非保守耦合系统的耦合损耗因子

研究利用子结构的导纳计算非保守耦合系统的耦合损耗因子的方法。首先,利用经典保守耦合系统统计能量分析能量平衡方程的形式,推导了非保守耦合系统中耦合损耗因子与结构振动能量比的关系;然后,给出了利用子结构的导纳计算结构振动能量比的方法;最后,实验测量了非保守耦合系统的耦会损耗因子,并与理论预测值比较。结果表明,理论预测和实验测量结果的一致性很好。     

Vibration analysis of harmonically excited non-linear system using the method of multiple scales

An analytical method is presented for evaluation of the steady state periodic behavior of non-linear systems. This method is based on the substructure synthesis formulation and a multiple scales procedure, which is applied to the analysis of non-linear responses. A complex non-linear system is divided into substructures, of which equations are approximately transformed to modal co-ordinates including non-linear term under the reasonable procedure. Then, the equations are synthesized into the overall system and the solution of the non-linear system can be obtained. Based on the method of multiple scales, the proposed procedure reduces the size of large-degree-of-freedom problem in solving the non-linear equations. Feasibility and advantages of the proposed method are illustrated by the application of the analytic procedure to the non-linear rotating machine system as a large mechanical structure system. Results obtained are reported to be an efficient approach with respect to non-linear response prediction when compared with other conventional methods.     

Prediction of rail corrugation using a rotating flexible wheelset coupled with a flexible track model and a non-Hertzian/non-steady contact model

This paper presents a model for simulating vehicle–track interaction at high frequencies for investigations of rail roughness growth. The dynamic interaction model developed employs a substructuring technique and the whole system consists of a number of substructures that can be modelled independently. The systems are coupled through the forces at the wheel–rail contact and the railpad. A coupled, rotating flexible wheelset, a flexible track model and a non-Hertzian/non-steady contact model have been implemented and results are presented here for a free wheelset on a symmetrical track system with initial random and sinusoidal roughness. Both rigid and flexible wheelsets are considered.     

Coordinated scheduling of electricity and natural gas infrastructures with a transient model for natural gas flow

This paper focuses on transient characteristics of natural gas flow in the coordinated scheduling of security-constrained electricity and natural gas infrastructures. The paper takes into account the slow transient process in the natural gas transmission systems. Considering their transient characteristics, natural gas transmission systems are modeled as a set of partial differential equations (PDEs) and algebraic equations. An implicit finite difference method is applied to approximate PDEs by difference equations. The coordinated scheduling of electricity and natural gas systems is described as a bi-level programming formulation from the independent system operator's viewpoint. The objective of the upper-level problem is to minimize the operating cost of electric power systems while the natural gas scheduling optimization problem is nested within the lower-level problem. Numerical examples are presented to verify the effectiveness of the proposed solution and to compare the solutions for steady-state and transient models of natural gas transmission systems.     

POWER FLOW ANALYSIS OF INDETERMINATE ROD/BEAM SYSTEMS USING A SUBSTRUCTURE METHOD

Based on the concepts of a subsystem structural dynamics approach, a general power flow analysis of an indeterminate vibrating system consisting of three rods is presented and discussed. This is achieved by complementing the normal dynamic equations with geometrical compatibility equations allowing assessment of power flow dynamic characteristics applied to and excited within the system. The method may be classified as a form of substructuring using free-free interface conditions. The displacement contribution of the external and boundary coupling forces is deduced, permitting the power flow between the interfaces of substructures to be determined. The method presented is used in a power flow analysis of a simple rod truss system and in a more complex system as demonstrated.     

On information-processing abilities of chaotic dynamical systems

A mechanism is suggested to explain the information processing abilities of simple natural brains, which, by experimental evidence, display behavior like chaotic dynamical systems while at rest. The Lorenz system of equations is dealt with as a case study, and a comparison of the suggested mechanism with the standard theory of neural networks is made.     

SOME GENERAL EFFECTS OF STRONG HIGH-FREQUENCY EXCITATION: STIFFENING, BIASING AND SMOOTHENING

Mechanical high-frequency (HF) excitation provides a working principle behind many industrial and natural applications and phenomena. This paper concerns three particular effects of HF excitation, that may change the apparent characteristics of mechanical systems: (1) stiffening, by which the apparent linear stiffness associated with an equilibrium is changed, along with derived quantities such as stability and natural frequencies; (2) biasing by which the system is biased towards a particular state, static or dynamic, which does not exist or is unstable in the absence of the HF excitation; and (3) smoothening, referring to a tendency for discontinuities to be effectively “smeared out” by HF excitation. Illustrating first these effects for a few specific systems, analytical results are provided that quantify them for a quite general class of mechanical systems. This class covers systems that can be modelled by a finite number of second order ordinary differential equations, generally non-linear, with periodically oscillating excitation terms of high frequency and small amplitude. The results should be useful for understanding the effects in question in a broader perspective than is possible with specific systems, for calculating effects for specific systems using well-defined formulas, and for possibly designing systems that display prescribed characteristics in the presence of HF excitation.     

