A model identification method of vibrating structures from incomplete modal information

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A MODEL IDENTIFICATION METHOD OF VIBRATING STRUCTURES FROM INCOMPLETE MODAL INFORMATION

ＡＭＯＤＥＬＩＤＥＮＴＩＦＩＣＡＴＩＯＮＭＥＴＨＯＤＯＦＶＩＢＲＡＴＩＮＧＳＴＲＵＣＴＵＲＥＳＦＲＯＭＩＮＣＯＭＰＬＥＴＥＭＯＤＡＬＩＮＦＯＲＭＡＴＩＯＮＺｈｅｎｇＸｉａｏｐｉｎｇ（郑小平）ＹａｏＺｈｅｎｈａｎ（姚振汉）ＱｕＳｈｉｓｈｅｎｇ（蘧时胜）...     

Time-dependent hydroelastic analysis of cavitating propulsors

A 3-D potential-based boundary element method (BEM) is coupled with a 3-D finite element method (FEM) for the time-dependent hydroelastic analysis of cavitating propulsors. The BEM is applied to evaluate the moving cavity boundaries and fluctuating pressures, as well as the added mass and hydrodynamic damping matrices. The FEM is applied to analyze the dynamic blade deformations and stresses due to pressure fluctuations and centrifugal forces. The added mass and hydrodynamic damping matrices are superimposed onto the structural mass and damping matrices, respectively, to account for the effect of fluid–structure interaction. The problem is solved in the time-domain using an implicit time integration scheme. An overview of the formulation for both the BEM and FEM is presented, as well as the BEM/FEM coupling algorithm. Numerical and experiment validation studies are shown. The effects of fluid–structure interaction on the propeller performance are discussed.     

Impulse Responses of Fractional Damped Systems

Considered are systems of single-mass oscillators with different fractional damping behaviour. Similar to the classical model, where the damping terms are represented by first derivatives, the eigensystem can be used to decompose the fractional system in frequency domain, if mass, stiffness and damping matrices are linearly dependent. The solution appears as a linear combination of single-mass oscillators. This is true even in the general case such that stability and causality are insured by the same argumentation as used in the linear dependent case.     

Impulse Responses of Fractional Damped Systems

Considered are systems of single-mass oscillators with different fractional damping behaviour. Similar to the classical model, where the damping terms are represented by first derivatives, the eigensystem can be used to decompose the fractional system in frequency domain, if mass, stiffness and damping matrices are linearly dependent. The solution appears as a linear combination of single-mass oscillators. This is true even in the general case such that stability and causality are insured by the same argumentation as used in the linear dependent case.     

Several solution methods for the generalized complex eigenvalue problem with bounded uncertainties

The aim of this paper is to evaluate the effects of uncertain-but-bounded parameters on the complex eigenvalues of the non-proportional damping structures. By combining the interval mathematics and the finite element analysis, the mass matrix, the damping matrix and the stiffness matrix were represented as the interval matrices. Firstly, with the help of the optimization theory, we presented an exact solution—the vertex solution theorem, for determining the exact upper bounds or maximum values and exact lower bounds or minimum values of complex eigenvalues of structures, where the extreme values are reached on the boundary of the interval mass, damping and stiffness matrices. Then, an interval perturbation method was proposed, which needs less computational efforts. A numerical example of a seven degree-of-freedom spring-damping-mass system was used to illustrate the computational aspects of the presented vertex solution theorem and the interval perturbation method in comparison with Deif’s method.     

An Internal Damping Model for the Absolute Nodal Coordinate Formulation

Introducing internal damping in multibody system simulations is important as real-life systems usually exhibit this type of energy dissipation mechanism. When using an inertial coordinate method such as the absolute nodal coordinate formulation, damping forces must be carefully formulated in order not to damp rigid body motion, as both this and deformation are described by the same set of absolute nodal coordinates. This paper presents an internal damping model based on linear viscoelasticity for the absolute nodal coordinate formulation. A practical procedure for estimating the parameters that govern the dissipation of energy is proposed. The absence of energy dissipation under rigid body motion is demonstrated both analytically and numerically. Geometric nonlinearity is accounted for as deformations and deformation rates are evaluated by using the Green–Lagrange strain–displacement relationship. In addition, the resulting damping forces are functions of some constant matrices that can be calculated in advance, thereby avoiding the integration over the element volume each time the damping force vector is evaluated.     

