薄板结构动力学特性建模解析

运用边界元法研究薄板结构的动力学特性。从薄板自由振动的微分方程式出发,由相应的静态基本解建立薄板自由振动的边界控制方程,并依据边界上的约束条件,推导出薄板结构在边界和域内的动力学方程。为了避免求域内项的积分,将上述两个方程进行联立求解,快速、准确地得到薄板结构的频率方程表达式。数值计算和实验结果表明,该文方法具有良好的解析计算精度和较高的计算效率。     

筋板结构动力学特性边界元法解析研究

研究加筋薄板结构动力学特性多域合成的边界元建模解析方法。将矩形板沿梁划分为若干个区域,同时把梁的约束等效为作用在薄板区域上的反力,基于板、梁元件的动态基本解,由边界元法推导出带约束反力的梁和薄板的兰量控制方程,并依据耦合边界上的连续条件,运用多域合成的解析方法快速地建立筋板结构的动力学方程。数值算例表明,文中方法不但节省了计算量,而且具有良好的计算精度。     

整机结构混合建模方法研究

提出基于动力边界元的混合建模方法研究整机结构的动态特性.通过对整机结构混合建模过程分析和结合条件的处理,采用动静态基本解,将结合部特性通过域内项合理地引入整机结构中,直接推导出整机结构边界动力学方程,高效地建立起相应的动力学模型.通过给出的算例和相应的动力学实验,结果表明文中的建模解析方法具有较好的精度和效率,在满足一定精度的要求下可以实现高效的计算.     

整机结构动力学特性边界元法解析

研究了考虑结合部特性的机床结构动力学特性的系统建模解析方法。将整机结构用梁元件、弹簧元件和集中质量元件来等效,并将结合部特性引入到整机模型中,基于边界元法建立了整机结构的动力学方程,快速地求得了整机结构相应的动力学特性。数值算例与实验结果表明,上述方法不但节约了计算量,而且具有很高的精度,可有效地解决各种复杂系统结构的动力学建模解析问题。上述方法对于提高机床结构的理论计算和设计水平具有十分重要的意义。     

加筋薄板的自由振动分析

加筋薄板是航空领域最常见的结构之一,加强筋对薄板振动模态有显著影响。为改善蒙皮加筋薄板的动力学特性,旨在研究板筋连接单元的动力学建模方法以及加强筋对蒙皮薄板振动的影响机制。首先研究加筋薄板铆接、点焊和滚焊连接形式的有限元建模方法,建立铆接、点焊和滚焊薄板构件的有限元动力学模型;然后探讨单向与双向加筋薄板构件的自由振动模态;最后,分析板筋连接形式和加筋安装方向对薄板振动模态的影响机制。结果表明,加强筋的设计对薄板模态影响明显,滚焊加强筋对薄板构件的模态频率影响相对最大。     

基于双参数模型的弹性地基薄板自由振动边界元解析

从双参数弹性地基薄板自由振动的微分方程式出发,通过建立双参数弹性地基薄板的动态基本解,运用边界元法(boundary element method,BEM)对双参数弹性地基板弯曲自由振动的动态特性进行解析研究,建立相应的边界积分方程式及动柔度方程式,采用频率扫描法求解其固有频率。算例研究表明,文中的方法计算简便、可行,具有良好的计算精度,同时该方法也适用于文克尔地基板动态特性解析。     

基于边界元法的混联数控机床整机结构动态特性解析

基于边界元法研究混联数控机床整机结构动态特性的解析和建模方法。首先采用粱单元、集中质量单元、弹簧单元及结合部单元建立混联机床整机结构动力学模型，基于边界元方法建立各单元的动力学方程式，通过单元合成方法推导出混联数控机床整机结构动力学方程，用频率扫描法得到整机结构的固有频率。基于所建立混联机床结构动态特性解析方法，开发相应的整机动态特性解析软件，实验证明，所建立混联机床整机动态特性解析方法及开发的软件是可靠的，不仅可以为混联数控机床加工过程中回避薄弱位姿状态提供依据，而且可以为混联数控机床的结构设计提供理论依据，对提高混联数控机床的设计水平具有重要意义。     

