Sweep Tests on Vibrating Systems with Power-Law Damping

The non-stationary response in vibrating systems with power-law damping, subjected to sweep tests is considered. Using the method of averaging, it is shown that the bifurcation delay persists in all forms of power-law damping, viz., Coulomb, orifice and cubic damping models. Experimental investigations on a soft type of isolator confirm the existence of delay in the jump phenomenon. These results also indicate that the softening nature of non-linearity can be profitably employed in the design of isolators and vehicle suspensions.     

Instability of Dual Eigenvalue Fourth-Order Systems

Investigations of the postbuckling behavior of an elastic structure at a twofold branching point generally involve a potential of the cubic type. However, when the cubic part vanishes identically (for example, when there is symmetry in both active coordinates), the potential becomes of the quartic type. Here, quartic potentials in normalized coordinates are considered and formulas for limit points and bifurcations on imperfect paths are given in terms of trigonometric polynomials. These are used in certain structural examples to show that a theorem of Ho is invalid unless extra conditions are placed on the potential. They are also used in a proof of the modified Ho theorem.     

Damping of Free Elastic Vibrations in Linear Systems

The possibility of using a Mises truss as an absorber of free elastic vibrations in a linear elastic system is examined. The nonlinear normal mode method is used to analyze nonlinear vibrations. A local nonlinear normal mode is shown to be favorable for vibration damping__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 110–117, February 2005.     

A Unifying Explanation for the Damping of Turbulence by Additives or External Forces

Recent calculations for the turbulent flow of a suspension of solid spheres in a gas were carried out by solving a Navier Stokes equation for the fluid that recognizes the presence of particles as external point forces. These show that a strong damping of the fluid turbulence can be realized at remarkably small volume fractions. The suggestion is made that the presence of point forces, pseudo-point forces, or added point shear stresses could provide a general explanation for turbulence suppression caused by additives or by the acceleration of a turbulent boundary-layer.     

Dynamic Behavior of Multilink Pendulums under Follower Forces

The results from studies of the dynamic behavior of a double pendulum under the action of a follower force are analyzed. It is pointed out that bifurcations and catastrophes of equilibrium states may occur at some values of the parameters. Differential equations are presented which describe the plane-parallel motion of a pendulum with an arbitrary number of links and angular and linear eccentricities of the follower force whose orientation depends on one parameter. The basic problems of dynamics of pendulums with different number of links are formulated __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 3–35, June 2005.     

结构阻尼模型及系统时域动响应

振动界对经典的非频变结构阻尼模型一直有种种争议,本文检查了它的前提并指出将该模型推广到系统时域动响应分析时导致的悖论.为了提供结构阻尼系统的时域动响应实用分析方法,文中分别提出了基于响应优势谱成份的粘性阻尼近似模型和基于粘弹性理论的三参数频变结构阻尼模型;它们既可逼近结构阻尼缓频变的特性,又可保证系统的时域动响应具有因果性.     

Analysis of Stability and Instability Regions in Parametrically Excited Hamiltonian Systems

Qualitative analysis of parametrically excited linear Hamiltonian systems is carried out. It is proved that the stability and instability regions are convex in the excitation frequency. Lower bounds for the boundaries of some instability regions are obtained expressed in the natural frequencies of the system in the absence of a parametric excitation. It is shown that a dominant high-frequency excitation affects the stability regions similarly to an increase of the natural frequencies. Some of these findings extend known results, obtained by asymptotic methods under the assumption that the parametric excitation is small or its frequency is large, to finite values of the excitation and frequency.     

Damping of Forced Vibrations in Systems of Connected Rigid Bodies

The problem of damping forced vibrations in a system of bodies linked by one-degree-of-freedom elastic joints is considered. The vibrations are damped by introducing additional bodies into the system. The controlled motion of these bodies compensates the effect of the external perturbation. The motion of a system of three bodies is studied in detail. To determine the sensitivity of the perturbation compensation method to the damping parameters, a numerical simulation is carried out     

动力扰动诱发巷道围岩冲击失稳的能量密度判据

能量积聚程度及积聚位置是判别冲击矿压是否发生的两个重要参数,运用ANSYS/LS-DY-NA模拟了应力波作用下巷道围岩的能量积聚过程及应力波强度对能量积聚程度的影响,得到了一定围岩应力状态下巷帮围岩能量积聚的大小、位置等结果.模拟研究表明:应力波是巷帮能量积聚、继而诱发冲击矿压的一个重要因素;应力波强度决定了最大能量密度值及其位置,随着扰动应力波强度的增加,巷道围岩的最大能量密度随之增加,最大能量密度点的位置渐渐向巷帮边界面靠近.研究结果对揭示煤矿冲击矿压的诱发机理及冲击矿压发生的预测预报具有重要意义.     

