Optimization of Internal Line Support Positions for Plates Against Vibration∗

ABSTRACT

This paper presents a simple numerical method for determining optimal positions of internal line supports for an arbitrarily shaped plate, so as to maximize the fundamental frequency of its transverse vibration. The vibration analysis is performed using the pb-2 Rayleigh-Ritz method. Because this method does not require discretization, since it treats the entire plate with its boundary conditions as a kind of superelement, the optimization problem becomes relatively easy to solve. To illustrate the method, trapezoidal, elliptical, and semi-circular plates with at most two internal line supports are considered. The optimization exercise, for optimal locations of internal line supports, demonstrates significant improvement in the value of fundamental frequency when compared to that of plates with specified positions of internal supports.     

Optimal driver seat suspension for a hybrid model of sitting human body

In the paper a general procedure is presented for the analytical synthesis of an optimal vibration isolation system of a human body including its sensitivity to vibration. The optimal active suspension of a seat has been obtained analytically for a human body represented alternatively by apparent mass weighted by standard frequency domain curves W(s) depicting discomfort levels. The analytical functions describing the optimal vibration isolation systems (OVISs) have been obtained in the general form for random stationary acceleration excitations, general forms of apparent mass M(s) of the sitting human body and a selected criterion of isolation. Analytical forms of complex functions depicting OVIS are presented for two cases of acceleration excitation: white noise (WN) and narrow band noise (NBN). The influence of particular forms of excitation and weighting function W(s) on the resultant vibration isolation is discussed. The analytical results, illustrated by a numerical example presented in the graphical form have been included.     

An Optimal Control Approach to Minimum-Weight Vibrating Beam Design

ABSTRACT

A gradient projection algorithm is applied to a class of vibrating cantilever beam optimization problems which are formulated as optimal control problems. The cross-section area is distributed along the beam for minimum total weight subject to fixed natural frequency constraints and a minimum allowed area limit. Three topics receive major emphasis: the effects of shear deformation and rotary inertia, higher-mode frequency constraints, and multiple frequency constraints. Computational results are presented for the cases of fixed fundamental frequency, fixed second-mode frequency, and fixed fundamental and second-mode frequencies under a variety of conditions.     

改进PSO算法在结构作动器位置优化中的应用

针对空间结构振动主动控制中的作动器位置优化问题, 提出了一种改进的粒子群(PSO) 优化方法, 以系统总能量为性能指标进行优化; 应用改进PSO方法对算例结构进行了计算, 并与其他算法的优化结果进行了对比; 结果表明: 几种优化方法计算结果相符; 且 PSO优化算法能更有效快速地解决复杂优化问题, 从而有效地进行结构的振动控制.     

An Optimal control least-squares method for the solution of advection dispersion problems

This paper discusses the numerical solution of advection dispersion equations using an Optimal control,H ¹, least-squares formulation, associated with a quasi-Newton conjugate gradient algorithm. The suggested algorithm represents an extension of the method proposed by Bristeauxet al., for the solution of nonlinear fluid flow problems.At each time step, the discretized differential equation is transformed into an optimal control problem. This problem is then stated as an equivalent minimization one, whose objective function allows the capture of the advective behavior of the equation for high values of the P_e number.A general presentation is made of the optimization algorithm. Validation runs, for a one-dimensional example, show fairly accurate results for a wide range of Péclet and Courant numbers. Comparisons with several numerical schemes are also presented.     

Optimal Shape Design of Multicomposite Structures

Abstract

The problem of the optimal shape design of an elastic composite structure with unspecified interfaces is discussed for the case of mean compliance constraint. The optimality conditions are derived, and the optimization of a circular plate with segmentwise constant thickness is considered in order to illustrate these conditions. The case of optimal plastic design is obtained as a limiting case of mean compliance design.     

