带裂纹矩形板自由振动解析解

选取带有补充项的双重正弦傅里叶级数作为振型函数通解,来解析研究带裂纹矩形板的自由振动特性。先将带裂纹矩形板分割成若干小矩形板,利用各小矩形板的边界条件,并结合振型函数中待定常数的物理意义,简化得到各小矩形板的振型函数,再结合各板的控制方程、未使用的边界条件、公共边协调条件及本文提出公共自由角点的协调条件,建立求解频率的代数方程组,然后将其转化为广义特征值问题来求解带裂纹矩形板的无量纲频率;最后选取具体参数进行计算并与文献结果对比,吻合良好,证明了本文采用的研究方法以及所提出公共角点协调条件的正确性和合理性。由于该振型函数能满足矩形板的任意边界约束,且其中的待定常数具有明确的物理意义,所以可使矩形板问题的求解统一化、简单化和规律化。     

桁架结构拓扑优化设计可行域研究

本文提出了桁架结构拓扑优化设计的k维可行子域、相邻可行子域、k维连通可行子域、k维奇异可行子域的定义，在这些定义的基础上，采用集合描述的方法，对Rozvany关于结构拓扑优化设计奇异最优解的定义进行了重新描述。基于以上定义，本文研究了桁架结构拓扑优化设计的可行域，证明了对于截面尺寸下限为零，且无尺寸上限的桁架结构受应力约束的拓扑优化设计问题，其设计空间不同拓扑的可行子域总是连通的，同时也给出了对于具有尺寸下限约束、具有局部稳定性约束的桁架结构拓扑优化设计的可行子域不连通的实例。     

直接施加本质边界条件的FE／EFG耦合算法及其数值实现

提出一种可以直接施加本质边界条件的有限元与无网格Galerkin（FE／EFG）耦合算法。将问题域分成FE和EFG两种类型的子域,采用转换矩阵耦舍两子域的交界面;通过另一转换矩阵将无网格区域本质边界上的名义位移转换成真实位移,从而可在其上直接施加本质边界条件;采用二次转换实现两种转换矩阵之间的协调。提出全域统一采用单元...     

Direct spectral domain decomposition method for 2D incompressible Navier-Stokes equations

An efficient direct spectral domain decomposition method is developed coupled with Chebyshev spectral approximation for the solution of 2D, unsteady and incompressible Navier-Stokes equations in complex geometries. In this numerical approach, the spatial domains of interest are decomposed into several non-overlapping rectangular sub-domains. In each sub-domain, an improved projection scheme with second-order accuracy is used to deal with the coupling of velocity and pressure, and the Chebyshev collocation spectral method (CSM) is adopted to execute the spatial discretization. The influence matrix technique is employed to enforce the continuities of both variables and their normal derivatives between the adjacent sub-domains. The imposing of the Neumann boundary conditions to the Poisson equations of pressure and intermediate variable will result in the indeterminate solution. A new strategy of assuming the Dirichlet boundary conditions on interface and using the first-order normal derivatives as transmission conditions to keep the continuities of variables is proposed to overcome this trouble. Three test cases are used to verify the accuracy and efficiency, and the detailed comparison between the numerical results and the available solutions is done. The results indicate that the present method is efficiency, stability, and accuracy.     

A weak formulation for interior acoustic analysis of enclosures with inclined walls and impedance boundary

A weak variational principle based approach is presented in this paper to study the sound field inside the acoustic enclosures with walls in arbitrary inclination and impedance conditions. The whole acoustic domain is firstly divided into several sub-cavities with trapezoidal and rectangular faces, and each sub-cavity is coupled with adjacent ones by matching the required continuity constraints on the interfaces on the basis of a modified variational principle and least-squares weighted residual method. By using this domain partitioning strategy, high-order acoustic modes and responses can be easily achieved. Chebyshev orthogonal polynomials of the first kind are employed as the wholly admissible unknown sound pressure functions for each sub-cavity without meshing process like FEM/BEM does, and then each physical domain is mapped into a square spectral domain. To demonstrate the convergence, accuracy and stability of the approach, the modal and sound response analyses of several configurations of cavities are examined and compared with available analytical solutions, or those obtained by using FEM. Effects of the weighted parameters together with the number of truncated polynomial terms and the divided cavity segments on the accuracy of present solutions are investigated. Key parametric studies concerning the influences of the geometrical properties as well as the impedance boundary of enclosing walls are also performed. It is demonstrated that the present method is a computationally efficient way to achieve interior sound predictions in mid-frequency range with a satisfactory accuracy of solutions.     

