留数定理、广义 Liouville 定理、Riemann-Schwarz 解析延拓定理及复应力函数奇性主部分析方法,获得了集中热源作用于准晶基体内任意一点时,准晶基体和圆形弹性夹杂内外温度场、声子场热应力的一般复势解。由此获得了含一条界面裂纹和两条界面裂纹时温度场以及声子场热应力的封闭形式解答,将所得结果与已有结果进行了对比,验证了该方法的有效性。最后通过数值算例分析了夹杂半径、点热源强度及裂纹角度对热应力和裂纹尖端热应力强度因子的影响规律。结果表明：随着热源强度的增大,裂纹尖端的声子场热应力也逐渐增大;随着裂纹角度的增大,裂纹尖端的声子场热应力强度因子变大;随着半径的增大,热应力强度因子的变化趋势越来越明显,并且取得的峰值越高,即裂纹角度和夹杂半径的增加,促进了裂纹的扩展。这些结论为准晶材料的结构设计和使用提供了科学依据。     

隔震结构非线性随机地震响应分析的复模态法

本对多自由度双线性滞变隔震结构在过滤白噪声地震激励下的随机响应问题进行了系统研究。首先建立了结构非线性运动方程；然后根据非线性随机振动理论对运动方程进行等效线性化；最后用复模态法获得了等效线性方程的解析解，将复杂的非线性随机响应问题简化为求解一元非线性代数方程问题，并给出了算例。从而建立了多自由度隔震结构非线性随机响应复模态分析的一整套计算方法。     

Temperature stresses in a cylinder in heat resistance tests under conditions of variable heat transfer

The temperature field of a cylinder cooled (heated) in liquid media is numerically determined with allowance for the temperature dependence of the heat transfer coefficient. The results obtained are compared with calculations for =const. Nonomgrams are given for calculating the maximum thermal stresses in the case of a linear dependence of heat transfer coefficient on temperature.     

Numerical calculation of primary slot leakage inductance of a Single-sided HTS linear induction motor used for linear metro

In the paper, the numerical method calculating asymmetric primary slot leakage inductances of Single-sided High-Temperature Superconducting (HTS) Linear Induction Motor (HTS LIM) is presented. The mathematical and geometric models of three-dimensional nonlinear transient electromagnetic field are established and the boundary conditions are also given. The established model is solved by time-stepping Finite Element Method (FEM). Then, the three-phase asymmetric primary slot leakage inductances under different operation conditions are calculated by using the obtained electromagnetic field distribution. The influences of the special effects such as longitudinal end effects, transversal edge effects, etc. on the primary slot leakage inductance are investigated. The presented numerical method is validated by experiments carried out on a 3.5 kW prototype with copper wires which has the same structures with the HTS LIM.     

Calculation of weight functions for three-dimensional bodies with cracks

A new algorithm is proposed for the numerical calculation of weight functions used in the determination of stress intensity factors by the finite elements method. The algorithm is based on the method of equivalent volume integration. It is shown that weight functions can be obtained for cracks in three-dimensional bodies with the stress intensity factor averaged over a small section of the crack front. A numerical example demonstrating the usefulness of the algorithm is presented.Moscow. Moscow Physico-Engineering Institute. Translated from Problemy Prochnosti, No. 11, pp. 32–36, November, 1989.     

Mathematical simulation of temperature field in a hollow rotating cylinder with nonlinear boundary conditions

An analytical solution is obtained of the nonlinear problem on heat conduction in a hollow infinite cylinder in view of the temperature dependence of its thermophysical characteristics. Results are given of calculations of temperature field for the roll of machine for continuous casting of slabs.     

均匀热流作用下含裂纹板I 型温度应力强度因子的解析解

研究一种新的温度边值问题。含中心裂纹无限大板受远场均匀热流作用,热流密度方向与裂纹有一夹角。当裂纹面上维持一恒定温差时,采用复变函数理论,得出了温度场、温度应力场与位移场的解析解。利用位移单值条件,确定出温度应力强度因子的解析表达式。针对铝合金LY12 材料进行了相应数值计算,分析了热流密度大小与方向对温度分布与温度应力强度因子的影响。研究表明:该文给定的温度边界条件下,只产生Ⅰ 型温度应力强度因子,不产生Ⅱ 型温度应力强度因子。温度应力场取决于热流密度沿裂纹方向的分量,垂直于裂纹方向的分量对温度应力场没有影响。     

