大型挤压油膜阻尼器非线性动力学分析与优化研究进展

挤压油膜阻尼器（Squeeze Film Dampers,SFDs）是旋转机械中常用的一类支承阻尼结构装置,能够改善转子系统的动力特性.当前工程实际中已经大量使用的两类不同结构形式的挤压油膜阻尼器,仍然存在着减振效果不稳定甚至会导致转子失稳,以及阻尼器动力学机制不清楚、建模和分析精度差、设计方法欠缺等理论技术难题.本文首先介绍两类典型SFD的结构形式和主要失效模式,然后详细叙述SFD动力学分析与优化设计方法在发展过程中的代表性研究成果,涉及SFD动力学特性、转子 SFD系统动力学特性研究、SFD动力学设计与优化等几个方面的研究,并对SFD的试验测试技术方面的成果进行评述.在此基础上,探讨目前先进航空发动机用大型挤压油膜阻尼器亟须开展的基础研究任务,特别强调了数据驱动与动力学解析模型融合的SFD动力学建模、分析与设计优化的发展方向.     

Response of geometrically nonlinear elastic structures to acoustic excitation—an engineering oriented computational procedure

In order to calculate the response of a structure to acoustic, random excitation, a design-oriented computational procedure is presented. The procedure is based on the normal-modes solution approach, and introduces the concept of stress modes. This concept permits the use of static loadings to solve the linear dynamic problem, thus the user can use his engineering judgment to predict the points at which maximum stresses and strains will be encountered during the dynamic loading. A static loading approach is also used to include geometrically nonlinear effects in the analysis.A practical application of the procedure, which has been developed in Lockheed-Georgia Company, is described. This procedure is used now to analyze the response of isotropic and composite skin structures to acoustic noise fields.     

Fuzzy adaptive backstepping robust control for SISO nonlinear system with dynamic uncertainties

In this paper, a fuzzy adaptive backstepping design procedure is proposed for a class of nonlinear systems with three types of uncertainties: (i) nonlinear uncertainties; (ii) unmodeled dynamics and (iii) dynamic disturbances. The fuzzy logic systems are used to approximate the nonlinear uncertainties, nonlinear damping terms are used to counteract the dynamic disturbances and fuzzy approximation errors, and a dynamic signal is introduced to dominate the unmodeled dynamics. The derived fuzzy adaptive control approach guarantees the global boundedness property for all the signals and states, and at the same time, steers the output to a small neighborhood of the origin. Simulation studies are included to illustrate the effectiveness of the proposed approach.     

Load dependent subspace reduction methods for structural dynamic computations

The evaluation of the dynamic response analysis of large structures by vector superposition requires in its traditional formulation the solution of a large and expensive eigenvalue problem. A new method of dynamic analysis using load dependent transformation vectors for systems subjected to fixed spatial distribution of dynamic loads was recently introduced by Wilson et al. as an economic alternative to the usual mode superposition method. New computational variants to generate a load dependent transformation basis for arbitrary transient loadings which are a function of space and time are presented. Numerical applications on a simple structural system are used to show the relative efficiency of the proposed solution procedure over classical solution methods using mode-displacement, mode-acceleration or the original (fixed) load dependent reduction method.     

一类具有未建模动态的非线性系统模糊自适应鲁棒控制

针对一类单输入单输出未建模动态不确定非线性系统,提出一种模糊自适应backstepping控制方法.设计中利用模糊逻辑系统逼近系统的未知函数,应用非线性阻尼项抵消系统的非线性不确定项,通过引入一个动态信号克服未建模动态.该模糊自适应控制方法保证了整个闭环系统的有界性,输出信号可调节到零的小邻域内.仿真结果进一步验证了该方法的有效性.     

A method for topology optimization of structures under harmonic excitations

This paper deals with topology optimization of large-scale structures with proportional damping subjected to harmonic excitations. A combined method (CM) of modal superposition with model order reduction (MOR) for harmonic response analysis is introduced. In the method, only the modes corresponding to a frequency range which is a little bigger than that of interest are used for modal superposition, the contribution of unknown higher modes is complemented by a MOR technique. Objective functions are the integral of dynamic compliance of a structure, and that of displacement amplitude of a certain user-defined degree of freedom in the structure, over a range of interested frequencies. The adjoint variable method is applied to analyze sensitivities of objective functions and the accuracy of the sensitivity analyses can also be ensured by CM. Topology optimization procedure is illustrated by three examples. It is shown that the topology optimization based on CM not only remarkably reduce CPU time, but also ensure accuracy of results.     

