L型耦合板相关激励下高频随机能量流分析

将板的能量流分析法应用于耦合板结构受随机激励的情形,并用无限板导纳近似有限板导纳的方法考虑了随机力的相关性对输入功率的影响。对在同一块板上受到两个相关或不相关随机力作用的L型耦合板的能量响应和功率流进行了计算,结果反映了能量密度的空间分布和功率在子结构间和内部的传递路径。两种相关激励条件下的结果对比表明,作用于所考虑位置上的随机激励间的相关性对耦合结构的能量响应及功率传递的影响很小。对该L型耦合板的响应用传统的统计能量分析法进行了求解,其结果与能量流分析法预测的主要能量场的响应基本一致,说明了考虑随机力间相关作用的能量流分析法应用的有效性。     

复杂耦合系统的统计能量分析及其应用

文章综合导纳分析法、经典统计能量分析方法和经典功率流理论的各自优点，提出适合复杂耦合系统的统计能量分析方法，为研究实际机械结构之间的振动传递规律、复杂机械系统的声辐射特性提供理论依据，为实际工程结构的振动隔离、噪声治理提供理论指导。文章首次提出统计能量分析参数必须统一定义，将影响实际机械结构相互之间能量传递的若干要素各自分离，并引入相应的参数分别开展研究。利用理论研究的成果，发展后的统计能量分析首次应用于水下航行器振动和噪声特性分析，预报了水下航行器的振动传递规律和辐射噪声级。理论分析与实验测试结果符合较     

能量有限元方法在复合材料层合梁耦合结构振动分析中的应用

以能量有限元方法(EFEM)建立控制方程,研究了复合材料层合梁受激励时的横向振动问题。该方法以结构中的能量密度作为变量,根据波动理论中功率流与能量密度的平衡关系建立了与傅里叶热传导方程类似的二阶偏微分方程组,通过有限元离散得到结构单元节点的能量密度矩阵形式方程。根据耦合连续平衡条件,建立耦合单元节点矩阵,从而对总矩阵方程进行组集及求解,得到结构中能量密度的分布。通过数值算例与传统有限元方法(FEM)结果做了对比,取得了较好的一致性。     

板结构-声场耦合分析的有限元-径向插值/有限元法

为提高板结构-声场耦合分析的计算精度,将有限元-径向点插值法(Finite Element-Radial Point Interpolation,FE-RPIM)推广到板结构-声场耦合问题的结构域分析中,推导了FE-RPIM/FEM法分析板结构-声场耦合问题的计算公式。板结构-声场耦合分析的FE-RPIM/FEM法在流体域中采用标准的有限元插值函数;在结构域中采用有限元-径向点插值法,其形函数由等参单元形函数和径向点插值函数相结合构成,继承了有限元法的单元兼容性和径向点插值法的Kronecker性质,提高了插值精度。以六面体声场-结构耦合模型为研究对象进行分析,结果表明,与板结构-声场耦合问题分析的有限元/有限元法(Finite element method/Finite element method, FEM/FEM)和光滑有限元/有限元法(Smoothed Finite Element Method/Finite Element Method, SFEM/FEM)相比,FE-RPIM/FEM在分析板结构-声场耦合问题时具有更高的精度。     

板结构-声场耦合分析的FE-LSPIM/FE-LSPIM法

为提高板结构-声场耦合分析的计算精度,将有限元-最小二乘点插值法(Finite Element-Least Square Point Interpolation Method,FE-LSPIM)推广到板结构-声场耦合问题的分析中,提出了板结构-声场耦合问题分析的FELSPIM/FE-LSPIM方法,推导了FE-LSPIM/FE-LSPIM分析板结构-声场耦合问题的计算公式。FE-LSPIM/FE-LSPIM方法应用有限元单元形函数和最小二乘点插值法进行局部逼近,继承了有限元法的单元兼容性和最小二乘插值法的二次多项式完备性,提高了计算精度。以一六面体声场-结构耦合模型为研究对象进行分析,结果表明,与板结构-声场耦合问题分析的FEM/FEM和光滑有限元/有限元(Smoothed Finite Element Method/Finite Element Method,SFEM/FEM)相比,FELSPIM/FE-LSPIM在分析板结构-声场耦合问题时具有更高的精度。     

T型耦合板结构振动特性研究

本文以T型耦合板为研究对象,在同时考虑面内振动和面外振动条件下采用改进傅立叶级数方法（Improved Fourier Series Method,IFSM）对其自由振动特性进行了计算分析。板结构的面内振动和面外振动位移函数表示为改进傅立叶级数形式,并引入正弦傅立叶级数以解决边界的不连续或跳跃现象。将位移函数的级数展开系数作为广义坐标,采用Rayleigh-Ritz方法对其进行求解。通过对不同边界条件及耦合连接情况下T型板自由振动特性进行计算,并将之与有限元法结果相比较,验证了本文方法的正确性和有效性,为耦合板结构的振动控制提供可靠的理论依据。     