基于不同时间步长时域非结构有限体积法模拟声-弹性耦合问题

介绍一种改进的时域非结构有限体积法(FVM),并将其应用于声-弹性耦合问题。在流体与固体介质中分别求解声波动方程与弹性波方程,根据交界面上的力平衡与质点振速连续条件考虑二者的相互作用。同时考虑双线性四边形单元的线性变化项及常数项,并结合常应变三角形单元处理混合网格问题。分别对三角形单元和四边形单元进行色散分析,给出声波动方程的稳定性条件。在不同介质中采用不同时间步长,提高计算效率。求解弹性波问题、声-弹性耦合问题,结果表明,改进后的方法求解声-弹性耦合问题是有效和准确的,并且具有良好的数值稳定性。     

Numerical simulation of flow‐induced noise using LES/SAS and Lighthill's acoustic analogy

We present a finite element (FE) formulation of Lighthill's acoustic analogy for the hybrid computation of noise generated by turbulent flows. In the present approach, the flow field is computed using large eddy simulation and scale adaptive simulation turbulence models. The acoustic propagation is obtained by solving the variational formulation of Lighthill's acoustic analogy with the FE method. In order to preserve the acoustic energy, we compute the inhomogeneous part of Lighthill's wave equation by applying the FE formulation on the fine flow grid. The resulting acoustic nodal loads are then conservatively interpolated to the coarser acoustic grid. Subsequently, the radiated acoustic field can be solved in both time and frequency domains. In the latter case, an enhanced perfectly matched layer technique is employed, allowing one to truncate the computational domain in the acoustic near field, without compromising the numerical solution. Our hybrid approach is validated by comparing the numerical results of the acoustic field induced by a corotating vortex pair with the corresponding analytical solution. To demonstrate the applicability of our scheme, we present full 3D numerical results for the computed acoustic field generated by the turbulent flow around square cylinder geometries. The sound pressure levels obtained compare well with measured values. Copyright © 2009 John Wiley & Sons, Ltd.     

A coupled IEM/FEM approach for solving elastic problems with multiple cracks

In this paper, the detailed two-dimensional infinite element method (IEM) formulation with infinite element (IE)–finite element (FE) coupling scheme for investigating mode I stress intensity factor in elastic problems with imbedded geometric singularities (e.g. cracks) is presented. The IE–FE coupling algorithm is also successfully extended to solve multiple crack problems. In this method, the domain of the primary problem is subdivided into two sub-domains modeled separately using the IEM for the multiple crack sub-domain, and the FEM for the uncracked sub-domain. In the IE sub-domain, the similarity partition concept together with the IEM formulation are employed to automatically generate a large number of infinitesimal elements, layer by layer, around the tip of each crack. All degrees of freedom related to the IE sub-domain, except for those associated with the coupling interface, are condensed and transformed to form a finite master IE for each crack with master nodes on sub-domain boundary only. All of the stiffness matrices constructed in the IE sub-domains are assembled into the system stiffness matrix for the FE sub-domain. The resultant FE solution with a symmetrical stiffness matrix, having the singularity effect of imbedded cracks in IEs, is required only for solving multiple crack problems.Using these efficient numerical techniques a very fine mesh pattern can be established around each crack tip without increasing the degree of freedom of the global FEM solution. One is easily allowed to conduct parametric analyses for various crack sizes without changing the FE mesh. Numerical examples are presented to show the performance of the proposed method and compared with the corresponding known results where available.     

