某飞机机翼颤振模型模态测试及分析

以某飞机机翼颤振缩比模型为研究对象,通过纯模态测试得到试验件前九阶模态参数。建立机翼梁架有限元模型并进行计算,得到各阶模态振型及频率。将各阶模态的计算结果与试验结果进行对比,频率的计算结果与纯模态试验值的误差均在5%以内,主要模态的振型计算结果与试验结果也基本一致,验证了有限元计算模型的准确性。在此基础上可以进行下一步的颤振分析,且试验结果可以作为机翼颤振模型风洞试验的参考依据。     

航空发动机模拟机匣动力学模型修正研究

针对有限元建模中由于各种误差(如建模误差等)会给计算结果精度带来影响的问题,提出了一种利用模型修正来提高有限元计算结果精度的方法。首次使用了一阶优化方法,以所测试的模态频率和振型为参考,对有限元模型进行修正。首先,以某航空发动机模拟机匣为研究对象,对其进行模态测试,得到其模态频率和振型。然后,以机匣的前10阶计算模态频率与测试模态频率之间误差最小为优化目标,使用Nastran软件对各部件有限元模型中单元的弹性模量进行了修正,并计算了模型修正前后的机匣模态频率和振型,同时与测试模态频率和振型进行对比。结果表明,修正后的有限元模型计算结果与测试结果吻合良好,二者模态振型一致,模态频率的最大误差不超过1%。由此说明修正弹性模量的模型修正方法合理、可行,适用于工程上大型复杂结构的有限元准确建模。     

基于简化模型的超高层结构传感器优化布置

对于自由度较多的超高层结构,传感器优化布置时应考虑多阶模态振型.由于存在空间耦合振动,根据振型质量参与系数难以准确选择出结构弱轴方向的高阶振型.基于等效刚度参数识别法,本文提出了一种将有限元模型沿弱轴方向先简化为等效串联多自由度体系,然后根据简化结构的物理参数来计算弱轴方向振型矩阵的方法,有效地解决了这一问题.以某超高层结构为例,根据计算得到的系统振型矩阵,首先由其转置的列主元QR分解得到传感器的初始布置方案,然后以模态置信度(MAC)矩阵的最大非对角元为目标函数,采用逐步累积算法逐步增加可降低此初始布置MAC非对角元的结构自由度,并考虑经济性因素,最终确定出了传感器的布置方案.     

铜陵长江大桥主跨的环境随机激励模态测试

随机激励法是桥梁检测研究的主要方法,检测获得的模态参数是判断判断桥梁运行状况的重要标志。本文采用自行开发的一套基于PC机的测试系统,对铜陵长江大桥主跨部分进行环境随机激励模态测试,记录了大桥主跨部分的动态过程。通过分析测试结果给出了铜陵长江大桥主跨部分垂直方向上的前五阶对称振型和第三阶反对称振动的振型以及相应的固有频率.为了验证测试结果,文中对大桥用二维有限元模型建模,用有限元软件ANSYS建立了该桥的二维有限元模型,并计算得到了桥的模态参数。结果表明,计算和测试结果吻合较好,从而验证了本文测试方法的可靠性。     

环形桁架结构模态实验及有限元仿真分析

针对大型可展开环形桁架天线结构开展了模态实验和有限元仿真分析。首先设计加工了环形桁架实验模型,采用锤击法对自由边界条件下环形桁架结构进行了实验模态分析,得到环形桁架结构的前六阶固有频率及其对应模态振型,并通过模态置信准则对实验结果进行了可靠性分析。其次,建立了环形桁架实验模型的有限元模型并进行模态分析,仿真得到其前六阶固有频率和模态振型。最后详细对比分析了实验结果与有限元仿真结果。结果表明:二者固有频率误差小于5%,且实验模态振型与有限元仿真模态振型一致,证明了本文分析结果真实可靠;同时,分析得到了环形桁架结构第一、二阶振型为椭圆形,第三、四阶振型为三角形,第五、六阶振型为四边形。     

