HOMOTOPY CONTINUATION ALGORITHM FOR STRUCTURAL DAMAGE IDENTIFICATION

I. INTRODUCTIONStructural damages due to the loss of sti?ness such as crack, localization bulking have remarkablein?uences on the physical properties of structure such as deformation, stress, frequency and modelshape. So the change of these properties can be used to identify the damage location and degree ofstructures. The damage identification techniques based on these properties’ changes have attractedmuch attention in recent years, and many approaches have been developed[1??5].Nowaday…     

索牵引并联机器人静态平衡位置的正解研究

研究了一种大跨度但运动缓慢的索牵引并联机器人的位置正解问题,此时可认为系统处于静平衡状态,但必须考虑柔索垂度的影响。索牵引并联机器人的静态平衡位置的正解就是确定机器人末端执行器的位置和姿态,使得系统能在给定的柔索长度下处于静平衡状态。这涉及到系统的非线性力学分析而不仅仅是一个几何问题。本文采用悬链线方程描述柔索的力学特性,结合索端位移与机器人末端执行器位移之间的关系推导出机器人的末端执行器位移与索长变化之间的增量关系,据此提出一种迭代策略完成正解计算。数值算例验证了本文方法的有效性。     

Disturbance compensation of a dual-arm underwater robot via redundant parallel mechanism theory

Disturbance compensation is one of the major issues for underwater robots to hover as a mobile platform and to manipulate an object in an underwater environment. This paper presents a new strategy of disturbance compensation for a mobile dual-arm underwater robot using internal torques derived from redundant parallel mechanism theory. A model of the robot was analyzed by redundant serial and parallel mechanisms at the same time. The joint torque to operate the robot is obtained from a redundant serial mechanism model with null-space projection due to redundancy. The joint torque derived from the redundant parallel kinematic model is calculated to perfectly compensate for disturbances to the mobile platform and is included in the solution of the joint torque based on the serial redundant model. The resultant joint torque can generate force on the end-effector for required tasks and forces for disturbance compensation simultaneously . A simulation shows the performance of this disturbance compensation strategy. The joint torque based on the algorithm generates the desired task force and the disturbance compensation force together, and a little additional joint torque can generate a large internal force effectively due to the characteristics of a redundant parallel mechanism. The proposed method is more effective than compensation methods using thrusting force on the mobile platform.     

Design and analysis of a novel 6-DOF redundant actuated parallel robot with compliant hinges for high precision positioning

This paper presents the design and modeling of a new 6-DOF 8-PSS/SPS compliant dual redundant parallel robot with wide-range flexure hinges. This robot can achieve either high accurate positioning or rough positioning as well as a 6-DOF active vibration isolation and excitation to the payload placed on the moving platform. Adopting a kind of wide-range flexure hinge, we establish the kinematics model of the macro parallel mechanism system via the stiffness model and Newton–Raphson method, then we build up the dynamics model using Kane’s method for the micro-motion system. The investigations of this paper will provide suggestions to improve the structure and control algorithm optimization for a novel compliant dual redundant parallel mechanism in order to achieve the feature of larger workspace, higher motion precision and better dynamic characteristics. The results will be helpful in modifying the structure of the prototype platform to enhance its high kinematics and dynamics properties.     

水下地磁辅助导航中地磁场延拓方法

水下地磁数据库的构建是实现地磁辅助导航的前提。利用水下航行器进行地磁测量从而建立水下地磁数据库,这种做法是不可行的,一种可行的解决方法是采用位场的延拓技术。采用位场的向下延拓技术,通过将海平面上航空测量得到的地磁数据进行向下延拓,得到水下地磁数据,以此来构建水下地磁数据库。将位场的向下延拓问题视为一类不适定问题,采用正则化方法中的Landweber迭代法来处理这类不适定问题,实现了地磁数据的向下延拓。仿真结果表明,该方法原理简单,抗噪声能力强,能够得到比较满意的延拓结果。     