Linearized and non‐linear acoustic/viscous splitting techniques for low Mach number flows

Computation of the acoustic disturbances generated by unsteady low‐speed flow fields including vortices and shear layers is considered. The equations governing the generation and propagation of acoustic fluctuations are derived from a two‐step acoustic/viscous splitting technique. An optimized high order dispersion–relation–preserving scheme is used for the solution of the acoustic field. The acoustic field generated by a corotating vortex pair is obtained using the above technique. The computed sound field is compared with the existing analytic solution. Results are in good agreement with the analytic solution except near the centre of the vortices where the acoustic pressure becomes singular. The governing equations for acoustic fluctuations are then linearized and solved for the same model problem. The difference between non‐linear and linearized solutions falls below the numerical error of the simulation. However, a considerable saving in CPU time usage is achieved in solving the linearized equations. The results indicate that the linearized acoustic/viscous splitting technique for the simulation of acoustic fluctuations generation and propagation by low Mach number flow fields seems to be very promising for three‐dimensional problems involving complex geometries. Copyright © 2003 John Wiley & Sons, Ltd.     

Uncertainty quantification for dynamics of geometrically nonlinear structures coupled with internal acoustic fluids in presence of sloshing and capillarity

In this paper, we propose an uncertainty quantification analysis, which is the continuation of a recent work performed in a deterministic framework. The fluid–structure system under consideration is the one experimentally studied in the sixties by Abramson, Kana, and Lindholm from the Southwest Research Institute under NASA contract. This coupled system is constituted of a linear acoustic liquid contained in an elastic tank that undergoes finite dynamical displacements, inducing geometrical nonlinear effects in the structure. The liquid has a free surface on which sloshing and capillarity effects are taken into account. The problem is expressed in terms of the acoustic pressure field in the fluid, of the displacement field of the elastic structure, and of the normal elevation field of the free surface. The nonlinear reduced-order model constructed in the recent work evoked above is reused for implementing the nonparametric probabilistic approach of uncertainties. The objective of this paper is to present a sensitivity analysis of this coupled fluid–structure system with respect to uncertainties and to use a classical statistical inverse problem for carrying out the experimental identification of the hyperparameter of the stochastic model. The analysis show a significant sensitivity of the displacement of the structure, of the acoustic pressure in the liquid, and of the free-surface elevation to uncertainties in both linear and geometrically nonlinear simulations.     

Dynamic 3D axisymmetric problems in continuously non-homogeneous piezoelectric solids

The meshless local Petrov-Galerkin (MLPG) method is used to analyze transient dynamic problems in 3D axisymmetric piezoelectric solids with continuously inhomogeneous material properties. Both mechanical and thermal loads are considered here. A 3D axisymmetric body is created by rotation of a cross section around an axis of symmetry. Axial symmetry of geometry and boundary conditions reduces the original 3D boundary value problem into a 2D problem. The cross section is covered by small circular sub-domains surrounding nodes randomly spread over the analyzed domain. A unit step function is chosen as test function, in order to derive local integral equations on the boundaries of the chosen sub-domains, called local boundary integral equations (LBIE). These integral formulations are either based on the Laplace transform technique or the time-difference approach. The local integral equations are non-singular and take a very simple form, despite of inhomogeneous and anisotropic material behaviour across the analyzed structure. Spatial variation of all physical fields (or of their Laplace transforms) at discrete time instants are approximated on the local boundary and in the interior of the sub-domain by means of the moving least-squares (MLS) method. The Stehfest algorithm is applied for the numerical Laplace inversion, in order to retrieve the time-dependent solutions.     