板结构-声场耦合分析的FE-LSPIM/FE法

为提高板结构-声场耦合分析的计算精度,将有限元-最小二乘点插值法(Finite Element-Least Square Point Interpolation Method,FE-LSPIM)推广到板结构-声场耦合问题的结构域分析中,提出了板结构-声场耦合问题分析的FE-LSPIM/FEM(Finite Element-Least Square Point Interpolation Method/Finite Element Method),推导了FELSPIM/FEM分析板结构-声场耦合问题的计算公式。此方法在结构域中应用四边形单元形函数和最小二乘点插值法进行局部逼近,继承了有限元法的单元兼容性和最小二乘插值法的二次多项式完备性,提高了结构域的计算精度;在流体域中应用标准有限元模型进行分析。以一六面体声场-结构耦合模型为研究对象进行分析,结果表明,与板结构-声场耦合问题分析的FEM/FEM和光滑有限元/有限元(Smoothed Finite Element Method/Finite Element Method,SFEM/FEM)相比,FE-LSPIM/FEM在分析板结构-声场耦合问题时具有更高的精度。     

随机有限元分析及其在复合材料中的应用

本文利用局部平均理论和随饥变量特征正交化方法给出了随机有限元分析的基本列式。应用本文提出的方法,分析了纤维分布具有微小随机性对复合材料位移场和应力场扰动的灵敏程度。     

人行激励下梁板结构与人体耦合作用研究

对于重要的梁板结构,应该考虑人行激励下的结构振动以及人体舒适度问题.根据单步落足曲线将人体等效为具有主体部分和耦合质量的时变动力模型,并建立了梁板结构与移动人体相耦合的动力平衡方程及其解析表达式.考虑行走速度和楼板长度等因素,按耦合分析方法对人体与结构的动力响应进行了研究和比较,结果表明人体的自振频率、行走步频和速度是影响结构动力响应和人体的舒适度的重要因素,在梁板结构设计时需要充分考虑上述因素从而有效降低结构振动强度.与等效静力法和不考虑人体耦合作用的动力方法相比,本文提出的动力耦合分析方法更加全面和准确.     

随机激励下结构优化功率流控制策略

本文提出了一种新的基于功率流的线性结构优化控制策略，其 目标是尽可能地减小 结构的净功率流，同时又保证控制器吸收的功率满足设计要求。文章推导出这种优化控制算子的一般表达式，通过简化的单自由度模型说明了它在减小随机激励下结构反应方面的 应用，并且给出了在平稳 白噪声和过滤白噪声激励下结构响应的数值计算结果。文章重点分析了在这种优化控制策略中加权函数的频率特性，并对其如何取值得出了一些建设性的结论。     

A coupled analysis method for structures with independently modelled finite element subdomains

A new method for analysing plate and shell structures with two or more independently modelled finite element subdomains is presented, assessed, and demonstrated. This method provides a means of coupling local and global finite element models whose nodes do not coincide along their common interface. In general, the method provides a means of coupling structural components (e.g., wing and fuselage) which may have been modelled by different analysts. In both cases, the need for transition modelling, which is often tedious and complicated, is eliminated. The coupling is accomplished through an interface for which three formulations are considered and presented. These formulations are: collocation, discrete least-squares, and hybrid variational. Several benchmark problems are analysed and it is shown that the hybrid variational formulation provides the most accurate solutions.     

基于能量有限元法的功能梯度梁振动分析

功能梯度材料(Functionally Graded Material,FGM)由于其优良的结构性能和重要的应用价值,近些年来得到了广泛的研究和关注。采用能量有限元法对功能梯度梁和耦合梁的弯曲振动特性进行研究,推导了功能梯度材料梁的能量密度控制方程、能量有限元矩阵方程以及耦合梁的能量有限元方程,从而得到梁中的能量密度和能量流。以一简支功能梯度梁为例,分别采用该方法和传统有限元法计算了梁弯曲振动时的能量密度,通过对比验证了能量有限元法求解的准确性。在此基础上进一步对耦合功能梯度梁结构的能量密度和能量流进行了求解,得到其能量分布特征。该研究为基于能量有限元法分析复杂功能梯度材料结构的振动特性提供了理论基础。     

A new finite element for thick laminates and sandwich structures using a generalized and unified plate theory

The contribution of this work is the implementation of a new elastic solution method for thick laminated composites and sandwich structures based on a generalized unified formulation using finite elements. A quadrilateral four‐node element was developed and evaluated using an in‐house finite element program. The C‐1 continuity requirements are fulfilled for the transversal displacement field variable. This method is tagged as Caliri's generalized formulation. The results employing the proposed solution method yielded coherent results with deviations as low as 0.05% for a static simply supported symmetric laminate and 0.5% for the modal analyses of a soft core sandwich structure. Copyright © 2016 John Wiley & Sons, Ltd.     

