功能梯度圆板的三维瞬态热弹性分析

基于线性热弹性理论的基本方程,采用两个位移分量,两个应力分量,温度变量和一个热流分量作为状态变量,应用状态空间理论,建立了功能梯度材料轴对称圆板结构在动态热载荷作用下的状态方程,考虑了运动惯性项以及热传导过程中的耦合效应,根据微分求积法,将状态方程沿径向进行离散.采用Laplace变换和打靶法,数值求解了材料常数按幂率变化的周边固支圆板在热冲击下的热响应.为求解功能梯度结构三维热弹性瞬态响应提供了一种方法.分析了组分材料分布对功能梯度圆板的热响应行为,包括板内温度变化,横向挠度以及板内应力分量的影响规律.     

基于微分求积法的轴向流作用下二维板复杂响应研究

研究轴向流作用下两端简支二维板线性稳定性及非线性复杂响应。用微分求积法对流场方程及二维板连续型运动方程统一离散,通过流固耦合边界条件将流场势函数用板的横向振动位移变量表示,获得二维板横向振动位移变量控制方程。通过特征值分析获得复频率及临界流速随流道高度变化。通过对壁板非线性动力响应数值模拟,采用分岔、相平面及庞加莱截面图等揭示壁板将发生的周期运动、拟周期、混沌等多种运动形式表明,壁板由周期倍化分岔或拟周期运动通向混沌。     

热弹性动力学耦合问题的插值型移动最小二乘无网格法研究

该文基于插值型移动最小二乘法,将无网格局部Petrov-Galerkin（MLPG）法用于二维耦合热弹性动力学问题的求解。修正的Fourier热传导方程和弹性动力控制方程通过加权余量法来离散,Heaviside分段函数作为局部弱形式的权函数,从而得到描述热耦合问题的二阶常微分方程组。然后利用微分代数方法,温度和位移作为辅助变量,将上述二阶常微分方程组转换成常微分代数系统,采用Newmark逐步积分法进行求解。该方法无需Laplace变换可直接得到温度场和位移场数值结果,同时插值型移动最小二乘法构造的形函数由于满足Kroneckerdelta特性,因此能直接施加本质边界条件。最后通过两个数值算例来验证该方法的有效性。     

求解载流薄壳二维磁弹性的差分法

本文针对在电磁场和机械场耦合作用下的载流薄壳的非线性变形问题进行了研究。给出了载流薄壳在耦合场作用下的二维电动力学方程、磁弹性非线性运动方程和Lorentz力表达式,通过变量代换将描述载流薄壳的磁弹性状态方程整理成含有10个基本未知函数的标准Cauchy型。并通过差分法及准线性化方法,将标准Cauchy型非线性偏微分方程组,变换成为能够用正交离散法编程求解的准线性微分方程组,实现了载流薄壳的磁弹性应力与变形的数值解。     

旋转半无限大体广义电磁热弹性耦合的二维问题

基于广义热弹性理论,研究了热和电可导的旋转半无限大体在其表面受随时间变化的热作用的广义电磁热弹性耦合的二维问题。半无限大体置于恒定的磁场中,受热作用产生膨胀变形,由于外加磁场的作用,介质中产生了感应的电场和感应的磁场。该文建立了电磁热弹性耦合的控制方程,利用正则模态法求解,得到了问题的解析解,并给出了各物理量的分布规律。可以看出,介质中呈现出电磁热弹耦合效应,由于旋转,位移和应力的幅值有很明显的降低,而旋转对温度和感应的磁场的影响不大。     

考虑热松弛的热弹耦合二维问题的有限元法

为了解决利用积分变换方法在求解Lord-Shulman（L-S）型广义热弹性耦合二维问题时由于数值反变换所引起的计算精度降低的问题,该文采用新近被应用的直接有限元方法,求解了基于L-S型广义热弹性理论的半无限大体受热冲击作用的动态响应问题,结果表明,该方法对求解L-S型广义热弹性耦合二维问题具有很高的精度。该文给出了L...     

分数阶热弹性理论下中空黏弹性圆柱热弹耦合动力响应EI北大核心CSCD

基于Ezzat型分数阶广义热弹性理论,引入Kelvin-Voigt黏弹性模型建立了黏弹性中空圆柱热弹耦合动力模型,探讨了黏弹性中空圆柱热弹耦合问题。中空圆柱体内外表面均有一定约束,且在其外表面处施加热冲击作用。给出Ezzat型分数阶双相滞后广义热弹性理论下问题的控制方程,结合Laplace变换和数值反变换技术对控制方程进行求解,最终得到中空圆柱中无量纲位移、温度、径向应力和环向应力的分布规律,并分析了黏弹性松弛时间因子和分数阶系数对各物理量的影响。结果表明:黏弹性松弛时间因子对于无量纲温度外的所有物理量均有明显影响,但对径向应力和环向应力的影响更为明显;分数阶系数对于所有物理量均有明显影响,在曲线峰值或谷值处影响最显著。     