Effects of thermo hydrodynamic (THD) floating ring bearing model on rotordynamic bifurcation

This paper introduces a numerical scheme for simulating instabilities of a nonlinear rotordynamic system including thermal effects in the fluid film bearings. The method utilizes shooting/arc-length continuation, and simultaneous, finite element based solutions of the variable viscosity Reynolds equation and the energy equation. This provides a means to investigate the effects of the thermo-hydrodynamic THD model on bifurcations and nonlinear rotordynamic stability. A “Jeffcott” type rigid rotor is modeled as supported on double-layered fluid film, floating ring bearings (FRB). The FRB are known to produce highly nonlinear forces as functions of relative and absolute internal displacements and velocities. Both autonomous (free vibration) and non-autonomous (mass unbalanced excitation) cases and algorithms are presented. The computational workload and execution time required for determining coexisting periodic solutions is significantly reduced by employing deflation and parallel computing methods. The THD model nonlinear responses and bifurcation diagrams are compared with isoviscous model results for various lubricant supply temperatures. The autonomous case, THD model orbit sizes and onset of Hopf and saddle–node bifurcations for coexisting steady state responses, may have significant differences relative to the isothermal model results. The onset of Hopf bifurcation is strongly dependent on thermal conditions, and the saddle–node bifurcation points are significantly shifted compared to the isothermal model. This tends to increase the likelihood of bifurcation from a machine operators standpoint. In the non-autonomous case, large unbalance forces create sub-synchronous and quasi-periodic responses at low spin speeds. The responses stability and onset of bifurcations of these responses are highly reliant on the lubricant supply temperature.     

一种非线性系统周期解的延拓算法

提出了一种非线性系统周期解的延拓算法。指出了非线性系统周期解在分岔点处由于雅可比矩阵奇异而导致一般延拓方法延拓失败问题;然后基于推广的打靶法的思想,将普通延拓算法推广,提出了一种用于周期解延拓的算法。对于非线性动力系统,该算法可以在已知某一参数下的周期解的基础上,求解出在一定参数范围内非线性动力系统的解随参数的连续变化情况。应用该方法对非线性柔性转子-轴承系统的周期解与参数的依赖关系进行了求解,验证了方法的有效性。     

Numerical Continuation Applied to Panel Flutter

The panel flutter formulation studied here includes a geometricnonlinearity. In a physical sense, the nonlinearity represents couplingbetween out-of-plane bending and in-plane stretching. To investigate theinitial condition response, the pseudo-arclength continuation method isapplied to this problem. The continuation method is an alternatenumerical method that complements direct numerical integration. Thelatter procedure is not necessarily computationally efficient when theparameter space under consideration is large. One strength ofcontinuation methods then is the ability to efficiently and accuratelydisplay the solution space, including certain bifurcations, for dynamicsystems. Results from the procedure are in substantial agreement withearlier studies, where applicable, where the panel undergoes cylindricalbending.     

轴承-转子系统Hopf分叉及其后动力学行为研究

采用长轴承解析模型研究滑动轴承支承的平衡单盘柔性转子-轴承系统的自激振动,把结合打靶法的延续算法应用于柔性平衡转子-轴承系统Hopf分叉后周期解的追踪和求解上,基于Floquet理论对周期解的稳定性加以分析.通过持续追踪周期解频率变化并与失稳固有频率进行对比,分析了自激锁相现象,研究了非线性油膜力自激源对系统的作用机理.运用Poincare映射、分叉图、及Lyapnov指数对周期解分叉、混沌及进入和脱离混沌的过程进行了分析.     