基于有限元的能量流分析方法研究

区别于传统的统计能量分析,通过对有限元方法计算结果的后处理也可进行能量流分析。为提高计算效率,分析过程中对某些与频率相关的积分进行了推导简化。在此基础上,以Matlab为平台编写了相关计算程序。而后,对具体算例进行基于有限元的能量流分析并与统计能量分析的结果进行比较。最后,基于此算例进一步对基于有限元的能量流分析方法进行改进并对相应的计算程序进行优化提高计算效率。     

Robust C0 high-order plate finite element for thin to very thick structures: mechanical and thermo-mechanical analysis

This paper presents a new C⁰ eight-node quadrilateral finite element (FE) for geometrically linear elastic plates. This finite element aims at modeling both thin and thick plates without any pathologies of the classical plate finite elements (shear and Poisson or thickness locking, spurious modes, etc). A C¹ FE was previously developed by the first author based on the kinematics proposed by Touratier. This new FE can be viewed as an evolution towards three directions: (1) use of only C⁰ FE approximations; (2) modeling of thick to thin structures; and (3) capability in multifield problems. The transverse normal stress is included allowing use of the three-dimensional constitutive law. The element performances are evaluated on some standard plate tests, and comparisons are given with exact three-dimensional solutions for plates under mechanical and thermal loads. Comparisons are made with other plate models using C¹ and semi-C¹ FE approximations as well as with an eight node C⁰ FE based on the Reissner–Mindlin model. All results indicate that the present element is highly insensitive to mesh distortion, has very fast convergence properties and gives accurate results for displacements and stresses. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic soil–structure interaction analysis of layered unbounded media via a coupled finite element/boundary element/scaled boundary finite element model

In this paper, a coupled model based on finite element method (FEM), boundary element method (BEM) and scaled boundary FEM (SBFEM) (also referred to as the consistent infinitesimal finite element cell method) for dynamic response of 2D structures resting on layered soil media is presented. The SBFEM proposed by Wolf and Song (Finite‐element Modelling of Unbounded Media. Wiley: England, 1996) and BEM are used for modelling the dynamic response of the unbounded media (far‐field). The standard FEM is used for modelling the finite region (near‐field) and the structure. In SBFEM, which is a semi‐analytical technique, the radiation condition at infinity is satisfied exactly without requiring the fundamental solution. This method, also eliminates the need for the discretization of interfaces between different layers. In both SBFEM and BEM, the spatial dimension is decreased by one. The objective of the development of this coupled model is to combine advantages of above‐mentioned three numerical models to solve various soil–structure interaction (SSI) problems efficiently and effectively. These three methods are coupled (FE–BE–SBFEM) via substructuring method, and a computer programme is developed for the harmonic analyses of SSI systems. The coupled model is established in such a way that, depending upon the problem and far‐field properties, one can choose BEM and/or SBFEM in modelling related far‐field region(s). Thus, BEM and/or SBFEM can be used efficiently in modelling the far‐field. The proposed model is applied to investigate dynamic response of rigid and elastic structures resting on layered soil media. To assess the proposed SSI model, several problems existing in the literature are chosen and analysed. The results of the proposed model agree with the results presented in the literature for the chosen problems. The advantages of the model are demonstrated through these comparisons. Copyright © 2004 John Wiley & Sons, Ltd.     

Analysis of adaptive plate structures by mixed layerwise finite elements

In this paper, a mixed layerwise finite element model for adaptive plate structures is presented. Static and free-vibration analysis of piezoelectric laminated plate structures is considered. A modified Reissner mixed variational principle is used to formulate the finite element model. The mixed functional is formulated using transverse stresses, displacement components and electrical potential as primary variables. The present model, in contrast with the standard layerwise displacement finite element model, fulfils the continuity of all primary variables across the interface between adjacent layers. The in-plane stress components and the electric displacements are evaluated in the post-computation through the piezolaminate constitutive equations. Two illustrative examples are presented for comparison. The predictions of the primary variables and the efficiency of the model, mainly with reference to the interlaminar stresses are discussed and compared with alternative three-dimensional solutions. The present solutions are found to be in good agreement with the benchmark solutions for the static and modal analysis problems.