区间参数振动系统的动力优化

对具有区间参数的多自由度振动系统的不确定性优化问题，提出一种新的区间优化方法．利用泰勒展开和函数的区间扩张，将区间优化问题转化为近似的确定性优化问题．该方法应用于多自由度线性扭振系统，并把区间设计变量的中值和不确定性半径取作优化参数．算例表明该方法是有效的．     

时滞耦合质量摆动力吸振器减振系统的等峰优化理论与实验

摆式调谐质量阻尼器因其便于安装、维修、更换,且经济实用,广泛应用于结构减振.它通过将摆的自振频率调谐到接近主系统的控制频率,使摆产生与主系统相反的振动,从而抑制或消除主系统的振动.本文通过对主系统无阻尼的被动减振系统和主系统有阻尼的时滞反馈主动减振系统进行多目标优化设计,实现了对主系统幅频响应曲线的等峰控制和共振峰与反共振峰差值的有效控制.首先,建立了时滞耦合质量摆动力吸振器减振系统的力学模型和振动微分方程,通过对主系统无阻尼的被动减振系统进行等峰优化,获得了减振系统的最优频率比和质量摆的最优阻尼比.对于主系统存在阻尼的被动减振系统,在该优化参数下主系统的幅频响应曲线等峰优化失效.其次,对于主系统存在阻尼的时滞反馈优化控制系统,采用CTCR方法得到了反馈增益系数和时滞的稳定区域.在保证系统稳定的前提下,通过调节反馈增益系数和时滞量两个控制参数能够实现对主系统幅频响应曲线的等峰控制.再次,对共振点处主系统振幅放大因子时滞敏感度和反馈增益系数敏感度进行分析,表明共振点幅值对反馈增益系数比对时滞更为敏感.最后,通过实验分别在频域和时域内对理论结果进行了验证.研究表明,通过采用时滞反馈对摆式调...     

拱形薄壳结构的减振降噪优化设计

基于拱形薄壳结构的动力仿真, 提出结构振动噪音最小、满足重量约束的约束阻尼厚度优化
设计模型. 利用K-S函数得到结构的振动加速度级, 将其作为结构减振降噪效果的评定参数,
采用响应面方法拟合目标函数, 并对其进行误差检验, 适当缩小设计变量范围调整
误差后, 响应面曲线的拟合程度较好. 最后采用二次规划方法求解模型, 经过优化设计, 结构第一阶固
有频率增加22.97%, 振动加速度级值减小12.96%, 结构的性能得到了很大提高.     

Shape Design Sensitivity Analysis for Optimization Problems with Local and Global Functionals

ABSTRACT

In this paper, problems of sensitivity analysis and shape design for elastic solids are investigated. Optimization criteria are provided by integral and local functionals defined on the internal region and the boundary of the body. New sensitivity analysis relations are derived and implemented in successive optimization algorithms. Important aspects of effective shape optimization algorithms are discussed.     

Analysis of Machining Stability for a Parallel Machine Tool

Abstract

Machine tool chatter is a self-excited vibration generated by chip thickness variation. It severely degrades the quality of the machined surface. The incidence of chatter is greatly affected by the dynamic characteristics of machine tool structure. This article extends chatter stability analysis to a machine tool equipped with a parallel mechanism. The vibration model of a parallel machine tool is derived, in which the legs of the parallel mechanism are considered as spring-damper systems. Then, the regenerative cutting dynamics is combined with the vibration model and stability analysis is performed. The chatter stability charts for various machining parameters are examined, with the example of the cubic parallel mechanism that is specially designed for machine tool use.     

Optimum design of dynamic vibration absorbers for a beam, based on H ∞ and H 2 Optimization

The solutions to H _∞ and H ₂ optimization problems of a variant dynamic vibration absorber (DVA) applied to suppress vibration in beam structures are derived analytically. The H _∞ optimum parameters such as tuning frequency and damping ratios are expressed based on fixed-point theory to minimize the resonant vibration amplitude, as well as, the H ₂ optimum parameters to minimize the total vibration energy or the mean square motion of a beam under random force excitation as analytical formulas. The reduction in maximum amplitude responses and mean square motion of a beam using the traditional vibration absorber is compared with the proposed dynamic absorber. Numerical results show the non-traditional DVA under optimum conditions has better vibration suppression performance on beam structures than the traditional design of DVA. Furthermore, comparing H _∞ and H ₂ optimization procedures shows that for a beam under random force excitation, use of H₂ optimum parameters resulting in smaller mean square motion than the other optimization.     

