轴向加速度运动弦线横向振动的数值计算方法

讨论轴向加速度运动弦线横向振动的数学模型、数值计算方法等问题。基于Coriolis加速度和Iagrangian应力公式，利用Newton第二定律导出轴向加速度运动弦线横向振动的动力学模型；通过线性变换将方程化为一阶无量纲的非线性微分方程组；并利用Crank-Nicoson的中点离散技巧，给出运动方程的单步二阶差分方法；算法把对运动方程和本构方程分别离散，使之可以用于不同本构的运动弦线的数值仿真。且方法对线性问题绝对稳定，对非线性问题也有较好的稳定性。作为应用实例，利用该方法对一类加速度运动弦线的横向振动进行数值仿真，利用弹性弦线的守衡公式检验数值结果的精度。并利用给出的数值方法分析速度、加速度、弹性模量等参数对弦线横向振动的影响。     

随机激励下掘锚联合机纵向非线性振动特性分析

将虚拟仿真方法、Bekker模型、Newmark-β法相结合,分析了打顶部锚杆孔时掘锚联合机的非线性振动特性。采用DYNA虚拟仿真获得锚杆钻头的阻力载荷,利用采样定理对载荷进行离散化处理,作为钻头的随机工作载荷;采用Bekker模型描述了掘进机履带与巷道底板间的非线性行为,再根据牛顿运动学定律建立了掘锚联合机多自由度非线性振动方程,利用Newmark-β法对方程进行了求解,分析了整机的振动特性,结果表明：受履带与底板间非线性接触力的影响,整机振动处于混沌态;锚杆钻机工作时,整机虽然存在着俯仰和横滚振动,但振动量很小,整机的竖直振动占主导地位。对掘锚联合机的振动特性进行了现场实验,测量打10组锚杆孔时掘进机本体的振动量,测量结果中有6组的振动量均方根值接近仿真值（1.5mm）,实验结果表明掘锚联合机的非线性模型在一定程度上可以视为是准确的。     

激光振动仪多普勒信号振动速度频谱的评定

在多普勒信号数字离散化处理的基础上。根据激光振动仪的振动速度的频谱分析,提出了用局部近似的方法来对振动速度进行评定和估算,得出了用局部多项式模型来减少离散傅里叶变换处理的维数。     

挥舞旋转运动薄板磁弹性振动分析

基于非线性薄板理论假设,建立了旋转运动柔性薄板在横向磁场环境下的振动方程。应用Maxwell电磁定律得出导电薄板的电磁本构关系,得到了Lorentz力的表达公式。在考虑了薄板横向变形引起的轴向缩短基础上,使用Hamilton原理推导出在磁场中旋转运动薄板的变分方程,并使用Galerkin法对方程进行离散,研究了旋转运动、磁场强度以及薄板长宽比对薄板振动的影响。     

被动隔振的非线性动力学研究

研究了由基础振动激励的被动隔振体的非线性振动特性和振动稳定性。考虑隔振系统的非线性刚度和隔振材料的非线性阻尼,建立了被动隔振体的非线性动力学方程;用谐波平衡法研究了其非线性振动特性,导出了频率响应方程;讨论了非线性因素的影响;分析了隔振体振动的稳定性,得出了稳定区和不稳定区的分界线方程。     

拉索平面内自由振动影响因素分析

考虑抗弯刚度、垂度和几何非线性的影响，建立了拉索非线性自由振动方程，针对考虑与否垂度和几何非线性，分别建立了线性无垂度和有垂度理论、非线性无垂度和有垂度理论，用谐波平衡法求得拉索振动固有频率的近似解析解。其结果与龙格-库塔积分法得到的结果较为一致。此外，还给出了抗弯刚度、垂度和几何非线性对拉索振动固有频率影响的定量判定。     

波纹圆薄板的非线性振动

以圆柱正交异性板代替波纹板［１］，试图通过在圆柱正交异性Ｋａｒｍａｎ型静力方程中引入惯性力来反映波纹板的动力学问题。求解时以正交完备Ｌｅｇｅｎｄｒｅ多项式构成挠度试函数，由相容方程找出应力函数，然后用加权残数法使平衡方程的残差极小化，得出时间函数的Ｄｕｆｆｉｎｇ方程。一次近似求得了波纹板线性振动时的固有频率及非线性固有频率，并得到了强迫振动时的幅频关系。一些结果与有关文献进行了比较，表明本文的尝试是可行的，以Ｌｅｇｅｎｄｒｅ多项式构成挠度函数收敛快、精度高。     