分数阶微分双参数黏弹性地基矩形板动力响应

基于弹性地基Pasternak双参数模型,利用分数阶微分得到黏弹性地基双参数模型,并在此基础上建立采用分数阶微分Kelvin模型的双参数黏弹性地基上弹性和黏弹性矩形板在动荷载作用下的动力方程;利用Galerkin方法和分段处理的数值计算方法求解四边简支的弹性和黏弹性地基板的动力方程,通过自由振动算例验证该求解方法的正确性;并分析冲击动荷载作用下分数阶微分Kelvin模型的分数阶、粘滞系数、水平剪切系数和模量参数对位移响应的影响。结果表明：分数阶微分黏弹性模型可以描述不同黏弹性材料的力学行为;分数阶取值0.5前后,矩形板位移响应值出现了不同的衰减发展形态;粘滞系数、水平剪切系数和模量系数取值越大,位移响应衰减速度越快。     

固定边载流矩形板的磁弹性效应分析

针对在电磁场和机械场耦合作用下的载流矩形板的二维磁弹性问题进行了研究.在给出矩形薄板的磁弹性非线性运动方程、几何方程、物理方程、电动力学方程和Lorentz力表达式的基础上,建立了差分格式和线性化迭代方程,给出了这些方程的数值解系统,并以固定边矩形板为例,计算了该板在电磁场和机械载荷耦合作用下的应力及变形,研究了侧向电...     

楔形体匀速和自由落体水弹性砰击的半解析法求解EI北大核心CSCD

针对二维弹性楔形体入水过程的流固耦合问题,提出一种基于耦合Wagner理论和模态叠加法的半解析解方法。结构湿表面的速度势基于Wagner理论求解并考虑了结构弹性影响。砰击压力根据伯努利方程求解,为提高求解精度考虑了伯努利方程中速度平方项。通过平均弹性速度修正模型推导出附加质量和阻尼矩阵,将其代入固体动力学方程从而建立统一的流固耦合方程,耦合方程通过基于隐式的Newmark-β算法实现求解。通过计算楔形体垂直恒速和自由落体入水两种运动状态,并与基于半解析、数值和试验的文献结果进行了对比,验证了所提理论的可靠性。     

Pressure and flow in fluid films constrained between translating and vibrating flexible surfaces

In this paper, the dynamic pressure and flow developed in a two-dimensional, viscous fluid film constrained between flexible surfaces are analyzed. The problem formulation assumes that the response of the flexible surface is governed by linear equations of motion, and the fluid motion is governed by linearized momentum equations including the unsteady inertia. Three states of the model are developed to describe the coupled fluid-structural response problem. The fluid dynamic pressure is derived in the frequency domain as a function of the fluid impedances and the surface transverse vibrations. The perturbed, coupled problem is described by an integral equation (in state vector form) that governs the coupled responses of the flexible surfaces. The integral equation is solved by a discretization method. The analysis is applied to a rigid slider bearing with a flexible, translating plate surface under the excitation of a harmonic point load. The accuracy of the discretization method is evaluated, and numerical results for the dynamic pressure and the plate response are presented.     

推进剂与贮箱液固耦合振动的动力学分析

分析液体燃料运载火箭的推进剂及贮箱的耦合振动时,为了精确建模、工程化快速计算及为火箭整体系统提供液固耦合燃料系统等效模态参数,根据有限元方法得到包含液体节点压力和结构节点位移的非对称形式的耦合动力学方程组,将表征液体运动的节点压力缩聚到液体自由面,使得方程对称化。通过等价Laplace方程边值问题的求解,得到耦合动力学方程中液体对结构的附加质量矩阵、附加刚度矩阵及耦合项。简易贮箱液固耦合模态分析的算例结果表明,该分析方法能够精确、快速地获得液固耦合系统的模态频率等动力学特性。从而使得高效率的液固耦合动力学分析在工程上应用成为可能,并为运载火箭等复杂液固耦合结构的有限元建模由简化模型向三维精确模型建立和工程化应用建立了基础。     

On the heat-flow distribution from and the temperature profile on an equally heated rectangle,calculated by series development

A method is proposed to approximate the solutions of a certain class of differential equations, linear or nonlinear, in two or three, dimensions, provided that the boundary conditions are given on a rectangle or a parallelepiped, respectively. For other boundary shapes the co-ordinate system must be transformed to meet that requirement. As in illustration, an example is given for the solution of Poisson's equation in two dimensions with a constant heat source, giving the temperatures on the rectangle together with the heat-flow distribution along its edges. The basis of the method is a Taylor-series development around one point; the result is given in terms of as many partial derivatives in that point as is desired. A similar method has already been described by Small² for the ‘heat equation’ ?θ/?t = ?²θ/?x²². Compared with finite difference and finite element solutions, these methods have the advantage that the solution is continuous, whereas first and second derivatives such as heat fluxes are available at hardly any effort. The results are compared with those of the exact solution. Even if the size of the determinant is limited to 4 × 4, the accuracy is already better than 98.98 per cent. When more effort is spent to solve a system of 10 equations, the accuracy is better than 99–95 per cent.     