不确定动力系统平稳随机响应分析

由于设计、建造以及测量等诸多不确定因素的影响,通常的有限元力学分析模型只是原型结构的一种均值近似,采用随机结构模型是更为合理的.本文应用随机矩阵模拟不确定线性动力系统有限元模型中质量阵、阻尼阵和刚度阵的随机不确定性,并进一步建立此类非参数概率系统在平稳随机外载作用下动力响应的虚拟激励高效求解算法.数值结果表明,均值有限元模型和随机矩阵模型的动力响应具有很大的差异.对于精细制造,模型的随机性是不能忽略的,本文提出的算法为此类问题求解提供了一条有效途径.     

High-order layerwise mechanics and finite element for the damped dynamic characteristics of sandwich composite beams

A high-order discrete-layer theory and a finite element are presented for predicting the damping of laminated composite sandwich beams. The new layerwise laminate theory involves quadratic and cubic terms for approximation of the in-plane displacement in each discrete layer, while interlaminar shear stress continuity is imposed through the thickness. Integrated damping mechanics are formulated and both laminate and structural stiffness, mass and damping matrices are formed. A finite element method and a beam element are further developed for predicting the free vibration response, including modal frequencies, modal loss factors and through-thickness mode shapes. Numerical results and evaluations of the present model are shown. Modal frequencies and damping of sandwich composite beams are measured and correlated with predicted values. Finally, parametric studies illustrate the effect of core thickness and face lamination on modal damping and frequency values.     

应用POD和Padé拟合的线性动力学系统辨识

提出了一种线性动力学系统辨识方法。应用Padé多项式对系统的动刚度曲线进行拟合,通过最小二乘法确定Padé多项式中的系数矩阵,利用遗传算法确定出Padé拟合式中的参数。通过比较系统动刚度矩阵的理论公式和Padé拟合式,辨识得到系统的质量阵、刚度阵和阻尼阵。当系统阶数较高时,可结合POD降阶技术对系统进行辨识,该方法适用于全阶模型和降阶模型。数值仿真算例表明,本文方法具有较高的精度和较好的鲁棒性。     

A COMPLEX PARAMETER MODEL UPDATING METHOD FOR DAMPING CHARACTERISTICS OF FINITE ELEMENT MODELS

阻尼对于结构动力学响应具有重要的影响,但有限元模型一般很难对阻尼特性进行精确建模.基于实测频响函数,研究了一种有限元模型阻尼特性的复参数修正方法.以待修正区域各单元质量、刚度矩阵的比例修正系数为复修正参数,建立了单元矩阵比例修正的灵敏度方程直接算法,并对比分析了复修正参数与不同阻尼特性之间的数学关系.以六自由度集中参数模型和25杆平面桁架模型为例,验证了复参数修正方法在阻尼特性修正中的有效性.     

Vertex solution theorem for the upper and lower bounds on the dynamic response of structures with uncertain-but-bounded parameters

The aim of this paper is to evaluate the effects of uncertain-but-bounded parameters on the dynamic response of structures. By combining the interval mathematics and the finite element analysis, the mass matrix, damping matrix, stiffness matrix and the external loads are represented as interval matrices and vector. With the help of the optimization theory, we present the vertex solution theorem for determining both the exact upper bounds or maximum values and the exact lower bounds or minimum values of the dynamic response of structures, in which these parameters reach their extreme values on the boundary of the interval mass, damping, stiffness matrices and the interval extemal loads vector. Three examples are used to illustrate the computational aspects of the presented vertex solution theorem.     