一个计算弹性矩形等厚板固有频率的近似公式

本文利用瑞利法得到了弹性矩形薄板频率估计的Ｗａｒｂｕｒｅｏｎ公式，并利用最优化方法对Ｗａｒｂｕｒｔｏｎ公式进行参数修正，修正后的经验公式改善了含自由边界矩形板的频率估计精度。     

槽道板结构的应力分析方法

分析板翅式换热器和微换热器的基本结构,通过引入小挠度薄板理论和弹性支承结构模型,解析计算槽道板结构的弯曲变形和弯曲应力,然后将这种分析法拓展到多层槽道板结构,进而利用有限元方法对其进行对比验证分析.结果表明,应用小挠度薄板理论和弹性支承结构模型分析槽道板结构的变形和应力具有较好的精度,为微小型装置或具有槽道结构设备的应力分析提供一种有效的方法和依据.     

冷轧板带出口板凸度的显式动力学有限元模拟

板凸度是板形的主要精度指标,传统计算板凸度的方法主要包括解析法和影响函数法。影响函数法较解析法计算精度高,但计算程序复杂,需要大量迭代计算。采用显式动力学方法对薄板的冷轧过程进行了弹塑性有限元模拟,并在后处理中提取了厚度位移数据,计算了不同宽度薄板的出口板凸度。其次,用新日铁板凸度预测模型计算了相同规格板带的出口凸度,并对相同规格的板带做了轧制实验。最后,比较了模拟、理论、实验三种方法得出的凸度值,验证了模拟结果的准确性。     

On the nonlinear vibration of heated corrugated circular plates with shallow sinusoidal corrugations

The large amplitude free vibration of corrugated circular plates with shallow sinusoidal corrugations under uniformly static temperature changes is investigated. Based on the nonlinear bending theory of thin shallow shells, the governing equations for corrugated plates are established from Hamilton's principle. These partial differential equations are reduced to corresponding ordinary ones by elimination of the time variable with Kantorovich averaging method following an assumed harmonic time mode. Then by introducing the Green's function, the resulting dynamic compatible equation and corresponding boundary conditions are converted into equivalent integral equations. Taking the central maximum amplitude of the plate as the perturbation parameter, the perturbation-variation method is used to dynamic equilibrium equation with the aid of Computer Algebra Systems, Maple, from which, the third-order approximate characteristic relation of frequency vs. amplitude for nonlinear vibration of heated corrugated plates is obtained, and the frequency–amplitude characteristic curve is plotted for some specific values of temperature and geometrical parameters. It is found that the rise in temperature will decrease the frequency and vice versa. The nonlinear effect weakens when corrugations become deeper and dense. The present method can easily be expanded for the analysis of nonlinear vibration problem for other heated thin plates and shells.     

轴向运动矩形板的谐波共振与稳定性分析

针对轴向运动矩形薄板的非线性振动问题,在给出薄板运动的动能和应变能的基础上,应用哈密顿变分原理,推得几何非线性下轴向运动薄板的非线性振动方程。通过位移函数和应力函数的设定,并应用伽辽金积分法,得到四边简支边界约束条件下受横向激励载荷作用轴向运动薄板的达芬型振动方程。利用多尺度法对系统的非线性谐波共振问题进行求解,得到稳态运动下关于共振幅值的幅频响应方程。依据李雅普诺夫运动稳定性理论对定常解的稳定性进行分析,得到解的稳定性判别式。通过数值算例,得到不同横向载荷和轴向速度下共振幅值的变化规律曲线图以及对应的相图,讨论分岔点变化以及倍周期运动规律,分析横向激励载荷和轴向运动速度对系统非线性动力学行为的影响。     

Analytical investigation on axisymmetric free vibrations of moderately thick circular functionally graded plate integrated with piezoelectric layers

In this paper, a free vibration analysis of moderately thick circular functionally graded (FG) plate integrated with two thin piezoelectric (PZT4) layers is presented based on Mindlin plate theory. The material properties of the FG core plate are assumed to be graded in the thickness direction, while the distribution of electric potential field along the thickness of piezoelectric layers is simulated by sinusoidal function. The differential equations of motion are solved analytically for two boundary conditions of the plate: clamped edge and simply supported edge. The analytical solution is validated by comparing the obtained resonant frequencies with those of an isotropic host plate. The emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. Good agreement between the results of this paper and those of the finite element analyses validated the presented approach.     