Simultaneous analysis and design optimization of nonlinear response

The optimal structural design requiring nonlinear analysis and design sensitivity analysis can be an enormous computational task. It is extremely important to explore ways to reduce the computational effort so that more realistic and larger-scale structures can be optimized. The optimal design process is iterative requiring response analysis of the structure for each design improvement. A recent study has shown that up to 90 percent of the total computational effort is spent in computing the nonlinear response of the structure during the optimal design process. Thus, efficiency of the optimization process for nonlinear structures can be substantially improved if numerical effort for analyzing the structure can be reduced. This paper explores the idea of using design sensitivity coefficients (computed at each iteration to improve design) to predict displacement response of the structure at a changed design. The iterative procedure for nonlinear analysis of the structure is then started from the predicted response. This optimization procedure is called mixed and the original procedure where sensitivity information is not used is called the conventional approach. The numerical procedures for the two approaches are developed and implemented. They are compared on some truss type structures by including both geometric and material nonlinearities. Stress, strain, displacement, and buckling load constraints are imposed. The study shows the mixed method to be numerically stable and efficient.     

Dynamic surface control approach to adaptive robust control of nonlinear systems in semi-strict feedback form

This article considers the adaptive robust control of a class of single-input-single-output nonlinear systems in semi-strict feedback form using radial basis function (RBF) networks. It is well known that the standard backstepping design may suffer from “explosion of terms”. To overcome this problem, the recently developed dynamic surface control technique which employs a first-order low-pass filter at each step of the backstepping design procedure is generalized to the nonlinear system under study. Our attention is paid to achieve guaranteed transient performance of the adaptive controller. At each step of design, a feedback controller strengthened by nonlinear damping terms to counteract nonlinear uncertainties is designed to guarantee input-to-state practical stability of the corresponding subsystem, and then parameter adaptations are introduced to reduce the ultimate error bound. Furthermore, for the output trajectory tracking problem, it is recommended to adopt the partial adaptation policy to reduce the computational burden due to “curse of dimension” of the RBF networks. Finally, numerical examples are included to verify the results of theoretical analysis.     

计入空气阻尼的MEMS微谐振器非线性动力学研究

针对横向振动MEMS微谐振器,计入非线性空气阻尼力,对微谐振器非线性动力学特性进行研究.建立微谐振器非线性动力学模型,计入滑移边界条件和稀薄气体效应,利用FLUENT和MATLAB对Navier-Stokes方程和动力学方程进行求解.经过与国外实验对比,可得出考虑非线性阻尼力的平板振幅值非常接近实验值,振幅峰-峰值误差仅为6%,且优于线性动力学的分析结果.为MEMS器件非线性动力学特性分析提供理论依据.     

Multi-extremum-modified response basis model for nonlinear response prediction of dynamic turbine blisk

For the nonlinear dynamic analyses of complex mechanical components, it is necessary to apply efficient modeling framework to reduce computational burden. The accurate surrogate model for approximating the nonlinear responses of several failures is a vital issue to provide robust and safe design conditions in complex engineering applications. In this paper, two different Modified multi-extremum Response Surface basis Models (MRSM) are proposed for dynamic nonlinear responses of failure capacities for turbine blisk responses. The proposed MRSM is established using two regression processes including regressed the input variables by linear or exponential basis functions in first calibrating phase and regressed the second-order polynomial basis function using inputs data provided by first stage in second calibrating procedure. A sensitivity analysis using MRSM is proposed to consider the variation of input variables on the nonlinear responses. In the sensitivity analysis procedure, the effects of input variables are evaluated using the calibrating results given from the first regressed process. To evaluate the performance of the proposed MRSM, three multi-extremum failure modes including radial deformation of compressor blisk, maximum strain, and stress of compressor blade and disk are considered. the prediction of MRSM of nonlinear responses for Thermal-fluid–structure system with dynamical nonlinear finite-element analyses is compared with response surface method (RSM) and artificial neural network (ANN). The predicted results of modeling approaches showed that the sensitivity analysis based on MRSM accurately provided the effective degree for input variables. The gas temperature has the highest effects on nonlinear responses of turbine blisk which is followed by angular speed and material density. The MRSM combined with basic exponential function performs better than other models, while the MRSM coupled with linear function is more accurate than ANN and RSM. The proposed MRSM models have illustrated the accurate and efficient framework for approximating dynamic structural analysis of complex components.

     

Finite element analysis of damping the vibrations of laminated composites

There are several ways of decreasing the vibration energy of structures, such as diminishing the source energy, designing structures with desired eigen-frequencies and excitation frequencies, using materials that have damping properties, etc. Special damping layers made of various viscoelastic materials are widely applied in structures subjected to dynamic loading, especially those used in ship building and aerospace technology. A typical structure is that whose basic layer is covered with a damping layer and a thin constraining layer. Such classical sandwich structures have been widely investigated, especially with reference to the analysis of elastic vibrations.     