多自由度线性阻尼系统的频域及时域响应分析

本文从分析频率方程解的形式出发，通过设定响应的频域形式，得出自由振动时域响应的显式解，并导出任意强迫振动的Ｄｕｈａｍｅｌ积分．文中的分析方法适用于系统质量、阻尼、刚度阵均为非对称的情形，且属于精确求解．     

Dynamic modeling and simulation of deploying process for space solar power satellite receiver

To reveal some dynamic properties of the deploying process for the solar power satellite via an arbitrarily large phased array (SPS-ALPHA) solar receiver, the symplectic Runge-Kuttamethod is used to simulate the simplified model with the consideration of the Rayleigh damping effect. The system containing the Rayleigh damping can be separated and transformed into the equivalent nondamping system formally to insure the application condition of the symplectic Runge-Kutta method©First, the Lagrange equation with the Rayleigh damping governing the motion of the system is derived via the variational principle. Then, with some reasonable assumptions on the relations among the damping, mass, and stiffness matrices, the Rayleigh damping system is equivalently converted into the nondamping system formally, so that the symplectic Runge-Kutta method can be used to simulate the deploying process for the solar receiver. Finally, some numerical results of the symplectic Runge-Kutta method for the dynamic properties of the solar receiver are reported. The numerical results show that the proposed simplified model is valid for the deploying process for the SPS-ALPHA solar receiver, and the symplectic Runge-Kutta method can preserve the displacement constraints of the system well with excellent long-time numerical stability.     

The analysis of arbitrarily-damped linear mechanical systems

Summary The analysis of arbitrarily-damped linear mechanical systems is the subject of this paper, the main issue being the analysis of nondecouplable systems. It is well known that decouplable systems occur when the damping matrix happens to be a linear combination of the mass and stiffness matrices. Systems with this type of damping are said to have proportional damping, which nevertheless seldom occurs in practice, but many a damped system is analyzed under the assumption that it is proportionally damped. In fact, this property allows the analyst to study these systems using the same approach as that applicable to their undamped counterparts. In this paper, we show that proportional damping need not be assumed in order to analyze the system at hand with the same approach as used to analyze undamped systems. Moreover, we propose an algorithm to determine the natural frequencies, the damped frequencies and the damping ratios of an n-degree-of-freedom damped system, that does not require the casting of the system into first-order form. In this way, the characteristic equation is derived naturally as a 2n-degree polynomial, computing its roots being then straightforward. Furthermore, we propose a semigraphical method to ease this calculation, which should be attractive to practicing engineers. Received 5 April 1999; accepted for publication 7 May 1999     

一维连续体释放和回收过程的构形计算

一维连续体的释放和回收过程由时变的动力学方程描述。将一维连续体离散为有限单元,建立其时变自由度的高维离散动力学模型。通过重新划分单元,重置系统质量、阻尼和刚度矩阵,以及位移和荷载向量,并基于改进的有限差分法,提出了一维连续体释放和回收过程的一种构形计算方法。以柔性索的面内运动为例,计算了其释放和回收过程的动力学构形,实...     

约束层阻尼板动力学问题的半解析解

利用条形传递函数方法(SDTFM)得到了约束层阻尼(CLD)板动力学问题的半解析解.首先对CLD板沿纵向离散成多个条形单元,基于Hamilton原理推导出条形单元的刚度矩阵和质量矩阵,仿照有限元法组集得到系统的总刚度矩阵和总质量矩阵.经Laplace变换后引入状态向量,采用分布参数传递函数方法在状态空间内建立CLD板的控制方程并进行求解.最后以对边固支和悬臂CLD板为例,得到了板的动力学特性和频响曲线,并与NASTRAN或相关文献结果进行了比较,吻合良好,验证了该方法的有效性.从推导过程和算例可以看出,该方法所需的单元数目少,获得的是半解析解,计算效率高且准确可靠.