索-梁组合结构主共振响应的时滞反馈控制

基于时滞加速度反馈控制策略对索-梁组合结构进行振动控制。根据Hamilton原理推导了索-梁组合结构非线性振动控制方程,运用多尺度法得到时滞反馈作用下索-梁组合结构主共振的一阶近似解,得出系统响应与控制参数的关系以及响应峰值和临界激励值与时滞参数的表达式。结果表明,主共振的响应存在多解和跳跃现象,调节控制增益和时滞值,可以有效抑制大幅振动。     

一类强非线性机械基础系统的亚谐振动解析解

建立了机械基础动力系统的强非线性动力学模型，利用能量法对该系统的周期解进行了解析研究，确定了系统动态参数满足周期解的条件、系统的周期解以及解的稳定性判别式。发现了亚谐振动，并给出了系统在满足周期解条件下的一组参数对应的主振动、1／3亚谐振动和1／5亚谐振动。最后利用数值积分方法计算了系统在给定条件下的主振动及亚谐振动解，考察了解析解的正确性。     

周期荷载激励下覆冰输电线的主共振及谐波共振分析

为了研究动态风对覆冰输电线非线性舞动特征的影响,在原有稳定风作用下覆冰输电线舞动控制方程中添加周期激励载荷,并建立了新的受迫-自激振动控制方程,该控制方程也适用于描述相邻档导线对舞动档导线运动特征的影响.运用多尺度法分别对弱激励和强激励下的受迫-自激振动求解,得到主共振和谐波共振的幅频响应函数,分析了受迫-自激系统的主...     

多关节机械臂系统非线性动力学分析

针对工程机械臂的非线性振动,研究了系统因周期运动失稳而产生Hopf分岔问题．工程机械臂在建模时往往忽略非线性因素,然而在特殊场合下非线性的影响不可忽略,本文利用拉格朗日法建立了新的非线性两关节机械臂系统的两自由度动力学方程,采用多尺度法对机械臂系统模型进行了求解,对系统发生主共振时的动力学行为进行了分析讨论．结果表明所求得的近似解析解与数值解具有较好的吻合性,同时由于系统方程中非线性项的影响,随着激励幅值与激励频率的变化,系统的振幅会发生跳跃,出现动态分岔现象．本研究为实际工程应用提供了一些理论依据和指导．     

强非线性动力系统周期解分析

给出一类强非线性动力系统周期解存在性，唯一性和稳定性的简易差别法以及周期解的摄动法。本差别法把问题归结为干扰力在相应的未扰系统振动周期上的功函数及其导数的讨论，其限制条件比现有结果弱。本摄动法可以认为是经典Ｌｉｎｄｓｔｅｄｔ－Ｐｏｉｎｃａｒｅ（Ｌ－Ｐ）法在强非线性振动系统的推广。它与Ｌ－Ｐ法的主要区别在于假设系统的振动频率为相角的非线性函数。     

非线性振子的主共振——基本参数共振

在本文里我们用多尺度法和数值方法研究了非一性振动系统在主共振－－基本参数共振时的分岔响应，得所结果说明在这个系统里存在着主共振与基本参数共振之间的相互作用。     

多自由度振动系统的快速控制

研究多自由度振动系统的时间最优控制问题．利用主振型的正交性，将多自由度系统的振动变换为一系列独立的主振动，在分别求得各阶主振动的快速控制表达式后，再由振型变换得整个系统的快速控制解，代入约束条件得最速时间应满足的方程，由计算机数值求得最速时间．     

保守系统强非线性强迫振动问题的一种解法

本文用新的改进的L-P法求得了一类保守系统强非线性强迫振动问题的一级近似共振周期解,近似解比已有改进的L-P法的相应解更加准确。     

变厚度圆板的非线性强迫振动

本文研究了厚度呈幂指数规律变化的变厚度圆饭的非线性强迫振动问题。文中首先用半解析法求解了动态Von Ka＇rma＇n大变形方程,导出了周期均布荷载作用下轴对称变厚度薄圆板的非线性强迫振动微分方程。然后用小参数摄动法求解了振动方程,得到了非线性的非共振周期解和共振周期解。绘制了振幅——频率关系图。     

温度场中非线性弹性地基上矩形薄板的主共振-主参数共振

为了研究温度场中非线性地基上矩形薄板受简谐激励的主共振-主参数共振问题,应用弹性力学理论建立其动力学方程,应用Galerkin方法将其转化为非线性振动方程.利用非线性振动的多尺度分析方法求得系统主共振-主参数共振的近似解,并进行数值计算.分析温度、地基系数、阻尼、几何参数、激励等对系统主共振-主参数共振的影响.得到了随参数变化响应曲线的变化规律.     

SUPPRESSION OF BENDING WAVES IN A PERIODIC BEAM WITH TIMOSHENKO BEAM THEORY

Active control of bending waves in a periodic beam by the Timoshenko beam theory is concerned. A discussion about the possible wave solutions for periodic beams and their control by forces is presented. Wave propagation in a periodic beam is studied. The transfer matrix between two consecutive unit cells is obtained based on the continuity conditions. Wave amplitudes are derived by employing the Bloch-Floquet theorem and the transfer matrix. The influences of the propagating constant on the wave amplitudes are considered. It is shown that vibrations are still needed to be suppressed in the pass-band regions. Wave-suppression strategy described in this paper is employed to eliminate the propagating disturbance of an infinite periodic beam. A minimum wave-suppression strategy is compared with the classical wave-suppression strategy.     