Designing robust structures - A nonlinear simulation based approach

This paper presents a generally applicable numerical procedure for designing robust structures under uncertainty, which can be coupled with any arbitrary nonlinear computational model for statical or dynamic structural analysis. Based on the results from an uncertain structural analysis several permissible design domains are determined with the aid of cluster analysis methods instead of traditionally computing only one particular set of crisp design parameter values; these represent design alternatives. To identify a preference solution, a discrete three-criteria optimization problem is formulated, which is focused on maximum structural robustness and includes a safety component. A measure for the global robustness of the design alternatives is introduced based on an analog to Shannon’s entropy. The goal of the resulting design is that the structural behavior is only marginally affected by uncertainty and by changes in the design parameters, which further provides comfortable decision margins to the construction engineer.The proposed procedure is demonstrated by means of a numerical example and of an example from engineering practice in vehicle crashworthiness design.     

Influence of Boundary Conditions on the Dynamic Characteristics of Squeeze Films in MEMS Devices

Micromechanical structures that have squeeze-film damping as the dominant energy dissipation mechanism are of interest in this paper. For such structures with narrow air gap, the Reynolds equation is used for calculating squeeze-film damping, which is generally solved with trivial pressure boundary conditions on the side walls. This procedure, however, fails to give satisfactory results for structures under two important conditions: 1) for an air gap thickness comparable to the lateral dimensions of the microstructure and 2) for nontrivial pressure boundary conditions such as fully open boundaries on an extended substrate or partially blocked boundaries that provide side clearance to the fluid flow. Several formulas exist to account for simple boundary conditions. In practice, however, there are many micromechanical structures such as torsional microelectromechanical system (MEMS) structures that have nontrivial boundary conditions arising from partially blocked boundaries. Such boundaries usually have clearance parameters that can vary due to fabrication. These parameters, however, can also be used as design parameters if we understand their role on the dynamics of the structure. We take a MEMS torsion mirror as an example device that has large air gap and partially blocked boundaries due to static frames. We actuate the device and experimentally determine the quality factor Q from the response measurements. Next, we model the same structure in ANSYS and carry out computational fluid dynamics analysis to evaluate the stiffness constant K, the damping constant D, and the quality factor Q due to the squeeze film. We compare the computational results with experimental results and show that without taking care of the partially blocked boundaries properly in the computational model, we get unacceptably large errors.     

Computationally Efficient Approaches to Characterize the Dynamic Response of Microstructures Under Mechanical Shock

We present computationally efficient models and approaches to simulate the response of microstructures under mechanical shock. These approaches include a Galerkin-based reduced-order model and a hybrid approach utilizing the response of structures to static loads combined with the dynamic shock spectrum of a spring-mass-damper system. To demonstrate the accuracy and efficiency of these approaches, we apply them on cantilever and clamped-clamped microbeams, and compare their predictions with analytical and finite-element (FE) results. We conclude that the hybrid approach is computationally efficient and accurate for microstructures behaving linearly in both quasi-static and dynamic loading conditions. The hybrid approach enables using simple analytical expressions that can be easily utilized by microelectromechanical system designers to judge the reliability of their devices. We show that reduced-order models are capable of capturing accurately the dynamic behavior of microstructures under shock pulses of various amplitudes (low-g and high-g), damping conditions, structural boundaries, and can capture linear and nonlinear behavior. Our results indicate that modeling the shock force as a quasi-static force for microstructures with low-natural frequencies may lead to erroneous results. High-g loading cases are investigated. Significant increase in the computational cost of simulations is reported when using traditional FE models because of the activation of higher order modes. The developed reduced-order model employing at least six modes is shown to be efficient in such cases. Design parameters are investigated to determine their effect on the shock resistance of microstructures. It is concluded that increasing air damping and tensile residual stresses improves the shock resistance of microstructures. A case study for the response of an optical fiber switch to shock is presented.     

Development and evaluation of a pseudo-force approximation applied to nonlinear dynamic contacts and viscoelastic damping

A pseudo-force approximation method is used to study the nonlinear dynamic contacts and the effect of viscoelastic damping of beam-mass-beam systems. A pseudo-contact element with nonlinear stiffness and damping approximated by polynomial functions is defined and evaluated. To improve the system dynamic responses, viscoelastic damping is introduced into the systems using the standard linear model. The nonlinear forces derived from surface elasticity, penetration, instant contact velocity and viscoelastic damper are added to an excitation force vector to avoid reformation of system matrices. The system's equations of motion are directly integrated using the Wilson-θ method with minor modifications to accommodate the dynamic contacts and the viscoelastic damping. A design equation is also proposed to estimate the required viscoelastic dampers.     