波导结构频散分析的特征频率法及在板条结构中的应用

提出一种求解波导结构频散特性的有限元特征频率法,该方法基于振动问题的特征频率计算理论,根据模态振型识别波数与模态类型,建立了相速度及群速度的求解方法。该方法可适用于任意波导结构的频散关系求解。首先分析满足收敛精度要求的最大网格单元尺寸与最小模型长度,并用该方法对简支板条结构的频散特性进行了计算。结果表明,有限元特征频率法适合求解波动频散关系,板条结构中模态受边界影响会产生同阶高次模态,边界尺寸决定新模态的截止频率;随频率的增大,同阶低次反对称模态会趋于一致;对称模态能量分布受边界影响较大。本文也为板条类结构导波实验结果的分析提供了理论依据。     

弹性连接旋转柔性梁动力学分析

采用Chebyshev 谱方法对考虑根部连接弹性的平面内旋转柔性梁动力学特性进行研究. 基于Gauss-Lobatto 节点与Chebyshev 多项式方法对柔性梁变形场进行离散,通过投影矩阵法施加固定及弹性连接边界条件. 利用Chebyshev 谱方法获得了系统固有频率和模态振型数值解,通过与有限元方法及加权残余法的比较,验证了方法的有效性. 分析了弹性连接刚度、角速度比率、系统径长比及梁的长细比等参数对系统固有频率及模态振型的影响. 研究发现:由于系统弯曲模态、拉伸模态的频率随各参数的变化规律不一致,将出现频率转向与振型转换现象;随着弹性连接刚度、角速度比率及系统径长比的增大,低阶弯曲模态频率增大并超过高阶拉伸模态频率,随着梁的长细比的增大,低阶拉伸模态频率增大并超过高阶弯曲模态频率.      

任意边界条件下环肋圆柱壳振动特性的建模与求解

边界条件对环肋圆柱壳的振动特性有重要影响。基于能量法,把环肋看作离散模型,构建了任意边界条件下加环肋圆柱壳的动力学模型。采用一种改进的傅里叶级数作为位移容许函数,通过瑞利里兹程序求解结构的拉格朗日方程,得到环肋圆柱壳的振动模态和频响特性。通过与实验和有限元(FEM)方法的计算结果进行对比,验证了论文方法的准确性,在此基础上分析了环肋偏心方式、截面尺寸、位置分布和边界弹簧刚度等参数对环肋圆柱壳振动特性的影响。     

钢筋混凝土梁振动特性参数与损伤状况关系的数值仿真研究

基于分离式有限元理论,分别建立了存在钢筋混凝土局部松脱等多种形式损伤的钢筋混凝土梁横向弯曲振动力学模型,利用此模型能够计算各种损伤梁的固有频率等振动特性参数。对这些振动特性参数与各种损伤的状况之间的关系进行了数值仿真研究。提出固有频率可以作为钢筋混凝土梁损伤定性辨识的指标;针对不同的损伤形式,位移模态振型、曲率模态振型和剩余模态力向量是对局部损伤位置敏感的振动特性参数,可以利用敏感参数的绝对残差向量进行局部损伤的定位辨识;敏感参数绝对残差向量的范数与损伤程度具有良好的单调性关系,可以作为局部损伤定量辨识的指标。     

有间隙折叠舵面的振动实验与非线性建模研究

针对折叠舵面内、外舵铰接处存在的间隙对地面振动响应的影响及间隙处的非线性建模方法展开研究.消除间隙,利用锤击法对线性折叠舵面进行模态实验,得到了前五阶模态参数;打开间隙,进行振动台扫频基础激励,实验结果表明间隙的存在会使结构的动力学响应产生非线性现象,如正反向扫描差异、跳跃、多谐波及频率漂移.非线性的影响主要体现在一阶弯曲模态上,激励量级的增大和间隙的减小均会使基频增大,且逐渐趋向于无间隙的结果,但对第二阶扭转模态的影响与第一阶相比较小.建立了折叠舵面的有限元模型.提出了一种适用于具有集中非线性的折叠机构的模型缩减方法,并对舵面进行了模态缩减.根据Hertz接触理论,用具有线性和3/2次刚度组合形式的非线性扭转弹簧来模拟铰接处的间隙和接触.通过比较锤击实验与数值计算得到的前四阶频率和振型对模型的线性部分进行验证.通过Bathe两子步隐式复合算法计算基础激励下非线性结构的动力学响应,得到的传递函数可以模拟实验中出现的频率变化特征,验证了连接处非线性建模方法的合理性.     