Assessment of shunted piezoelectric devices for simultaneous noise and vibration reduction: comparison of passive,active and hybrid networks

Structural vibration and noise control of a cavity-backed three-layered smart piezo-coupled rectangular panel system under harmonic or transient loads is achieved by using purely active, passive, and hybrid active/passive piezoelectric shunt networks. Problem formulation is based on the classical lamination plate theory, Maxwell’s equation for piezoelectric materials, linear circuit theory, and wave equation for the enclosed acoustic domain. The orthogonal mode expansions along with the modal coupling theory are employed to obtain the coupled differential equations of the electro-mechanical-acoustic system, which are then put into the convenient state-space form, and subsequently solved numerically in both frequency and time domains. A triple-mode hybrid RLC shunt circuit, in series with an external active voltage source and connected to a single electroded piezoelectric segment, is tuned to the dominant resonance frequencies of the composite structure. The linear quadratic optimal control (LQR) theory is adopted for obtaining the active control gains. The frequency and time domain performances of the passive, active and hybrid multi-modal piezoelectric systems are calculated and discussed in terms of sensor output voltage, local sound pressure, and control effort. It is found that the hybrid control methodology with properly tuned circuit parameters can be an excellent candidate for simultaneous vibration and structure-borne noise control of the cavity-coupled smart panel with decreased control effort. Also, the active control strategy integrated in the hybrid control system is demonstrated to enhance the overall system damping characteristics and improve the control authority at frequencies where the passive shunt network performs weakly. Limiting cases are considered and correctness of the mathematical model is verified by using a commercial finite element software as well as by comparisons with the literature.     

Determination of correlation functions of turbulent velocity and sound speed fluctuations by means of ultrasonic technique

An experimental study of the propagation of high-frequency acoustic waves through grid-generated turbulence by means of an ultrasound technique is discussed. Experimental data were obtained for ultrasonic wave propagation downstream of heated and non-heated grids in a wind tunnel. A semi-analytical acoustic propagation model that allows the determination of the spatial correlation functions of the flow field is developed based on the classical flowmeter equation and the statistics of the travel time of acoustic waves traveling through the kinematic and thermal turbulence. The basic flowmeter equation is reconsidered in order to take into account sound speed fluctuations and turbulent velocity fluctuations. It allows deriving an integral equation that relates the correlation functions of travel time, sound speed fluctuations and turbulent velocity fluctuations. Experimentally measured travel time statistics of data with and without grid heating are approximated by an exponential function and used to analytically solve the integral equation. The reconstructed correlation functions of the turbulent velocity and sound speed fluctuations are presented. The power spectral density of the turbulent velocity and sound speed fluctuations are calculated.     

物理信息依赖核函数配点法的研究进展

在过去几十年里, 尽管有限元等传统计算方法已被成功用于众多科学与工程领域, 但是其在数值模拟无限域波传播、大尺寸比结构、工程反演和移动边界问题时仍面临计算量大、计算效率低、网格生成困难等计算难题. 本文介绍一类基于物理信息依赖核函数的无网格配点法及其在上述难点问题中的应用. 物理信息依赖核函数配点法的关键在于构建能反映问题微分控制方程物理信息的基函数. 基于这些物理信息依赖核函数, 该方法无需/仅需少量配点对所求微分控制方程进行离散, 即可有效提高计算效率. 本文首先介绍满足常见齐次微分方程的基本解、调和函数、径向Trefftz函数以及T完备函数等典型物理信息依赖核函数. 接着依次介绍非齐次、非均质、非稳态以及隐式微分方程构造物理信息依赖核函数的方法. 随后, 根据所求问题特点, 选用全域配点或局部配点技术, 建立相应的物理信息依赖核函数配点法. 最后, 通过几个典型算例验证所提物理信息依赖核函数配点法的有效性.      

Topology optimization of a plate coupled with acoustic cavity

Optimization of the topology of a plate coupled with an acoustic cavity is presented in an attempt to minimize the fluid–structure interactions at different structural frequencies. A mathematical model is developed to simulate such fluid–structure interactions based on the theory of finite elements. The model is integrated with a topology optimization approach which utilizes the moving asymptotes method. The obtained results demonstrate the effectiveness of the proposed approach in simultaneously attenuating the structural vibration and the sound pressure inside the acoustic domain at several structural frequencies by proper redistribution of the plate material.Experimental verification is carried out by manufacturing topology optimized plates and monitoring their vibration and sound radiation into a rigid acoustic cavity. The measured sound pressure and plate vibration are found to be in good agreement with the predictions of the mathematical model.The presented theoretical and experimental techniques present valuable tools in the design of a wide variety of critical structures which must operate quietly when subjected to fluid loading.     

