随机参数板梁组合结构的动力特性分析

以随机物理参数板梁组合结构为对象,研究了基于概率的结构动力特性分析方法。利用随机因子法,建立了考虑结构弹性模量和质量密度同时具有随机性时结构的刚度矩阵和质量矩阵;从结构振动的瑞利商表达式出发,利用代数综合法推导出结构特征值随机变量数字特征的计算表达式。通过算例,分析了结构物理参数随机性对结构动力特性的影响,并表明文中模型和方法的合理性与可行性。     

基于模糊因子法的模糊智能桁架结构动力特性分析

研究了模糊参数压电智能桁架结构的动力特性分析问题。在压电主动杆和被动杆的物理参数和几何尺寸 同时具有模糊性时,利用模糊因子法建立了结构刚度矩阵和质量矩阵;从结构振动的瑞利商表达式出发,利用区间 运算推导出结构特征值模糊变量的计算表达式。通过算例分析了模糊智能桁架结构参数的模糊性对其动力特性的 影响,并验证了本文方法的合理性与可行性。     

随机平面桁架动力特性蒙特卡罗法的节俭研究

考虑平面桁架所有结构参数的随机性，通过随机因子法和对随机参数间相关性的研究，对结构的质量矩阵和刚度矩阵的随机性提出了两种近似处理方法。第1种方法能获得结构动力特性均方根上限，第2种方法能获得结构动力特性随机性的近似解，这两种方法都能显著节俭Monte—Carlo数值模拟法求解的计算量。算例表明，该方法不但节省了数值模拟的时间，且具有较好的精度。     

基于概率的桁架结构随机振动响应分析研究

研究了具有随机物理参数和几何参数的桁架结构在随机振动激励下的动力响应问题.从结构在随机振动激励下其振动响应在频率域上的表达式出发,利用求解随机变量函数矩的方法和求解随机变量数字特征的代数综合法,导出了桁架结构的位移响应均方值和应力响应均方值的均值、方差和变异系数的计算表达式.通过算例分析了结构物理参数和几何参数的随机性对桁架结构在随机振动激励下动力响应随机性的影响,得出了若干有用的结论,为随机桁架结构的动力设计奠定了基础.     

随机智能桁架结构闭环控制平稳随机响应分析

研究平稳随机激励下随机智能桁架结构的闭环动力响应问题。同时考虑智能桁架结构的物理参数、几何尺寸和阻尼的随机性，利用矩法和代数综合法，从结构平稳随机响应在频域上的表达式出发，分别导出随机智能桁架结构在平稳随机激励下闭环位移响应均方值和应力响应均方值的均值、方差的计算表达式。通过算例考察结构物理参数、几何尺寸和阻尼的随机性对结构位移响应均方值与应力响应均方值随机变量随机性的影响，并获得若干有意义的结论。     

随机参数链式结构系统的动力特性分析

以随机参数链式结构系统为研究对象,根据链式扭振系统的传递矩阵法建立了求解系统固有频率的方程,对系统的转动惯量和扭转刚度具有随机性时的系统动力特性进行了分析,利用代数综合法推导出系统特征值随机变量数字特征的计算表达式,并提出基于概率的结构动力特性求解方法。通过算例验证了所建模型的合理性和所提方法的正确性、有效性,并考察了系统物理参数的随机性对其动力特性的影响。     

随机参数智能桁架结构在随机力下的闭环控制动力响应分析

针对随机参数压电智能桁架结构研究了基于概率的结构闭环控制系统动力响应分析模型与方法。利用振型迭加法导出了结构的物理参数、外荷载幅值以及闭环系统控制力同时具有随机性时 ,结构动力响应随机变量的数字特征计算表达式。通过算例考察了智能结构物理参数、外荷载幅值以及控制力的随机性对结构闭环控制系统动力响应的影响 ,并获得了一些有意义的结论     

随机参数刚架结构的平稳随机位移响应动力可靠性分析

研究物理参数具有随机性的刚架结构的平稳随机位移响应动力可靠性的计算方法。考虑结构的物理参数具有随机性，从结构随机响应的频域表达式出发，利用求解随机变量数字特征的代数综合法和矩法，导出随机参数刚架结构在平稳随机激励下的位移及速度响应均方值的数字特征，再由动力可靠性的Poisson公式导出结构动力可靠度的计算公式。通过算例就各参数的随机性对结构动力可靠度的影响进行分析，验证本文方法的可行性。     

随机参数弹性连杆在平稳随机激励下的动力可靠性分析

研究随机参数弹性连杆机构在平稳随机激励下的动力响应分析。利用拓广的随机因子法,从求解系统固有频率的瑞利商公式出发,得出物理参数和几何参数均为随机变量的弹性连杆时变固有频率的均值和方差。从动力平稳随机响应在频域上的表达式出发,利用求解随机变量函数的矩法和数字特征的代数综合法,计算出随机参数弹性连杆机构在平稳随机激励下弹性位移和速度的均方值的均值、方差表达式,由动力可靠度的公式导出其动力可靠度的均值和方差的计算公式。通过算例,分析机构物理参数和几何尺寸的随机性对机构动力可靠度随机性的影响。     

随机参数非线性鞭天线结构的随机风振响应分析

在考虑结构物理参数和几何参数随机性的情况下,在时域上对几何非线性鞭天线结构的随机风振响应进行了分析。应用Monte Carlo数字模拟与结构动力有限元相结合的方法进行结构响应计算,其中利用了分段精细时程积分算法。获得了结构位移响应的均值和均方值随时间的变化历程,考察了结构中各随机参数对响应的影响,并对其中的影响参数进行了敏感性分析。     