空间框架结构动力不稳定区域的确定

讨论了大型空间框架结构在周期性载荷作用下动力不稳定区域的确定,提出了求解非齐次方程的方法,使动力稳定性分析的范围得以扩展。     

The Dynamics of Finite-Dimensional Systems Under Nonconservative Position Forces

General theorems on the stability of stationary states of mechanical systems subjected to nonconservative position forces are presented. Specific mechanical problems on gyroscopic systems, a double-link pendulum with a follower force and elastically fixed upper tip, multilink pneumowheel vehicles, a monorail car, and rail-guided vehicles are analyzed. Methods for investigation of divergent bifurcations and catastrophes of stationary states are described     

Dynamic Bifurcation of Multibody Systems

In this paper, the process of loss of stability of multibody systems and structures is analyzed. A novel approach is presented and applied to the statically loaded spatial systems for the analysis of a dynamic response of systems imposed on impact, high velocity compulsive motion, or percussive forces. The analysis is based on the solution of the dynamic equations and eigenvalue problem of systems, and of the resultant motion simulation. The flexible systems are discretized using the finite element method. The dynamic equations are derived with respect to the relative coordinates of the finite elements. Large flexible deflections due to a loss of stability are simulated. The initial forms of the possible deformations are defined by the computed eigenvectors solving the eigenvalue problem for the system stiffness matrix. The critical forces and system deflections are then analyzed. Examples of bifurcation of beam and beam structure imposed on compulsive motion, percussive forces, and impact are presented.     

Graphene Size and Morphology: Peculiar Effects on Damping Properties of Polymer Nanocomposites

Experimental Mechanics - Nanomaterials with their extremely high free surfaces can effectively augment damping in nanocomposites via frictional sliding along the interface of nanomaterials and a...     

Dynamic Analysis of a Two-Mass System with Essentially Nonlinear Vibration Damping

A nonlinear system with two degrees of freedom is considered. The system consists of an oscillator with relatively large mass, which approximates some continuous elastic system, and an oscillator with relatively small mass, which damps the vibrations of the elastic system. A modal analysis reveals a local stable mode that exists within a rather wide range of system parameters and favors vibration damping. In this mode, the vibration amplitudes of the elastic system and the damper are small and high, respectively__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 102–111, January 2005.     

粘弹性阻尼结构系统振动特性的迭代分析

含粘弹性阻尼材料结构系统的振动特性分析是相当复杂的,求解比较困难,本文给出了一种有效的迭代解法。文中首先定义了广义Rayleigh商,指出求广义Rayleigh商的驻值问题等价于原特征问题的求解;由近似估计得到的特征向量,广义Rayleigh商给出一个较好的特征值近似估计。据此构造了迭代方法,并成功地计算了一些例子。     

Stability Analysis of Continuous Systems with Structural Perturbations

The paper is a survey of the development of the direct Lyapunov method based on matrix-valued functions for systems with structural perturbations. Sufficient conditions for stability in the large, uniform asymptotic stability in the large, exponential stability in the large, and instability of nonlinear continuous systems under structural perturbations are presented.     

Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time.     

Principal Trajectories of Forced Vibrations for Discrete and Continuous Systems

Principal trajectories of forced vibration of linear and nonlinear continuous systems are introduced as such motions in which the system is equivalent to a Newtonian particle in the function space of the system configurations. The corresponding 'effective mass' of the particle gives physical characteristics of the system response, so that zero effective mass is associated with resonance. The methodology can be viewed as a complementary tool to the method of normal modes, when considering the class of forced vibrating systems, since the related basis accounts for the system physical properties as well as the external forcing factor. In particular, it is shown that a two degrees of freedom system can possess an infinite discrete set of in-phase and out-of-phase forced vibrations of the normal modes type. The corresponding forcing vector-functions obey the second Newton law due to the definition of principal trajectories.