Coupled thermoelasticity of functionally graded cylindrical shells

The coupled thermoelastic response of a functionally graded circular cylindrical shell is studied. The coupled thermoelastic and the energy equations are simultaneously solved for a functionally graded axisymmetric cylindrical shell subjected to thermal shock load. A second-order shear deformation shell theory that accounts for the transverse shear strains and rotations is considered. Including the thermo-mechanical coupling and rotary inertia, a Galerkin finite element formulation in space domain and the Laplace transform in time domain are used to formulate the problem. The inverse Laplace transform is obtained using a numerical algorithm. The shell is graded through the thickness assuming a volume fraction of metal and ceramic, using a power law distribution. The results are validated with the known data in the literature.     

Response of flexure–torsion coupled composite thin-walled beams with closed cross-sections to random loads

A study of the flexure–torsion coupled random response of the composite beams with solid or thin-walled closed-sections subjected to various types of concentrated and distributed random excitations is dealt with in this paper. The effects of flexure–torsion coupling, shear deformation and rotary inertia are included in the present formulations. The random excitations are assumed to be stationary, ergodic and Gaussian. Analytical expressions for the displacement response of the composite beams are obtained by using normal mode superposition method combined with frequency response function method. The present method can produce the effective solutions for the composite Timoshenko beams with circumferentially antisymmetric (CAS) configuration and more general beam assemblages of connected beams. The influences of flexure–torsion coupling, shear deformation and rotary inertia on the random response of an appropriately chosen composite beam from the literature are demonstrated and discussed.     

Stochastic response of an axially loaded composite Timoshenko beam exhibiting bending–torsion coupling

A spectral finite element method is proposed to investigate the stochastic response of an axially loaded composite Timoshenko beam with solid or thin-walled closed section exhibiting bending–torsion materially coupling under the stochastic excitations with stationary and ergodic properties. The effects of axial force, shear deformation (SD) and rotary inertia (RI) as well as bending–torsion coupling are considered in the present study. First, the damped general governing differential equations of motion of an axially loaded composite Timoshenko beam are derived. Then, the spectral finite element formulation is developed in the frequency domain using the dynamic shape functions based on the exact solutions of the governing equations in undamped free vibration, which is used to compute the mean square displacement response of axially loaded composite Timoshenko beams. Finally, the proposed method is illustrated by its application to a specific example to investigate the effects of bending–torsion coupling, axial force, SD and RI on the stochastic response of the composite beam.     

Dynamics of solid propellant motor composite casing under impact pressure

A dynamic behavior of solid propellant motor composite casing under the action of an internal impact pressure is treated. This pressure describes the engine operation. The thin-walled casing consists of the cylindrical shell and two bottoms. These bottoms are truncated hemisphere. The casing is clamped along two edges of the bottoms. A shear, a rotary inertia and stress–strain relations for an orthotropic material are accounted. Semi analytical method is suggested to analyze the structure stress–strain state. The thin-walled casing dynamic is described by large dimension system of the ordinary differential equations.     

Coupled bending and torsional vibration of nonsymmetrical axially loaded thin-walled Bernoulli–Euler beams

The dynamic transfer matrix is formulated for a straight uniform and axially loaded thin-walled Bernoulli–Euler beam element whose elastic and inertia axes are not coincident by directly solving the governing differential equations of motion of the beam element. Bernoulli–Euler beam theory is used, and the cross section of the beam does not have any symmetrical axes. The bending vibrations in two perpendicular directions are coupled with torsional vibration and the effect of warping stiffness is included. The dynamic transfer matrix method is used for calculation of exact natural frequencies and mode shapes of the nonsymmetrical thin-walled beams. Numerical results are given for a specific example of thin-walled beam under a variety of end conditions, and exact numerical solutions are tabulated for natural frequencies and solutions calculated by the other method are also tabulated for comparison. The effects of axial force and warping stiffness are also discussed.     

