Problem of Vibration Testing of Space Structures

The results of numerical analysis of the parameters of the first-order synergistic effect are analyzed. They are formalized by means of the amplitude-phase-frequency characteristics of a space structure in absolute coordinates as applied to vibration-reliability problems. The synergistic factor is used to estimate quantitatively and qualitatively the synergistic effect of the vibration parameters of the housing on the vibration stability of the test structure __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 116–121, July 2005.     

GLOBAL BIFURCATION AND CHAOS IN A VAN DER POL-DUFFING-MATHIUE SYSTEM WITH A SINGLE-WELL POTENTIAL OSCILLATOR

The global bifurcation and chaos are investigated in this paper for a van der Pol-Duff-ing-Mathieu system with a single-well potential oscillator by means of nonlinear dynamics. The au-tonomous system corresponding to the system under discussion is analytically studied to draw all globalbifureation diagrams in every parameter space, These diagrams are called basic bifurcation ones. Thenfixing parameter in every space and taking the parametrically excited amplitude as a bifurcation param-eter, we can observe how to evolve from a basic bifurcation diagram to a chaos pattern in terms of nu-merical methods. The results are sufficient to show that the system has distinct dynamic behavior, Fi-nally, the properties of the basins of attraction are observed and the appearance of fractal basin bound-aries heralding the onset of a loss of structural integrity is noted in order to consider how to control theextent and the rate of the erosion in the next paper.     

Amplitude bounds of linear forced vibrations

Summary For reasons of safety and reliability, the maximum amplitudes of vibration responses must be taken into account in engineering. The exact maximum amplitudes are available from solving linear differential equations. However, for large scale systems, it requires too much computation time to be useful. Therefore, simple amplitude bounds are of great interest for engineers. Up to now, only for classically dampled linear systems, some approximate amplitude bounds were presented. In this paper, amplitude bounds of linear forced vibrations are presented for general dampled linear vibrating systems. For transient, harmonic and step excitations, the presented amplitude bounds show simple relations to the system parameters, and are easy to calculate. The advantage is the possibility to judge the level of vibrations, and to choose appropriate parameters at design. Compared with the approximate underestimating amplitude bounds available in literature, the presented amplitude bounds are overestimating the maximum amplitude and, therefore, can be safely applied to general damped vibrating systems.The paper is dedicated to Prof. Dr.-Ing. Dr.-Ing. E.h. Dr.h.c. mult, Erwin Stein, on the occasion of his 65th birthday.     

Forced oscillations of a vertical continuous rotor with geometric nonlinearity

Nonlinear forced oscillations of a vertical continuous rotor with distributed mass are discussed. The restoring force of the rotor has geometric stiffening nonlinearity due to the extension of the rotor center line. The possibility of the occurrence of nonlinear forced oscillations at various subcritical speeds and the shapes of resonance curves at the major critical speeds and at some subcritical speeds are investigated theoretically. Consequently, the following is clarified: (a) the shape of resonance curves at the major critical speed becomes a hard spring type, and (b) among various kinds of nonlinear forced oscillations, only some special kinds of combination resonances have possibility of occurrence.     

变系数曲线支承矩形厚板自由振动的傅里叶分析

本文给出了变系数曲线支承的Ａｍｂａｒｓｕｍｉａｎ矩形厚板自由振动问题的级数解，将位移和剪力在板域内展成重傅里叶级数，将其导数在边界上展成单傅里叶级数，通过傅里叶变换将控制微分方程和边界条件转化成关于位移级数的系数的一组无穷线性代数方程，最终将板的自由振动问题转化为矩阵特征值问题。     

考虑摆振的裂纹转子运动及阵发性混沌

在考虑含裂纹转子盘的摆振运动的情况 ,建立了盘的运动方程并进行数值求解。在裂纹很小时 ,横向振动是与转速相同的同频振动 ,而盘的摆振包含多种倍频成分。当裂纹较大时 ,横向振动会出现阵发性混沌。当摆振的幅值随时间不断增大到一定极限时 ,横向振动的稳定的周期或拟周期运动被打破 ,出现阵发性混沌。同时还出现通过拟周期进入混沌的现象。当裂纹很深时 ,会出现多个新的共振区 ,在此区域振幅迅速发散。盘的偏心距U的增大 ,会抑制混沌 ,使混沌运动锁定到周期运动     

区间参数振动系统的动力优化

对具有区间参数的多自由度振动系统的不确定性优化问题，提出一种新的区间优化方法．利用泰勒展开和函数的区间扩张，将区间优化问题转化为近似的确定性优化问题．该方法应用于多自由度线性扭振系统，并把区间设计变量的中值和不确定性半径取作优化参数．算例表明该方法是有效的．     

矩形弹性壳液耦合系统中的重力波分析

根据非线性动力学理论，建立了矩形壳液耦合系统的非线性振动方程组，通过数值求解，发现当激振频率为壳体固有频率与重力波频率之和，且激振力足够大时，会产生大幅低频重力波，通过实验验证，发现了壳液耦合系统中存在的大幅低频重力波现象，实验结果与理论结果基本吻合。     

周期集中载荷作用下球形扁壳的非线性振动问题

本文用半解析法推导了周期集中载荷作用下,周边固定球形扁壳的非线性振动微分方程.然后用小参数法求出了非线性的非共振周期解和共振周期解.绘出了不同几何特征参数下的振幅——频率图.     

Nonstationary Vibrations of a String with Time-Varying Length and a Mass-Spring Attached at the Lower End

The purpose of this paper is to study the nonstationary vibration of a string with time-varying length and a mass-spring system attached at the lower end. The string is hung vertically and excited sinusoidally by a horizontal displacement at its upper end. The mass is supported by a guide spring horizontally and has two-degrees-of-freedom, vertical and horizontal. It is shown analytically that axial velocity of the string influences the peak amplitude of the string vibration at the passage through resonances. Moreover, it is shown numerically that the amplitudes of both the string and the mass vibrations depend on the sign of the axial velocity, when the natural frequency of the mass-spring system is close to the frequency of the excitation. The above two theoretical results are confirmed experimentally with a simple experimental setup.