轴向载荷作用下细长柔性旋转梁横向振动响应分析

将水平井柔性钻柱简化为轴向载荷作用下的细长柔性梁,建立了考虑几何大变形的非线性动力学方程,并且利用多重尺度法得到了柔性梁横向振动的平均方程。因钻柱转速和轴向力是影响钻柱振动的两个主要参数,故用改变转速的方法来对平均方程进行非线性动力学响应分析,给出了一阶、二阶模态下钻柱随转速变化的分叉图和不同转速下的相图。分析结果表明,系统响应经历了从周期到混沌再到二倍周期的变化过程,振动幅值有跳变现象出现,在共振条件下,柔性旋转梁振动幅值是有限值,并非无穷大,当轴向力发生变化时,可以通过控制转速变化达到定性、定量地控制柔性钻柱横向振动的目的。     

空心轴偏置盘转子系统横向非线性振动特性研究

将能量守恒法、拉格朗日方程、增量谐波平衡法和四阶龙格-库塔法相结合,分析了空心轴偏置盘转子系统的横向非线性振动特性。首先对空心轴偏置盘转子系统进行非线性建模求出总机械能,并用拉格朗日方程建立非线性振动方程。然后,采用增量谐波平衡法对非线性方程进行数值计算,求出幅频特性曲线,并用四阶龙格-库塔法进行积分计算。最后,分析了不同参数对偏置盘转子系统非线性振动的影响。结果表明:外阻尼系数、偏心质量与偏心半径乘积仅影响非线性振幅大小;空心轴内径,盘在轴的位置除了影响非线性振幅大小外,还会影响非线性振动的频率。     

复合材料薄壁箱梁的非线性自由振动分析

根据复合材料特性、梁的几何非线性和哈密尔顿原理,建立了复合材料薄壁梁的模型及非线性平衡方程。基于悬臂梁的边界条件,对非线性自治系统进行有限差分离散处理,得到了系统的质量和刚度矩阵。运用MATLAB振动工具箱进行模态分析,求得CUS和CAS架构下薄壁箱梁的前三阶固有频率与铺层角的变化关系,并对两种架构下的结果进行对比分析。在有限差分离散的基础上建立非线性薄壁梁的状态空间,运用时间离散和MATLAB振动工具箱对非线性自治系统进行仿真,求得CUS架构下不同铺层角度时的时间位移曲线和非线性振动幅度与铺层角之间的变化关系。     

Modeling of Coriolis mass flow meter of a general plane-shape pipe

The vibration of a general plane tube with a flowing fluid, which is the measuring element in a Coriolis mass flow meter (CMF), is studied. The dynamic stiffness matrix method is used to model such a tube. The tube is divided into straight and circular elements. The elements dynamic stiffness matrices are derived from the equations of motion. By assembling the elements matrices into a global matrix the natural frequencies are obtained. The mode shapes are obtained by applying the boundary conditions at the supports and the compatibility conditions at the nodes. The effects of the flow velocity on the natural frequency and the relative phase difference are modeled. The method is applied to different tube shapes. The results are compared to the published data which reveals good agreement.     

Effects of dissipative forces on Coriolis flowmeter readings

An indirect measurement method based on recording the phase difference of resonance vibrations of two symmetrical halves of the flow-carrying tube is used to quantify the mass flow rate of the current fluid in Coriolis mass flowmeters (CMFs). A variant of modeling the CMF vibration system is analyzed, which allows taking into account the influence of the dissipation of oscillations of a measuring tube with fluid flowing through it on the dependence between the mass flow rate of the fluid and the phase difference recorded by the sensor. The steady-state CMF vibration mode is considered as the result of the superposition of two principal vibrations of the measuring tube. The first principal coordinate corresponds to the deformation of the measuring tube along the lowest natural mode excited by an external driving force in the resonance mode. Vibrations of the other principal coordinate correspond to deformation in a natural mode corresponding to a higher natural frequency than the frequency of the exciting force. The relationship of the amplitudes of the principal coordinates is established on the basis of the gyroscopic coupling of the principal vibrations that occurs when a fluid flows through a tube. The coefficients of gyroscopic coupling are determined as a result of 3D finite-element simulation of the steady-state vibration mode of the measuring tube with a flowing fluid. The simulation is performed for five variants of the shape of the axis of the measuring tube, taking into account the distribution of the gyroscopic forces of the flowing fluid. Quantitative estimates of the influence of dissipative forces on the flowmeter readings are obtained on the example of dissipative forces of linear viscous friction. A comparison of the CMF simulation results for different tube axis shapes demonstrates how the phase shift arising in the vibration system is affected by the dissipation level and the proximity of the natural frequencies of the flowmeter measuring tube at a fixed mass flow rate of the fluid.     

