样条有限条法解多层复合板的动力问题

采用样条有限条法,即一个方向为解析函数解,另一个方向为样条函数插值,分析了考虑横向剪切变形和转动惯量效应的多层复合板的横向振动,推导了板的刚度矩阵、质量矩阵及振动微分方程,计算了两种不同边界条件下板的固有频率。与普通有限条法相比,此法除具有未知量少的优点,由于条与条之间用样条插值,使整个域内位移及其导数均连续,计算精度大大提高。     

楔形杆轴纵扭固有振动的摄动解

采用摄动法研究了楔形杆轴的固有纵扭振动 ,并且推导出了其固有纵扭振动的振型函数及频率特征方程。通过实例计算证明了该摄动解不仅计算简便 ,而且计算精度与 Bessel函数解的计算精度相当 ,对强、弱楔度楔形杆轴纵扭固有振动都适用。     

渐近法在负载钢丝绳固有振动中的应用

结合Liouville-Green变换,改进了求解变系数二阶线性齐次方程的渐近法.并采用改进后的渐近法研究了负载钢丝绳的固有振动同题,推导出了其固有振动的频率特征方程.实例表明,改进后的渐近法不但比Bessel函数法计算简便,而且精度也高.     

四边固支矩形薄板固有振动的理论计算和有限元分析

基于理论计算有限元方法分析了四边固支矩形板结构的自由振动问题,求得了四边固支矩形板的振动固有频率和振型。利用双向梁函数构造了四边固支矩形板的振型函数,并根据位移变分原理求得了矩形板的固有振动特性。在板单元理论的基础上,利用有限元法推导了薄板振动的质量矩阵和刚度矩阵。由于工程实际中只关心板结构振动的横向位移幅值,利用静力凝聚法将质量矩阵和刚度矩阵中转动自由度上的质量和刚度凝聚到横向振动自由度上,以达到降低模型阶目的,为板结构振动主动控制奠定基础。     

剪切变形对水轮发电机组轴系横振的影响分析

提出了一种考虑剪切效应的三结点弹性轴段单元,并将其用于轴系振动的分析。给出了三结点单元的插值函数,推导了弯曲刚度矩阵和剪切刚度矩阵,得到了单元的运动方程。研制了考虑剪切效应的有限元计算程序。按七种不同弯曲刚度计算了单圆盘转子(算例1)和某水轮发电机组轴系(算例2)的模态频率和临界转速,得出了模态频率和临界转速的变化规律和不同方法的相对误差。计算结果表明,剪切变形对于轴系振动的模态频率和临界转速均有一定的影响。算例1的结果显示,当轴的弯曲刚度较大(k=EI/l3>106N·m-1)时,必须考虑剪切效应;当轴的刚度较小(k≤106N·m-1)时,可以忽略剪切变形的影响,由此所带来的计算误差不超过2%。算例2的计算结果表明,考虑剪切变形作用时,一阶模态频率和临界转速的结果比不考虑剪切时大1.5%以上,且随着轴的刚度的增大,相对误差也逐渐增大。     

基于主轴分解法的变截面梁变形分析

针对传统变截面弹性梁大挠度变形计算方法求解过程复杂、适用性差、结果精度低等问题,基于结构刚度主轴分解法,将变截面弹性梁离散成为具有若干个6自由度弹性关节的串联机构,对结构刚度矩阵进行计算,运用机构学方法,将变形问题转化为多自由度冗余机构的约束-静力平衡问题.构建优化目标函数,基于梯度下降法,采用旋量理论方法和指数积方式简化问题的计算过程,快速获取变截面弹性梁的位形信息,迭代求解得到梁的大挠度变形结果.通过与Abaqus软件仿真结果和实验结果对比,在误差允许范围内,采用此新方法能够获得准确结果,且求解过程快速简便,适用性广.     

重频结构大修改动力重分析的矩阵摄动法

为拓展矩阵摄动法在结构重分析中的适用范围,提高重分析计算精度,针对重频结构参数大修改提出了重频结构动力重分析的矩阵摄动法。采用高次增量法将反映重频结构参数改变的质量矩阵和刚度矩阵的增量分别表示为小参数ε的一次与二次幂项之和,根据矩阵摄动理论推导得到重特征值的二阶摄动解及相应特征向量的一阶摄动解。数值算例表明,所提出方法极大提高了重频结构大修改下的动力重分析计算精度。     

求解复杂轴扭振动力特性的一种近似分析方法

应用模态摄动法求解非均质变截面复杂轴的扭转振动的模态特性。在这一方法中,选择与复杂轴约束条件相同、等截面均匀轴的扭转振动解析模态函数作为近似分析的基函数,采用Ritz展开和摄动分析相结合的方法,把复杂轴扭振的变系数微分方程的求解,转化为一组代数方程组的求解。虽然这一方法应用了结构振动分析中常用的Ritz展开原理,但避免了关于模态广义坐标的特征值问题的求解,通过代数方程组的求解,可逐一求得复杂轴的扭转振动的模态特性,简化了求解的难度。通过2个算例的分析表明,该方法简单实用,且具有较高的精度。     