Numerical Analysis of the Impact of the Interior Nozzle Geometry on Low Mach Number Jet Acoustics

The flow and acoustic fields of subsonic turbulent hot jets exhausting from three divergent nozzles at a Mach number M=0.12 based on the nozzle exit velocity are conducted using a hybrid CFD-CAA method. The flow field is computed by highly resolved large-eddy simulations (LES) and the acoustic field is computed by solving the acoustic perturbation equations (APE) whose acoustic source terms are determined by the LES. The LES of the computational domain includes the interior of the nozzle geometry. Synthetic turbulence is prescribed at the inlet of the nozzle to mimic the exit conditions downstream of the last turbine stage. The LES is based on hierarchically refined Cartesian meshes, where the nozzle wall boundaries are resolved by a conservative cut-cell method. The APE solution is determined on a block structured mesh. Three nozzle geometries of increasing complexity are considered, i.e., the flow and acoustic fields of a clean geometry without any built-in components, a nozzle with a centerbody, and a nozzle with a centerbody plus struts are computed. Spectral distributions of the LES based turbulent fluctuated quantities inside the nozzle and further downstream are analyzed in detail. The noise sources in the near field are noticeably influenced by the nozzle built-in components. The centerbody nozzle increases the overall sound pressure level (OASPL) in the near field with respect to the clean nozzle and the centerbody-plus-strut nozzle reduces it compared to the centerbody nozzle due to the increased turbulent mixing. The centerbody perturbed nozzle configurations generate a remarkable spectral peak at S t=0.56 which also occurs in the APE findings in the near field region. This tone is generated by large scale vortical structures shed from the centerbody. The analysis of the individual noise sources shows that the entropy term possesses the highest acoustic contribution in the sideline direction whereas the vortex sound source dominates the downstream acoustics.     

具有随机参数的含裂纹板弯曲应力强度因子的统计分析

本文首次应用随机有限元法研究了具有随机参数的含裂纹板裂纹尖端弯曲应力强度因子的统计性质。文中首先给出了杂交模式的裂纹尖端奇异单元的刚度矩阵,然后基于随机场的局部平均理论和一阶泰勒展开得到了应力强度因子均值和方差的计算公式。作为数例,详细讨论了杨氏模量、泊松比及板厚度的不确定性对应力强度因子的影响。     

一种考虑薄壁散射效应的声学计算模型

采用薄壁边界元/FW-H理论混合方法建立了考虑薄壁声学散射效应的数值计算模型.这种声学计算模型可以预测存在薄壁如风扇机匣、蜗壳等条件下的声波的传播及散射问题.计算模型的建立主要包含噪声源的计算和声源的传播两方面:首先建立FW-H的频域方程,并采用计算流体力学方法计算流场,通过流场数据计算气动噪声源;然后采用薄壁面边界元法计算固壁对声波的散射,并计算声波在固壁散射后的声场分布.数值计算结果和实验结果及经典的叶轮机管道风扇噪声理论进行了对比,结果表明,这种计算模型与理论计算结果及实验结果吻合较好,可以准确的预测机匣壁的散射效应对声源传播的影响.     

蜂窝层芯夹层板结构振动与传声特性研究

蜂窝层芯夹层板应用于飞行器、高速列车等交通工具的主体及底板结构时需要考虑其振动及隔声特性. 针对声压激励下的四边简支蜂窝层芯夹层板结构,应用基于Reissner夹层板理论的结构振动方程建立了的声振耦合理论模型(声压以简支模态双级数的形式引入振动控制方程),结合流固耦合条件求解了声振耦合系统控制方程,应用有限元模拟对理论预测进行了验证. 基于理论模型的数值计算结果,系统研究了蜂窝层芯夹层板结构的振动特性和传声特性,刻画了层芯厚度、蜂窝壁厚、夹层板面内尺寸和声压入射角度等关键系统参数对夹层板振动和传声特性的影响,为此类结构的工程优化设计提供了必要的理论参考.