功率超声珩磨缸套加工中谐振系统的试验研究

针对特种加工方法－－功率超声振动加工中的关键技术－－谐振系统的研究进行了一系列的试验研究，从为幅杆、弯曲振动圆盘、振子系统等方面进行了详细的介绍。     

金属材料加工中的振动利用问题

综合评述了几十年来在金属材料加工中利用振动的若干理论和试验成果。主要包括振动拉伸、振动切削、振动剪切、振动轧制的试验和工程应用情况。对振动加工的机理问题进行了探讨,并提出了在这一领域有待深入研究的主要课题。     

Free vibration analysis of multi-directional functionally graded circular and annular plates

This paper addresses the free vibration of multi-directional functionally graded circular and annular plates using a semianalytical/ numerical method, called state space-based differential quadrature method. Three-dimensional elasticity equations are derived for multi-directional functionally graded plates and a solution is given by the semi-analytical/numerical method. This method gives an analytical solution along the thickness direction, using a state space method and a numerical solution using differential quadrature method. Some numerical examples are presented to show the accuracy and convergence of the method. The most of simulations of the present study have been validated by the existing literature. The non-dimensional frequencies and corresponding displacements mode shapes are obtained. Then the influences of thickness ratio and graded indexes are demonstrated on the non-dimensional natural frequencies.     

Dynamic analysis of a short cylinder piezo motor

The bar-type traveling wave ultrasonic motor is simple, inexpensive, easy to use, and suitable for miniaturization. Its operating performance is significantly affected by the dynamic behavior of the vibrator. In this work, the analytical equations for calculating the dynamic behavior of the motor vibrator are presented using the ring model. The natural frequencies and vibrating modes of the motor are investigated using the analytical equations. Changes in the natural frequencies along with the motor parameters are analyzed. The forced responses of the vibrator to two input signals with a phase difference of 90° are given. A FEM analysis in ANSYS is used to simulate the natural frequencies and vibrating modes of the vibrator. A test is conducted to illustrate the analytical calculative results.     

Nonlinear flexural vibration of rectangular moderately thick plates and sandwich plates

Nonlinear flexural vibration is investigated for rectangular Reissner moderately thick plates and sandwich plates. The fundamental equations and boundary conditions are expressed in unified dimensionless form for rectangular moderately thick plates and sandwich plates. Highly accurate solutions of series form with many different movable and immovable boundary conditions, especially with unsymmetrical boundary conditions, are obtained by means of the method of harmonic balance and by developing a new technique of mixed Fourier series in nonlinear analysis. The nonlinear partial differential equations are reduced to an infinite set of simultaneous nonlinear algebraic equations, which are truncated in numerical computations. Solutions of the nonlinear fundamental frequency of rectangular plates are obtained by iteration. The multimode approach includes not only the influences of transverse shearing deformation and rotatory inertia, but also the coupling effect of vibrating modes on the nonlinear fundamental frequency. The present solutions are satisfactory in comparison with other available results.     

三维振动台的正弦扫频分析与模态分析

三维振动台采用振动方法完成对复杂异型曲面工件进行表面强化和抛光处理，为了探讨振动台的固频与振型对强化抛光的影响，本文首先对三维振动台进行Y向与Z向模态试验，得到了三维振动台的各阶模态，为了纵模态分析中确定强化抛光用模态，将模态分析中所得的各阶固频，对三维振动台进行正弦激振，同时将模态分析与正弦激振相结合，获得了适合三维振动台的抛光工艺模态。     

机械振动对光学系统指向精度的影响

针对机械振动对光学系统性能影响的预测问题，基于矩阵光学和机械振动学理论，建立了振动响应对光学系统性能失调和光束稳定性的分析模型，并以某光学系统为例，给出了数值仿真方法。数值结果表明，仿真模型是合理的，可用于预测评价光学平台机械结构设计的优劣。     

一种研究异步电动机振动的新方法

在理论上建立了异步电动机转矩的模型,提出了异步电动机振动边频结构分析法。并进一步讨论了振动机电调特性和边频带非迭混特性。结合故障实例,对异步电动机的磨损动不平衡和电压波动实测振动信号进行了处理和分析。实验结果与理论结论相一致。因而表明,边频结构分析法是研究异步电动机振动的一种有效方法。它可应用于异步电机振动特征频率的识别、状态监测和故障诊断。