Vibration analysis of nonhomogeneous orthotropic cylindrical shells including combined effect of shear deformation and rotary inertia

This paper is the result of an investigation on the vibration of non-homogeneous orthotropic cylindrical shells, based on the shear deformation theory. Assume that the Young’s moduli, shear moduli and density of the orthotropic material are continuous functions of the coordinate in the thickness direction. The basic equations of non-homogeneous orthotropic cylindrical shells with the shear deformation and rotary inertia are derived in the framework of Donnell-type shell theory. The ends of a non-homogeneous orthotropic cylindrical shell are considered as simply supported. The basic equations are reduced to the sixth-order algebraic equation for the frequency using the Galerkin method. Solving this algebraic equation, the lowest values of non-dimensional frequency parameters for non-homogeneous orthotropic cylindrical shells with and without shear deformation and rotary inertia are obtained. Calculations, effects of shear stresses and rotary inertia, orthotropy, non-homogeneity and shell geometry parameters on the lowest values of non-dimensional frequency parameter are described. The results are verified by comparing the obtained values with those in the existing literature.     

Natural frequencies of composite beams with a variable fiber volume fraction including rotary inertia and shear deformation

The present study is concerned with the vibration analysis of symmetric composite beams with a variable fiber volume fraction through thickness. First-order shear deformation and rotary inertia have been included in the analysis. The solution procedure is applicable to arbitrary boundary conditions. Continuous gradation of the fiber volume fraction is modeled in the form of an m-th power polynomial of the coordinate axis in the thickness direction of the beam. By varying the fiber volume fraction within the symmetric composite beam to create a functionally graded material （FGM）, certain vibration characteristics are affected. Results are presented to demonstrate the effects of shear deformation, fiber volume fraction, and boundary conditions on the natural frequencies and mode shapes of composite beams.     

一种复合材料的大挠度曲梁单元

本文研究了加劲壳的非线性有限元分析方法,提出了一种梁元素来模拟加筋。该元素具有曲轴线,任意形状的薄壁剖面和任意铺层方式,与三维退化曲壳元素完全协调,相对于壳中面可以有偏心,所分析的结构可以是层合复合材料加劲壳或各向同性材料单层加劲壳。     

Dynamic analysis of laminated cross-ply composite non-circular thick cylindrical shells using higher-order theory

Here, the dynamic analysis of laminated cross-ply composite non-circular thick cylindrical shells subjected to thermal/mechanical load is carried out based on higher-order theory. The formulation accounts for the variation of the in-plane and transverse displacements through the thickness, abrupt discontinuity in slope of the in-plane displacements at the interfaces, and includes in-plane, rotary inertia terms, and also the inertia contributions due to the coupling between the different order displacement terms. The strain–displacement relations are accurately accounted for in the formulation. The shell responses are obtained employing finite element approach in conjunction with direct time integration technique. A detailed parametric study is carried out to bring out the effects of length and thickness ratios, eccentricity parameters and number of layers on the thermal/mechanical response characteristics of non-circular shells.     

Influences of large deformation and rotary inertia on wave propagation in piezoelectric cylindrically laminated shells in thermal environment

Influences of large deformation (geometrical non-linear) and rotary inertia on wave propagation in a long, piezoelectric cylindrically laminated shell in thermal environment is presented in this paper. Nonlinear dynamic governing equations of piezoelectric cylindrically laminated shells are derived by means of Hamilton’s principle. The wave propagation modes are obtained by solving an eigenvalue problem. Numerical examples show that the characteristics of wave propagation in piezoelectric cylindrically laminated shells are relates to the large deformation, rotary inertia and thermal environment of the piezoelectric cylindrically laminated shells. The effect of large deformation, rotary inertia and thermal load on wave propagation in the piezoelectric cylindrically laminated shells is discussed by comparing with the result from the small deformation (geometrical linear shell theory). This method may be used to investigate wave propagation in various laminated material, layers numbers and thickness of piezoelectric cylindrically laminated shells under large deformation. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.