局部约束阻尼开口柱壳的减振分析及优化

为了缩减开口柱壳结构的振动,本文基于Lagrange方程以及Sanders薄壳理论建立了局部约束阻尼开口柱壳的动力学模型,分析了粘弹性单元分段数和厚度、阻尼单元占空比以及约束层敷设角和厚度对结构前三阶模态损耗因子和固有频率的影响,得到了各参数对结构振动特性的影响规律.并以前三阶损耗因子为目标,应用NSGA-Ⅱ遗传算法对...     

Free vibration of composite laminated plate with complicated cutout

Abstract

This paper presents the free vibration analysis of a composite laminated square plate with complicated cutout. The problem formulation is based on the higher order shear deformation plate theory HDST C⁰ coupled with a curved quadrilateral p-element. The elements of the stiffness and mass matrices are calculated analytically. The curved edges are accurately represented using the blending function method. A calculation program is developed to determine the fundamental frequencies for different physical and mechanical parameters such as the cutout shape, plate thickness, fiber orientation angle, and boundary conditions. The results obtained show a good agreement with the available solutions in the literature. New results for the fundamentals frequencies of a composite laminated plate with complicated cutout are presented.     

Some problems of optimizing shell shape and thickness distribution on the basis of a genetic algorithm

We consider problems related to designing axisymmetric shells of minimal weight (mass) and the development of efficient nonlocal optimization methods. The optimization problems under study consist in simultaneous search for the optimal geometry and the shell thickness optimal distribution from the minimal weight condition under strength constraints and additional geometric constraints imposed on the thickness function, the transverse cross-section radii distribution, and the volume enclosed by the shell. Using the method of penalty functions, we reduce the above optimal design problem to a nonconvex minimization problem for the extended Lagrange functional. To find the global optimum, we apply an efficient genetic algorithm. We present the results of numerical solution of the optimal design problem for dome-like shells of revolution under the action of gravity forces. We present some data characterizing the convergence of the method developed here.     

Mode Finding in Nonlinear Structural Eigenvalue Calculations

Abstract

The eigenvalue problems resulting from stiffness matrix formulations of structural vibration and buckling problems are nonlinear if substructures are analyzed exactly, or if classical frequency (vibration problems) or load factor (buckling problems) dependent member equations are used. This makes rapid calculation of accurate free vibration or buckling modes difficult. This paper presents several techniques which might overcome this difficulty, examines them theoretically and experimentally, and gives some of the ways in which the more successful techniques can be incorporated in mode finding methods. Coincident eigenvalues (i.e., natural frequencies or critical load factors) are included.     

Some Optimization Problems for Vibroprotective Systems

Some analytically solvable problems of optimal protection against vibration and shocks are considered in linear and nonlinear formulations. In the linear formulation, they can be solved by using up-to-date methods of systems theory (optimization in Hardy H ₂ H spaces, solution of the algebraic Riccati equation, synthesis of optimal systems under uncertainty, etc.). An expression is presented for the optimal nonlinear characteristic (tangensoid) of a damper with a limited free running under broadband stochastic vibrations. Relations linking the free running of the damper, the vibroload of the damped device, and the vibration intensity are derived for the optimal nonlinear system     

Unexpected Results in Structural Optimization*

ABSTRACT

Examples are presented to show that optimal designs may have unexpected properties that require particularly careful formulation of problems of structural optimization.     

Matlab编程实现求解基于振型叠加法的多自由度动力学系统的时域和频域响应

给出了求解多自由度动力学系统响应的M atlab程序,这些程序基于振型叠加法可用于求解由质量矩阵M和刚度矩阵K以及常见阻尼矩阵描述的线性离散系统的时域和频域解.对于无阻尼系统,用户可以选择数值解或符号解析解(以时间或频率表示),并利用复模态叠加法计算了阻尼系统的数值解.总结了模态叠加方法下动力学响应的求解,并在简短的M atlab程序中实现.以三自由度系统和悬臂梁模型为例说明了程序的应用.这些程序也可用于工程应用中,通过对商用有限元软件包产生的质量和刚度进行后处理,产生感兴趣的时域和频域响应.