Effects of amplitude-dependent damping and time constant on wind-induced responses of super tall building

Full-scale measurements of wind-induced responses of a 79-storey tall building, Di Wang Tower, were conducted during the passages of several typhoons. The amplitude-dependent damping ratios of the super tall building were obtained from the measurements. A Monte Carlo simulation procedure was developed in this study to generate fluctuating along-wind and across-wind forces acting on this building. The wind-induced responses of Di Wang Tower were numerically evaluated in time domain on the basis of the generated fluctuating wind forces and the established finite element model of the building. The predicted dynamic responses of the building using the actual amplitude-dependent damping characteristics were compared to those computed with constant damping parameters assumed by the structural designers to evaluate the adequacy of current design practices and to investigate the effect of amplitude-dependent damping on the wind-induced responses. Finally, the effect of time constant on the wind-induced responses of Di Wang Tower was studied by comparing the time domain computational results with those from conventional spectral analysis method. Some of the research findings resulted from this combined experimental and numerical study are expected to be of interest and practical use to professionals and researchers involved in the design and analysis of super tall buildings.     

A systematic approach on computational analysis and optimization design: for a nonlinear coupling shock absorber

The aim of this article is to provide a systematic approach to perform computational simulation and optimization design of parameters matching selection for a nonlinear coupling shock absorber. A theoretical mathematical model with nonlinear coupling for shock absorber is induced based on relative literature. The model considers the coupling of quadratic damping, viscosity damping, coulomb damping and nonlinear spring. Approximate computational solution is deduced by introducing harmonic balance method and Fourier transform method. These approximate theoretical solutions include output response of the system, absolute acceleration transmissibility in vibration or impact, and the maximum relative displacement in impact process, etc. The approximate computational results are compared with those obtained by numerical integration to confirm the validity of the mathematical model. In the meantime, an optimization design model for parameters is built. The design example is illustrated to confirm the validity of the modeling method and the theoretical solution.     

Simple robust output-feedback controller for uncertain nonlinearsystems

A robust output-feedback controller is designed by using an observer plus backstepping procedure to solve the tracking problems of a class of uncertain nonlinear systems. In the design procedure, three techniques are applied: a) a single filter whose dynamic order is the same as the system order is constructed; b) a normalization signal is introduced; c) positive nonlinear functions that are used to generate the normalization signal and to construct nonlinear damping terms can be chosen freely. The designed controller has a very simple structure and can be applied to track much broader classes of reference signals. It can guarantee the global boundness of all closed-loop signals and make the output tracking error arbitrarily small. Technique c) may provide the designer with the possibility to find a better choice of positive nonlinear functions for our controller to achieve similar tracking performance with less control effort     

Nonlinear static and dynamic damped response of isotropic, elastic circular plates

Nonlinear static and dynamic response analysis of clamped-in and simply supported boundary conditions, and immovably constrained and stress-free edge conditions for circular plates of isotropic elastic material with damping, subjected to step pressure pulse excitation are presented. The Von Karman relations are used which are reduced to coupled nonlinear partial differential equations and solved by a one-term solution, applying the Ritz-Galerkin technique to the deflection equation. This yields an ordinary nonlinear differential equation in time. The nonlinear dynamic damped response is obtained by applying the ultraspherical polynomial approximation technique. Plots of static deflection to thickness ratio versus non-dimensional load for different boundary and edge conditions, and the effect of damping on the nonlinear dynamic response for different values of non-dimensional damping factor are presented.     

静止无功补偿器的自适应逆推无源反馈控制设计

通过将耗散系统理论和自适应逆推(adaptive backstepping)非线性控制算法相结合, 克服了无源反馈方法只能为输入输出相对阶为1的系统设计控制律的限制, 为带有静止无功补偿器的单机无穷大电力系统设计了鲁棒自适应控制器. 设计中兼顾了系统遭受不确定扰动以及阻尼系数难以精确测量情况下控制器的鲁棒性和自适应能力. 理论分析证明所提算法可保证系统内所有状态变量一致有界且渐近稳定, 系统误差全局渐近稳定. 仿真结果也表明, 所提算法使系统母线电压, 发电机功角以及转子角速度的暂态响应性能优于传统逆推算法, 系统误差迅速收敛至零, 与理论证明结果一致.