碰摩转子系统的随机响应分析

针对仅考虑质量偏心的 Jeffcott转子碰摩的动力学方程 ,进行了转子碰摩系统的随机响应分析 ,研究了把转轴刚度和阻尼、偏心距和定子的刚度作为随机参数的随机系统的响应 ,并给出了数值分析解 ;讨论了参数的随机变化对转子碰摩系统的影响。     

Diffusion as a model of formation and development of surface topography

Changes of surface topography in tribological systems are due to inelastic processes as plastic deformation, detaching of wear particles and their reintegration into the surfaces. Due to these processes, the material particles are transported either along a surface or from one tribological partner to the other. Both processes are due to random interactions between surface asperities and are stochastic processes. The stochastic mass transfer between the surfaces is interpreted and described in the paper as a random deposition, the transport along a surface as a `diffusion' processes with some effective diffusion coefficient. We consider the development of the surface topography due to the described two kinds of random processes. There exist some stationary (in statistical sense) random surface topography with a power spectrum (spectral density) typical for many real frictional surfaces. The parameters of the model can either be obtained from comparison with measured topography or extracted from simulations at a lower space scale. The proposed mass transport model further allows to determine the wear rate in the system.     

Roles of domain decomposition method in plate vibrations: Treatment of mixed discontinuous periphery boundaries

The detailed development of a domain decomposition method (DDM) for the vibrational modelling of rectangular plates with mixed-edge boundary conditions is presented. In the DDM, the complex plate domain is decomposed into small simple subdomains and the appropriate shape function of each subdomain is represented by sets of admissible orthogonal polynomials generated using the Gram-Schmidt recurrence process. The continuity matrices that couple the eigenvectors of adjacent subdomains are derived based on the satisfaction of continuity conditions along the interconnecting boundaries. The stiffness and mass matrices of each subdomain after pre- and post-multiplication by the respective continuity matrices are assembled to form the global stiffness and mass matrices. To demonstrate the effectiveness and accuracy of the DDM, a vibration study of several partially mixed edge plates has been carried out. Convergence tests for example problems are presented in which the accuracy of the results is established. The frequency parameters and mode shapes obtained, where possible, are verified by comparison with data published in the open literature.     

Generalized buckling analysis of laminated plates with random material properties using stochastic finite elements

A generalized layer-wise stochastic finite element formulation is developed for the buckling analysis of both homogeneous and laminated plates with random material properties. The pre-buckled stresses are considered in the derivation of geometric stiffness matrix and the effect of variation in these stresses on the mean and coefficient of variation of buckling strength is studied. The mean buckling strength of plates under uniform stress assumption exactly matches with those reported in the literature. However, it is shown that the actual mean buckling strength of plates can be significantly different based on the pre-buckled stress analysis which depends on boundary constraints, principal material directions, aspect and thickness ratios of plates. The statistics of buckling strength is determined using a Taylor series expansion based mean centered first order perturbation technique. The stochastic finite element solutions obtained using layer-wise plate theory is also validated with analytical solutions presented in this paper. Parametric studies are conducted for different aspect ratios, ply orientations and boundary conditions.     

板的弹塑性断裂随机有限元分析

在幂律非线性随机有限元基础上,借助小扰动随机性概念,系统地提出解决板的弹塑性断裂随机有限元分析方法,并给出以单边裂纹板为例进行弹塑性断裂参数及其对基本随机变量变化率数值计算的算例和方法的应用说明.     

基于链间耦合的并联悬架的刚度优化

针对越野车辆座椅刚度提升问题,提出了利用并联机构作为座椅悬架主体结构的方案。为保证悬架装置具有高精度位姿和高刚度结构,对链间耦合与固有频率进行研究。首先,通过能量法、虚功原理和扰动理论,可以获得机构的广义质量和广义刚度矩阵;其次,弹性耦合和惯性耦合是基于以上两个广义矩阵而定义的两个指标来测量并联机构的耦合程度,通过Cholesky分解法获得机构的固有频率;然后,为了获得较小的弹性耦合、惯性耦合和较大的固有频率,以固有频率作为目标函数来优化悬架装置的结构参数;最终,对优化结果综合分析,获得最优结构参数用于改进装置结构。     

Direct identification of non-proportional modal damping matrix for lumped mass system using modal parameters

Several damping materials have been employed to reduce the vibration of marine structures. In this paper, a new method of identifying system matrices for non-proportional damping structures using modal parameters is proposed. This method has two advantages. First, the mass and stiffness matrices do not need to be calculated using the FEM, so errors due to the inaccuracy of these matrices can be reduced. Second, various indirect methods can be used to identify modal parameters such as natural frequencies, modal damping ratios and mode shapes. Three case studies of lumped mass systems with non-proportional damping are carried out to verify the performance of the proposed method in this study.     

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.     

基于遗传算法的降阶模型修正方法研究

以实验模态数据修正降阶模型为研究对象，由于所测量的特征对阶数通常小于模型阶数，造成了特征方程为超越方程。为了求解超越方程以确定质量与刚度修正矩阵，提出随机给定超越方程中的多余变量值，采用遗传算法来寻优。为了使修正矩阵的范数较小，对多余变量值进行了约束处理。为了达到修正目的，通过不断改变多余变量值，并采用基于实代码遗传算法来确定优化结果，最后给出了一个计算实例。该算法的优点是可以得到多组最优阶，精度较高；缺点是计算量较大，不适合于动态模型修正。