阻尼谐振动

Firstly, this paper researched the mechanism of tubing string vibration when natural gas flows in horizontal well tubing string. Secondly, established whole tubing string undamped and damped vibration system model according as reasonable assumption data of one horizontal well. Apply finite element analysis software to calculate tubing string natural characters, simple harmonic dynamic behavior of stable gas production and nonlinear dynamic behavior. Finally, this paper carried out the safety varied frequency of gas well and the method of vibration reduction.

本文首先从理论和数值模拟研究了天然气在水平井油管柱内的流动诱发油管柱振动的机理，然后在合理假设的基础上结合某水平井数据建立了全井段油管柱无阻尼和有阻尼振动系统模型，利用有限元软件计算分析了油管柱固有特性、稳产简谐动力学响应和非线性动力学响应，针对油管柱振动规律提出了天然气安全调节频率范围和减振措施。

The method of multiple scales was used to solve the Duffing equation, the solutions were used to analyze qualitatively the effect of boundary conditions, ratio of damp, external excitation, and ratio of inner radius to outer radius on the second-harmonic resonance of an annular thin plate.

用多尺度方法求此振动控制方程的3次超谐共振解和1/3亚谐共振解，并且定性地探讨边界条件、内外半径比、激振力和阻尼对环形薄圆板在这两种次谐共振下的动态响应。

The vibro-impact systems are familiar with the non-smooth dynamic systems.The dynamics research of the vibro-impact systems not only is significant in theory but also has practical values in engineering.Firstly,using the Poincaré map method,we get an existent criterion of single impact period-n motion in a two-degree-of-freedom vibro-impact system with damper.It is shown that our conclusions are valid through the numerical simulations.Moreover,the satiability of periodic motions is studied and the correspon...

基于Poincaré映射的方法，通过解析的方法导出了一类具有阻尼的两自由度碰撞振动系统的单碰周期n次谐运动存在性判据，经过数值模拟验证了理论分析的正确性，并给出了分析其稳定性的判别公式，通过数值模拟，讨论系统的局部分岔与全局分岔，同时比较了系统参数变化对其周期运动的影响，发现在强阻尼、弱激励、小质量比、较大恢复系数下系统将会出现较多的有规律的周期碰撞。

The distribution of gear's contact stress, root stress, and contact engagement line in the engagement situation of gear pairs, were obtained on the base of explicit integration method. 3. Adopting the method of system matrix, the torsional vibration differential equation of general shafting was gained. The simple harmonic forms of excitation torque under the normal combustion or piston flameout of in-line engine and v-type engine were analysed. The decoupled algorithm of free vibration and forced vibration and the solution to the vibration damper's energy of resistance and the off-resonance calculation were studied. The sensitivity formulations of the natural frequency and vibration mode to physical parameters of system were derived by solving the eigenvalue problem. These sensitivity formulations provided the theoretical base for the dynamic modification of structure.

运用系统矩阵法建立了轴系的扭振微分方程，并对直列和V型发动机在正常发火和气缸熄火工况下的激振力矩进行了详细的简谐分析；基于精确方法推导了自由振动和强迫振动的解耦算法，给出了能量法计算中的减振器阻尼功求解和非共振计算方法；并研究了曲轴系扭振非线性分析中的变惯量问题，得到了单缸转动惯量的精确求解公式以及变惯量和固有频率的关系式；最后，从特征方程和振型正交性出发，推导了固有频率和振型对轴系转动惯量和刚度等物理参数的灵敏度，为扭振系统的结构动力学修改提供了理论基础。

Taking a single disk rotor with hinged ends as research object, to a different forward and backward whirling type the effect and its innate laws of the magnitude and acting direction of the constant torque on the stability are proposed by means of the eigenvalue theory of real linear systems.

以两端简支的单圆盘转子为对象，利用非线性振动理论的多尺度方法，研究了简谐扭矩作用下具有时变参数激励系统的近似解，指出系统出现不稳定组合式共振的可能性并给出了定常扭矩、简谐扭矩、外阻尼对不稳定区域边界条件的影响。

Simulations of forced response of mistuned bladed disks with non-linear dry friction damping were performed.

摘要基于谐波平衡法，提出一种可用于分析含有非线性摩擦阻尼叶盘振动响应的多谐波法，对含有非线性干摩擦阻尼的失谐叶盘系统的受迫响应进行仿真计算。

The resonant features of both tuned and mistuned systems are investigated by using this method under various system coupling strengths, viscous dampings, and dry friction dampings, etc.

利用该方法对带有叶间干摩擦阻尼的叶盘受迫振动响应进行了仿真计算，分析了叶盘系统在谐调和失谐两种情况下受耦合强度、黏性阻尼和干摩擦阻尼等系统参数影响下的共振特性。

Because the error mainly comes from theresonant region, the error correction method can only be used in resonant region, andcan effectively improve the efficiency of the statistical analyzing solutions. Two types of the mistuned bladed disks, whose friction damping are blade dryfriction damping and blade-to-blade dry friction damping, are modeled respectively. Amulti-harmonic method which can employ the fast Fourier transformationtechnique is proposed to investigate the vibratory response of the bladed disks withthese two types of nonlinear friction damping. Formulations of the solution for thesetwo types of motion functions are deduced. The characteristics of the forced responseof the bladed disks with these two dry friction damping are analyzed and summarizedunder various system parameters. The vibratory response of the bladed disk with dryfriction scatter mistuning is investigated.

针对叶盘系统中两类主要的非线性干摩擦阻尼形式，分别建立了具有叶片干摩擦阻尼和叶间干摩擦阻尼的失谐叶盘系统的非线性力学模型；提出了一种可利用快速傅立叶变换技术的多谐波分析方法；分别推导了具有这两类干摩擦阻尼形式的叶盘系统运动方程的求解公式；在各种系统参数条件下，研究了干摩擦阻尼失谐叶盘系统的受迫振动响应特性；对具有干摩擦散乱失谐的叶盘系统振动响应进行了研究，分析总结了干摩擦散乱失谐对叶盘系统振动响应特性的特殊影响规律。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。