Theory of the current to a plane wall probe in the regime of a continuous medium

A method is suggested for calculating the total current to a plane wall probe located in the side surface of a hypersonic aircraft. The applicability of the method is limited by weaker conditions than those used in the well known works [1]. Comparisons of the results of probe experiments with those obtained from SHF inspection of the plasma and with calculations of other authors in the region of their applicability demonstrated satisfactory agreement.Sergo Ordzhonikidze Moscow Aviation Institute, Moscow, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 1–2, pp. 119–122, July–August, 1994.     

Nonlinear deformation behaviour of auxetic cellular materials with re‐entrant lattice structure

Recent frontiers in material development are represented by a class of so‐called auxetic metamaterials that, thanks to their structure rather than composition, are characterized by a negative Poisson's ratio. In the present paper a two‐dimensional auxetic plate, made by structural straight elements forming a lattice periodic structure with re‐entrant cells, is considered. A thorough discussion on the linear and geometrically nonlinear deformability of the auxetic plate is presented. The key geometric parameters governing the deformability of the plate are identified, and some analytical expressions for calculating the Poisson's ratio, as a function of the applied strain, are given. Numerical (finite element) analyses and experimental tests on 3D printed specimens are carried out to verify the theoretical findings. For the latter ones, full field strain maps are obtained by means of a suitable interpolation of the sampled displacement field measured by digital image techniques.     

光源相关色温计算方法的讨论

本从光源的色温及相关色温的定义出发,讨论了色温的三种计算方法。     

Crack growth in ferroelectric ceramics under electric loading

Summary A crack with growth in ferroelectric ceramics under purely electric loading is analyzed. The crack tip stress intensity factor for the growing crack under small scale conditions is evaluated by employing the model of nonlinear domain switching. The electrical fracture toughness is obtained from the result of the stress intensity factor. It is shown that the ferroelectric material can be either toughened or weakened as the crack grows. Fatigue crack growth in a ferroelectric material under cyclic electric loading is also examined. The incremental fatigue crack growth under cyclic electric loading is obtained numerically. The fatigue crack growth rate is affected strongly by the electrical nonlinear behavior. It is found that the curve of fatigue crack growth rate versus electric field intensity factor is linear on the log-log plot at intermediate values of the electric field intensity factor.     

Kinetics of the temperature field induced by the emission of a laser with time-varying intensity

The kinetics of the temperature field when a medium is heated with a laser beam with a Gaussian intensity distribution over the radius and different time dependences are obtained. Numerical estimates are given.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 6, pp. 1098–1104, June, 1977.     

Coupled thermo-mechanical analysis of one-layered and multilayered plates

The paper considers a fully coupled thermo-mechanical analysis of one-layered and multilayered isotropic and composite plates. In the proposed analysis, the temperature is considered a primary variable as the displacement; it is therefore directly obtained from the model and this feature permits the temperature field to be evaluated through the thickness direction in three different cases: – static analysis with imposed temperature on the external surfaces; – static analysis of structures subjected to a mechanical load, with the possibility of considering the temperature field effects; – a free vibration problem, with the evaluation of the temperature field effects. In the first case, imposing a temperature at the top and bottom of the plate, the static response is given in term of displacements, stresses and temperature field; the proposed method is very promising if compared to a partially coupled thermo-mechanical analysis, where the temperature is only considered as an external load, and the temperature profile must be a priori defined: considering it linear through the thickness direction or calculating it by solving the Fourier heat conduction equation. In the second case, a mechanical load is applied. The fully coupled thermo-mechanical analysis gives smaller displacement values than those obtained with the pure mechanical analysis; the temperature effect is not considered in this latter approach. The third case is the free vibration problem. The fully coupled thermo-mechanical analysis permits the effect of the temperature field to be evaluated: larger frequencies are obtained with respect to the pure mechanical analysis. Carrera’s Unified Formulation is applied to obtain several refined models with orders of expansion in the thickness direction, from linear to fourth-order, for displacements and temperature. Both equivalent single layer and layer wise approaches are considered for the multilayered plates. At present, no benchmarks are available within the framework of a fully coupled theory. This work aims to fill this gap.