Influence of the electric current waveform on the dynamic response of the electrified composites

The influence of the electric current waveform (DC, AC and pulsed currents) on the dynamic electromagnetic, thermal, and impact response of the composite plate is studied. The analysis includes solving Maxwell’s equations in the electrified composite plate to determine an electric-current induced magnetic field and heat transfer equation to estimate the electric-current-induced heating. In addition, the dynamic mechanical response of the electrified composite plate subjected to impact and various electromagnetic loads (DC, AC, pulsed electric currents and a constant magnetic field) is analyzed by solving a coupled system of equations of motion and Maxwell’s equations in the composite plate. The results show that the dynamic response of the plate is highly dependent on the characteristics of the electromagnetic field, and the pulsed electromagnetic fields are most effective in reducing vibrations caused by the application of dynamic mechanical loads.     

Orthotropic piezoelectric patches for control of symmetric laminates via an integral equation

Formulation of the problem for the feedback displacement control of a vibrating laminated plate with orthotropic piezoelectric sensors and actuators is given in terms of an integral equation. The objective is to develop a formulation which facilitates the numerical solution to obtain the eigenfrequencies and eigenfunctions of the piezo-controlled plate. The control is carried out via piezoelectric sensors and actuators which are of orthorhombic crystal class mm² with poling in the z direction. The initial formulation of the problem is given in terms of a differential equation which is the conventional formulation most often used in the literature. The conversion to an integral equation formulation is achieved by introducing an explicit Green’s function. Explicit expressions for the kernel of the integral equation are given and the method of solution using the new formulation is outlined. The solution technique involves approximating the integral equation with an infinite system of linear equations and using a finite number of these equations to obtain the numerical results.     

Coupled horizontal and rocking vibrations of a rigid circular plate on a transversely isotropic bi-material interface

This paper investigates the coupled rocking and horizontal vibratory response of a rigid circular plate embedded in viscoelastic, transversely isotropic, three-dimensional unbounded media. The boundary-value problem corresponding to the case of distributed horizontal and rocking ring loads at a bi-material interface is solved to obtain the required influence functions for the solution of the present problem. The case of an embedded rigid plate is formulated in terms of a discretized integral equation, which couples the rigid body displacements of the plate with the tractions acting over its contact surface through a set of displacement influence functions. The system of resulting discretized integral equations is solved numerically. The solution results in the tractions over each disc element. This paper carefully takes into account the coupling of the rocking and horizontal responses of the plates that is typical of non-homogeneous interfaces, i.e., their horizontal displacements due to rocking moments and their rotations due to horizontal loads. The dynamic direct and cross compliances of the embedded plate are shown for different governing parameters such as frequency of excitation and bi-material configuration. The present results are useful to the study of dynamic response of deeply buried foundations and anchors in non-homogeneous soils.     

带弹性隔板圆柱形储液罐的流-固耦合特性研究

该文研究带有环形弹性隔板的部分充液刚性圆柱罐中液体与隔板的耦合振动特性。将液体域分割成两个圆柱子域和两个圆环柱子域,利用分离变量法和叠加原理求得各子域内液体运动势函数的解。将环形薄板的湿模态用干模态展开以求解环形薄板与液体耦合振动的微分方程。对液体子域间的界面连续条件作Fourier 展开并对表面波方程作Bessel 展开,得到环形薄板与液体耦合振动的频率和对应模态。数值结果与流-固耦合专用软件ADINA 的结果进行了比较,显示出很好的一致性。     

横向磁场中机械载荷作用梁式薄板的非线性主共振

研究了磁场环境中受机械载荷作用梁式薄板的非线性主共振问题。在给出薄板的非线性电磁弹性耦合运动基本方程及电磁力表达式的基础上，得到了横向稳恒磁场和机械载荷共同作用下梁式薄板的振动方程。应用伽辽金积分法，并进行无量纲化处理，进一步导出了相应的非线性振动微分方程。采用平均法对主共振问题进行了求解，得到了稳态运动下的幅频响应方程。通过算例给出了几种情况下的幅频响应曲线图和时间历程图，分析了板厚和磁场对系统振动的影响。