转子-轴承系统局部边界参数识别方法

为了提高实际工程中转子系统某一局部结构的动力特性和计算效率,便于局部振动分析并简化系统建模,提出了一种局部约束参数识别方法。考虑系统各部件间的耦合效应,对转子系统的轴和盘片结构进行分解,建立子系统与主系统。通过动力学方程推导,获得局部求解,识别子系统与主系统的边界单元约束刚度与阻尼。通过识别的约束刚度阻尼建立子系统,计算其各个节点的响应,并将其与整体模型的对应节点响应结果进行对比验证,证明了该方法的可行性。该方法为旋转构件局部结构的建模与振动分析提供了便利。     

TRANSVERSE VIBRATION CHARACTERISTICS OF VISCOELASTIC RECTANGULAR PLATE WITH CRACK

Based on the two-dimensional viscoelastic differential constitutive relation and the thin plate theory, the differential equations of motion of the viscoelastic plate with an all-over part-through crack are established and the expression of additional rotation induced by the crack is derived. The complex eigenvalue equations of the viscoelastic plate with crack are derived by the differential quadrature method, and the 8method is used at the crack continuity conditions. Dimensionless complex frequencies of a crack viscoelastic plate with four edges simply supported, two opposite edges simply supported and other two edges clamped are calculated. The effects of the crack parameter, the aspect ratio and dimensionless delay time of the material on the transverse vibration of the viscoelastic plate are analyzed.     

Free vibration analysis of sandwich beam carrying sprung masses

In this paper, free vibration of three-layered symmetric sandwich beam carrying sprung masses is investigated using the dynamic stiffness method and the finite element formulation. First the governing partial differential equations of motion for one element are derived using Hamilton’s principle. Closed form analytical solution of these equations is determined. Applying the effect of sprung masses by replacing each sprung mass with an effective spring on the boundary condition of the element, the element dynamic stiffness matrix is developed. These matrices are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by the use of numerical techniques and the well known Wittrick–Williams algorithm. Free vibration analysis using the finite element method is carried out by increasing one degree of freedom for each sprung mass. Finally, some numerical examples are discussed using the dynamic stiffness method and the finite element formulation. After verification of the present model, the effect of various parameters such as mass and stiffness of the sprung mass is studied on the natural frequencies.     

Winkler地基上材料非线性矩形薄板1/3次亚谐共振

为研究Winkler地基上材料非线性矩形薄板受简谐激励的非线性振动,应用弹性力学理论建立其动力学方程,并由Galerkin方法将其转化为非线性振动方程。应用非线性振动的多尺度法求得系统1/3次亚谐共振的近似解,并进行数值计算。分析激励、几何参数、阻尼系数、非线性参数对共振响应曲线的影响。     

Vibration amplitude and thermal effects on the nonlinear behavior of thin circular functionally graded plates

In this paper, the nonlinear free axisymmetric vibration of a thin circular functionally graded plate in thermal environment is formulated in terms of von-Karman's dynamic equations, and a semi-analytical approach is developed. The plate thickness is constant and the material properties of the functionally graded plate are assumed to vary continuously through the thickness, according to a power-law distribution of the volume fraction of the constituents. For harmonic vibrations, by using assumed-time-mode method and Kantorovich time averaging technique, governing equations are solved. The nonlinear frequencies and associated stresses are determined at large amplitudes of vibration. Effects of material compositions and thermal loads on the vibration characteristics and stresses are examined. The numerical results obtained here are compared with available published results, based on various approaches.