Nonlinear Dynamics and Stability of a Machine Tool Traveling Joint

In this work, we investigate the nonlinear dynamics and stability of a machine tool traveling joint. The dynamical system considered includes contacting elements of a lathe joint and the cutting process where the onset of instability is governed by mode coupling. The equilibrium equations of the dynamical system yield a unique fixed point that can change its stability via a Hopf bifurcation. The unstable domain is primarily governed by the cutting tool location, the contact stiffness of the joint and the depth of material to be removed. Self excited vibrations due to a mode coupling instability evolve around the unstable fixed point and one or more limit cycles may coexist in the statically unstable domain. Stability and accuracy of the approximate analytical solutions are analyzed by applying Floquet analysis. Perturbation of the dynamical system with weak periodic excitation results with periodic and aperiodic solutions.     

雨刮器非线性摩擦振动的稳定性与分岔特性

针对雨刮器建立2自由度非线性摩擦振动动力学模型,基于复模态理论计算复特征值并进行稳定性及其对刮刷速度的依赖性分析;通过数值计算分析摩擦振动对刮刷速度的分岔特性,并利用相轨迹、庞加莱映射、频谱特性分析不同刮刷速度下的非线性振动现象.研究发现:摩擦-速度特性的负斜率是导致系统不稳定的根本原因,增大刮刷速度有利于提高系统的稳定性;在高、低刮速区,随着刮刷速度的下降,系统振动形态遵循周期→准周期→混沌的演化规律,并会伴随显著的粘滑振动;仅高速区的周期振动和非振动条件下,刮刷时无附加的粘滑振动.     

Bifurcation Analyses in the Parametrically Excited Vibrations of Cylindrical Panels

We consider parametrically excited vibrations of shallow cylindrical panels. The governing system of two coupled nonlinear partial differential equations is discretized by using the Bubnov–Galerkin method. The computations are simplified significantly by the application of computer algebra, and as a result low dimensional models of shell vibrations are readily obtained. After applying numerical continuation techniques and ideas from dynamical systems theory, complete bifurcation diagrams are constructed. Our principal aim is to investigate the interaction between different modes of shell vibrations under parametric excitation. Results for system models with four of the lowest modes are reported. We essentially investigate periodic solutions, their stability and bifurcations within the range of excitation frequency that corresponds to the parametric resonances at the lowest mode of vibration.     

Nonlinear vibrations of cylindrical shells filled with a fluid and subjected to longitudinal and transverse periodic excitation

The paper proposes an approach to studying the nonlinear vibrations of thin cylindrical shells filled with a fluid and subjected to a combined transverse–longitudinal load. Methods of nonlinear mechanics are used to find and analyze periodic solutions of the system of equations that describes the dynamic behavior of the shell when the natural frequencies of the shell and the frequencies of both periodic forces are in resonance relations.     

STUDY OF PARAMETRIC VIBRATION OF GYROSCOPIC CONTINUA BASED ON NONLINEAR NORMAL MODES AND A NUMERICAL ITERATIVE APPROACH

以脉动流输流管为例,利用非线性模态技术和一种数值迭代法研究陀螺连续体的非线性参数振动响应问题. 通过谐波平衡法将系统非线性非自治控制方程转化为拟自治方程,并在状态空间上利用不变流形法构造系统的非线性模态. 以对应自治系统的解为初值,采用一种数值迭代法来求解拟自治控制方程的模态系数,结果证明了该迭代法的快速收敛性. 在频域分析中得到了幅频响应和相空间上的不变流形,而在时域复模态分析中则发现了参激陀螺系统的正交相位差和行波振动现象.     

The effect of parametric excitation on a self-excited three-mass system

This contribution deals with the quenching of self-excited vibrations by means of parametric excitation due to periodic variation of spring stiffness. A three-mass chain system is investigated in detail. It is shown that the self-excitation can be fully or partly suppressed in a particular frequency interval.     

干摩擦控制振动的应用

干摩擦能衰减机械振动的现象早为人们所熟悉。但是很长一段时期,干摩擦应用到控制振动上的例子不多见。这是由于干摩擦的性能不好掌握和干摩擦会使系统变为非线性,设计、计算就很复杂。 干摩擦振动系统是非线性系统。以振动系统中的一个干摩擦接头来说明。当接头上的力     

Influence of periodic excitation on self-sustained vibrations of one disk rotors in arbitrary length journals bearings

Interaction of forced and self-sustained vibrations of one disk rotor is described by nonlinear finite-degree-of-freedom dynamical system. The shaft of the rotor is supported by two journal bearings. The combination of the shooting technique and the continuation algorithm is used to study the rotor periodic vibrations. The Floquet multipliers are calculated to analyze periodic vibrations stability. The results of periodic motions analysis are shown on the frequency response. The quasi-periodic motions are investigated. These nonlinear vibrations coexist with the periodic forced vibrations.     

A numerical treatment of the periodic solutions of non-linear vibration systems

Direct numerical integration can be used to find the periodicsolutions for the equations of motion of nonlinear vibrationsystems.The initial conditions are iterated so that theycoincide With the terminal conditions.The time interval ofthe integration(i.e.,the period)and certain parameters ofthe equations of motion can be included in the iterations.Theintegration method has a variable stoplength.This Sbooting method can produce periodic solutions witha shorter computex time.The only error occurs in the numeri-cal integration and it can therefore be estimated and madesmall enough.Using this method one can treat a variety ofvibration problems.such as free conservative.forced.para-meter-excited and self-sustained vibrations with one or se-veral degrees-of-freedom.Unstable solutions and those Whichare sensitive to parameter Changes can also be calculated.Thestability of the solutions is investigated based on the thecryof differential equations with periodic coefficients.The ex-trapolation method and the proc