Riccati-Type Equations, Generalised WZNW Equations, and Multidimensional Toda Systems

We associate to an arbitrary ℤ-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional extension of these equations is given. The generalisation of the associated Redheffer–Reid differential systems appears in a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established. Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given. Received: 3 August 1998 / Accepted: 21 December 1998     

Experimental modal substructuring to couple and uncouple substructures with flexible fixtures and multi-point connections

Modal substructuring or component mode synthesis (CMS) has been standard practice for many decades in the analytical realm, yet a number of significant difficulties have been encountered when attempting to combine experimentally derived modal models with analytical ones or when predicting the effect of structural modifications using experimental measurements. This work presents a new method that removes the effects of a flexible fixture from an experimentally obtained modal model. It can be viewed as an extension to the approach where rigid masses are removed from a structure. The approach presented here improves the modal basis of the substructure, so that it can be used to more accurately estimate the modal parameters of the built-up system. New types of constraints are also presented, which constrain the modal degrees of freedom of the substructures, avoiding the need to estimate the connection point displacements and rotations. These constraints together with the use of a flexible fixture enable a new approach for joining structures, especially those with statically indeterminate multi-point connections, such as two circular flanges that are joined by many more bolts than required to enforce compatibility if the substructures were rigid. Fixture design is discussed, one objective of which is to achieve a mass-loaded boundary condition that exercises the substructure at the connection point as it is in the built up system. The proposed approach is demonstrated with two examples using experimental measurements from laboratory systems. The first is a simple problem of joining two beams of differing lengths, while the second consists of a three-dimensional structure comprising a circular plate that is bolted at eight locations to a flange on a cylindrical structure. In both cases frequency response functions predicted by the substructuring methods agree well with those of the actual coupled structures over a significant range of frequencies.     

Free transverse vibration analysis of an elastically connected annular and circular double-membrane compound system

In this paper, free transversal vibrations of a systems of two annular and circular membranes connected by a Winkler elastic layer are studied using analytical methods and numerical simulation. At first the motion of each system is described by two homogeneous partial differential equations. The general solutions of the free vibrations are derived by the Bernoulli-Fourier method and the boundary problems are solved. The natural frequencies and natural mode shapes of vibrations of systems under consideration are determined. The investigation of free vibrations prove that the double-membrane systems execute two kinds of vibrations, synchronous and asynchronous. Then for each system two models formulated by using finite element representations are prepared. The FE models are manually tuned to reduce the difference between the natural frequencies of the analytical solutions and the natural frequencies of the FE model calculations, respectively.     

Dynamical aspects in the optical bloch equations

In quantum optics, some models are considered to describe many aspects of the dynamics of atoms coupled to an electromagnetic field (laser). The simplest atomic model is of course the two-level-atom which is governed by the Bloch optical equations. In general this system is solved in the steady state or by using some approximations. An extended analytic approach is considered for this coupled equations. The separation approach of coupled differential equations is always possible with a sequence of special transformation into nonlinear differential equations. The conditions that permit an exact solution of three coupled systems are extracted in a natural manner. The case of sodium atom moving along the axis of a standing-wave is investigated in some details.     

A general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear/time-dependent internal boundary conditions

The subject of this paper is the development of a general solution procedure for the vibrations (primary resonance and nonlinear natural frequency) of systems with cubic nonlinearities, subjected to nonlinear and time-dependent internal boundary conditions—this is a commonly occurring situation in the vibration analysis of continuous systems with intermediate elements. The equations of motion form a set of nonlinear partial differential equations with nonlinear, time-dependent, and coupled internal boundary conditions. The method of multiple timescales, an approximate analytical method, is applied directly to each partial differential equation of motion as well as coupled boundary conditions (i.e. on each sub-domain and the corresponding internal boundary conditions for a continuous system with intermediate elements) which ultimately leads to approximate analytical expressions for the frequency-response relation and nonlinear natural frequencies of the system. These closed-form solutions provide direct insight into the relationship between the system parameters and vibration characteristics of the system. Moreover, the suggested solution procedure is applied to a sample problem which is discussed in detail.     