The Study of a Parametrically Excited Nonlinear Mechanical System with the Continuation Method

The dynamic behavior of a one-degree-of-freedom, parametrically excited nonlinear system is investigated. The Galerkin method is applied to the principal and fundamental parameteric resonance of the system. The continuation method is used to study the change of harmonic oscillation with respect to the variation of excitation frequency. The numerical stability analysis of the trivial solution is carried out and the stable and unstable regions of the trivial solution are given. They are found to agree with the results obtained by the analytical method of Galerkin. Periodic solutions are traced and the coexistence of multi-periodic solutions is observed With the change of excitation frequency the large amplitude periodic-2 oscillation is found to be in the same closed branch with the small amplitude periodic-2 solution. In addition, the bifurcation pattern of the trivial solution is found to change from subcritical Hopf bifurcation into supercritical Hopf bifurcation with the increase of excitation amplitude. Combined with the conventional numerical integration method, new complex dynamic behavior is detected.     

Numerical continuation of high Reynolds number external flows

A numerical continuation method for the compressible Reynolds‐Averaged Navier–Stokes equation with the Spalart–Allmaras turbulence model is presented and applied to the flow around a 2D airfoil. Using continuation methods it is possible to study the steady flow states of a system as a parameter such as angle of attack is varied. This approach allows unstable solutions to be calculated, which are important for understanding the nonlinear dynamics of the system. Furthermore, this method can be used to find any multivalued solutions that exist at a single parameter value. The eigenvalues of the system are calculated using the Cayley transform to precondition the eigenvalue solver ARPACK. The eigenvalues are important as they show the stability of the solutions as well as accurately detect parameter values at which bifurcations take place. Copyright © 2010 John Wiley & Sons, Ltd.     

The buckled states of rectangular plates

In this paper, based on the generalized variational principle of plates, the buckled states of rectangular plates under uniaxial compression are studied by use of the finite element method and the numerical analysis results under various boundary conditions are obtained by using the continuation calculation method.     

Green’s functions for bending problem of a thin anisotropic plate with an elliptic hole

The Green’s functions have not been studied in open literatures for the bending problem of an anisotropic plate with an elliptic hole subjected to a normal concentrated force and a concentrated moment. In this paper, the problem is investigated and the Green’s functions are first obtained by using the complex potential approach. The techniques of conformal mapping transformation and analytic continuation are used to derive the closed-form complex stress functions. The Green’s functions obtained have some potential applications in the analysis of composite structures such as the modification of the displacement compatibility model for notched stiffened composite panels and the formulation of a new method for interlaminar stress analysis around holes of laminates.     

A Bifurcation Analysis of the Dynamics of a Simplified Shell Model

We study parametrically excited vibrations of a shallow cylindrical panel. The mathematical model is a system of two partial differential equations based on Donnell's shallow shell theory. The original equations are discretised using Galerkin approximations and all calculations are performed through symbolic manipulations. A bifurcation analysis of a system model with two degrees of freedom is accomplished by continuation techniques. The importance of the second degree of freedom as well as some open questions concerning the modelling of shell vibrations are discussed.     

考虑关节摩擦的空间机器人动力学建模与参数辨识

研究了考虑关节摩擦影响的空间机器人系统的动力学建模与参数辨识问题．采用单向递推组集方法和虚功率原理建立了含有关节摩擦的多体系统动力学方程,推导了关节摩擦对系统动力学方程的贡献,采用基于腕力传感器信号和最小二乘法的辨识方法进行了系统惯性参数的辨识．数值仿真结果验证了数学模型的正确性与辨识方法的有效性．     

Dynamics of a liquid film sheared by a co-flowing turbulent gas

Consider the dynamics of a thin laminar liquid film flowing over an inclined wall in the presence of a co-flowing turbulent gas. The solution to the full two-phase flow problem poses substantial technical difficulties. However, by making appropriate assumptions, the solution process can be simplified and can provide valuable insights. The assumptions allow us to solve the gas and liquid problems independently. Solving for the gas flow reduces to finding perturbations to pressure and tangential stresses at the interface, influencing the liquid problem through the boundary conditions. We analyze the effect of gas flow on the liquid problem by developing an integral-boundary-layer model, which is valid up to moderate liquid Reynolds numbers. We seek solitary-wave solutions of this model under the influence of gas flow via a pseudo-arclength continuation method. Our computations demonstrate that as a general trend, the wave speed increases with increasing the gas shear and the liquid flow rate. Further insight into the problem is provided via time-dependent computations of the integral-boundary-layer model.     

A numerical bifurcation study of friction effects in a slip-controlled torque converter clutch

Friction plays a key role in the efficiency and stability of the slip-controlled torque converter clutches. The effects of friction on the dynamics and stability of a slip-controlled torque converter clutch system using a bifurcation-analysis-based approach is presented in this paper. A three degree-of-freedom nonlinear driveline model with integral feedback action to control the clutch slip speed has been utilized for this study. The clutch interface friction is dependent on the slip speed and is a function of the static friction constant, μ ₀, the low velocity friction constant μ ₁, and the low velocity exponential rate, γ. Using one-parameter numerical continuation, local Hopf bifurcations of the subcritical type are observed as the friction parameters μ ₁ and γ were varied at low slip speeds. The continuation results are verified using simulations of the full nonlinear model. Stick-slip and undesirable oscillations of the model inertia elements are observed for certain parameter values. As the slip speed is increased, the bifurcation instability occurs at an increasingly higher value of μ ₁ signifying an improved tolerance of negative friction gradient at higher slip speeds. Smaller exponential rates γ are tolerated at higher slip speeds before the bifurcation instability occurs. For the range of parameter values considered, no bifurcations occur for a slip speeds higher than 3.4 and 4.5 rad/s with μ ₁ and γ as the continuation parameters, respectively. These values of slip speeds are much lower than the system’s first mode of torsional vibration of 16 Hz (≈100 rad/s).     

求解非线性动力系统周期解大范围收敛方法

对于多自由度非线性动力系统,提出一种求解周期解的大范围收敛方法,这种算法对处理非线性动力系统有较强的功能。结合数值延拓算法,为求解具有系统参数的非线性动力系统在整个系统参数范围内的周期解提供了有效的方法。     

Investigation on 3Dt wake flow structures of swimming bionic fish

A bionic experimental platform was designed for the purpose of investigating time accurate three-dimensional flow field, using digital particle image velocimetry (DSPIV). The wake behind the flapping trail of a robotic fish model was studied at high spatial resolution. The study was performed in a water channel. A robot fish model was designed and built. The model was fixed onto a rigid support framework using a cable-supporting method, with twelve stretched wires. The entire tail of the model can perform prescribed motions in two degrees of freedom, mainly in carangiform mode, by driving its afterbody and lunate caudal fin respectively. The DSPIV system was set up to operate in a translational manner, measuring velocity field in a series of parallel slices. Phase locked measurements were repeated for a number of runs, allowing reconstruction of phase average flow field. Vortex structures with phase history of the wake were obtained. The study reveals some new and complex three-dimensional flow structures in the wake of the fish, including “reverse hairpin vortex” and “reverse Karman S-H vortex rings”, allowing insight into physics of this complex flow.     

弹性支承滑动轴承－转子系统稳定性的研究

本文研究弹性支承滑动轴承－转子系统的动力稳定性问题，建立了弹性支承滑动轴承－Ｊｅｆｆｃｏｔｔ转子系统的力学模型，采用牛顿延拓法从理论上对该转子轴承系统的动力稳定性进行了分析，讨论弹性支承的刚度对系统稳定性的影响，从而提出提高系统稳定性的有关措施。最后，依据理论分析，利用Ｊｅｆｆｃｏｔｔ转于实验台，作者设计和加工了一副弹性支承器，通过刚性支承和弹性支承两个对比实验，对理论分析的结果进行了验证。实验结果表明，弹性支承能提高转子动力稳定性。