复杂结构的损耗因子和耦合损耗因子的测量方法

本文介绍利用测量结构振动能量比,测量组装结构的损耗因子和耦合损耗因子的方法。这种方法既适合于保守耦合结构,也适合于非保守耦合结构。这种方法的优点是同时可测量得到结构损耗因子、耦合损耗因子和间接耦合损耗因子,而不需要知道各子结构的模态密度。耦合损耗因子不仅包括共振传输而且也包含低频的非共振传输的影响。利用这种方法测量了转动机械系统的损耗因子和耦合损耗因子并用修正的统计能量分析平衡方程预测了结构振动响应。然后与实测的结构振动平均响应比较,一致性非常好。     

光孤子约束系统的量子场论

光孤子系统可用奇异Lagrange量描述,系统含Dirac约束.通常按对应原理写出系统对易关系和量子运动方程时,未计及约束.文中对该系统进行严格的Dirac括号量子化,给出了系统的对易关系和量子运动方程,还对系统进行了路径积分量子化,并根据量子水平的Noether定理,导出了系统在时空平移变换不变性下的量子能量和动量守恒.系统还具有相位变换下的不变性,相应导出了系统的粒子数守恒.     

On the definition of the natural frequency of oscillations in nonlinear large rotation problems

Computational multibody system algorithms allow for performing eigenvalue analysis at different time points during the simulation to study the system stability. The nonlinear equations of motion are linearized at these time points, and the resulting linear equations are used to determine the eigenvalues and eigenvectors of the system. In the case of linear systems, the system eigenvalues remain the same under a constant coordinate transformation; and zero eigenvalues are always associated with rigid body modes, while nonzero eigenvalues are associated with non-rigid body motion. These results, however, cannot in general be applied to nonlinear multibody systems as demonstrated in this paper. Different sets of large rotation parameters lead to different forms of the nonlinear and linearized equations of motion, making it necessary to have a correct interpretation of the obtained eigenvalue solution. As shown in this investigation, the frequencies associated with different sets of orientation parameters can differ significantly, and rigid body motion can be associated with non-zero oscillation frequencies, depending on the coordinates used. In order to demonstrate this fact, the multibody system motion equations associated with the system degrees of freedom are presented and linearized. The resulting linear equations are used to define an eigevalue problem using the state space representation in order to account for general damping that characterizes multibody system applications. In order to demonstrate the significant differences between the eigenvalue solutions associated with two different sets of orientation parameters, a simple rotating disk example is considered in this study. The equations of motion of this simple example are formulated using Euler angles, Euler parameters and Rodriguez parameters. The results presented in this study demonstrate that the frequencies obtained using computational multibody system algorithms should not in general be interpreted as the system natural frequencies, but as the frequencies of the oscillations of the coordinates used to describe the motion of the system.     

Quantum-hydrodynamic approach to the problem of electron exchange between atomic particles and nanosystems

The application of quantum-hydrodynamic methods for solving the problem of electron exchange between atomic particles and solid surfaces, and nanosystems has been examined. The derivation of a system of equations that is alternative to the nonstationary Schrödinger equation is given to describe the dynamics of electronic processes with variable charge and current densities. A comparison of results of solving the nonstationary Schrödinger equation and the quantum-hydrodynamic system of equations shows that both approaches give a good coincidence. The numerical solution to the system of quantum-hydrodynamic equations has a number of advantages, because it does not lead to oscillations at the boundary of the computational mesh and nor to the problem of exponential growth in numerical complexity for many-electron systems.     

Discrete exterior geometry approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems

This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a discrete analogue of the Stokes–Dirac structure and demonstrate that it provides a natural framework for deriving finite-dimensional port-Hamiltonian systems that emulate their infinite-dimensional counterparts. The spatial domain, in the continuous theory represented by a finite-dimensional smooth manifold with boundary, is replaced by a homological manifold-like simplicial complex and its augmented circumcentric dual. The smooth differential forms, in discrete setting, are mirrored by cochains on the primal and dual complexes, while the discrete exterior derivative is defined to be the coboundary operator. This approach of discrete differential geometry, rather than discretizing the partial differential equations, allows to first discretize the underlying Stokes–Dirac structure and then to impose the corresponding finite-dimensional port-Hamiltonian dynamics. In this manner, a number of important intrinsically topological and geometrical properties of the system are preserved.     

The axisymmetrical response of a circular cylindrical double-shell system with internal damping

The axisymmetrical response of a circular cylindrical double-shell system with internal damping to a time-dependent surface load is determined by the matrix analysis method. For this purpose, the equations of vibration of the system based upon the Goldenveizer-Novozhilov theory are written as a coupled set of first order differential equations by the use of the state vector of the system. Once the vector has been determined by quadrature of the equations, the steady state response is calculated numerically together with the natural frequencies in terms of the elements of the transfer matrix of the system under any combination of boundary conditions. By the application of the method, the dynamic response and the resonant frequencies (the natural frequencies) are calculated numerically for a double-shell system simply supported at the edges.