基于频响函数的惯性参数识别改进方法北大核心CSCD

针对质量线法难以快速精确获取大型复杂构件质量的问题,根据振动微分方程和刚体加速度变换关系,推导出频响函数与质量转化的表达式,结合几何中心对称和力矩平衡的原理,提出基于频响函数的惯性参数识别改进方法。联合Adams与Hypermesh建立驾驶室和发动机总成的仿真模型,筛选振动试验获取的频响函数以识别质量,分析该方法结合质量线法识别结果的误差。通过模态试验得到简单构件和某型号卡车驾驶室总成的惯性参数,将其与MPC转动惯量平台测试的结果对比,验证该方法的工程测试精度。研究结果表明:刚体质量识别的仿真结果相对误差最大不超过0.4%,工程测量相对误差最大不超过4.6%,且该方法简单方便,降低测试成本,减小工作量,显著提高了惯性参数识别的效率。     

8轮扭杆摇臂式月球车车轮与月面间动载荷分析

对车轮与月面间的动载荷进行分析是为了改善月球车行驶平顺性和操纵稳定性.针对8轮扭杆摇臂式月球车结构特点,即每2个与同一摇臂连接的车轮所传递的月面不平度输入相互耦合,对月面不平度的激励进行了等效处理,得到了等效月面不平度函数,以此为基础建立了7自由度月球车振动模型及其振动微分方程.通过对振动微分方程进行傅立叶变换及运用Runge-Kutta数值分析方法进行求解,利用Matlab软件编程计算,确定了8轮扭杆摇臂式月球车悬挂系统的刚度与阻尼合理取值范围.     

Vibration control of multi-story building structure by hybrid control using tuned liquid damper and active mass damper

This study proposes a hybrid control methodology that combines tuned liquid damper (TLD) and active mass damper (AMD) to suppress vibrations of multi-story building structure effectively. To this end, a dynamic model that can predict the vibration of multi-story building structure coupled with TLD and AMD is derived using the energy approach. The TLD that is mainly designed to suppress the main natural mode is developed with a multi-degree-of-freedom model to investigate the effect of the TLD on natural modes of structure numerically. The AMD is an active vibration controller that can suppress remaining resonant peaks, including ones resulting from the application of the TLD as well as other higher modes of interest. In this way, the proposed control can utilize the advantages of TLD and AMD simultaneously. We set up an experimental apparatus to verify the performance of the hybrid control methodology. The numerical and experimental results show that the proposed hybrid control method can successfully suppress the vibrations of multi-story building structure. The dynamic model derived in this study can also accurately predict the actual behavior of the system.

     

变质量-负刚度动力吸振器试验研究

针对传统动力吸振器“窄带”缺陷,设计了一种新型的变质量-负刚度动力吸振器,从而可以使吸振器具有较好的低频有效性。建立变质量-负刚度动力吸振器的动力学方程并分析了吸振器的工作原理;搭建了变质量-负刚度动力吸振器试验台,编制了PID控制程序;对吸振器减振性能进行了动力学仿真和试验研究。研究结果表明,所设计的吸振器连续可调,有效频带比传统吸振器频带宽了17.3%。     

An exact solution for in-plane vibrations of an arch having variable curvature and cross section

An exact solution for in-plane vibration of arches with variable curvature as well as cross section has been developed using the famous Frobenius method combined with the dynamic stiffness method. The effects of shear deformation and rotary inertia are taken into account. A convergent solution is always guaranteed without numerical difficulties. An important by-product of this series solution is that the first known dynamic stiffness matrix for an arch with variable curvature and variable cross section is also explicitly formulated. Some new numerical results are given for non-dimensional frequencies of parabolic arches with a certain type of variation of cross section along the arch that is often used in practical structures. Extensive and accurate (six significant figure ) non-dimensional frequency tables and graphic charts are presented for a series of parabolic arches showing the effects of rise to span length, slenderness ratio, and variation of cross section.     

Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness

The free vibration analysis of laminated conical shells with variable stiffness is presented using the method of differential quadrature (DQ). The stiffness coefficients are assumed to be functions of the circumferential coordinate that may be more close to the realistic applications. The first-order shear deformation shell theory is used to account for the effects of transverse shear deformations. In the DQ method, the governing equations and the corresponding boundary conditions are replaced by a system of simultaneously algebraic equations in terms of the function values of all the sampling points in the whole domain. These equations constitute a well-posed eigenvalue problem where the total number of equations is identical to that of unknowns and they can be solved readily. By vanishing the semivertex angle (α) of the conical shell, we can reduce the formulation of laminated conical shells to that of laminated cylindrical shells of which stiffness coefficients are the constants. Besides, the present formulation is also applicable to the analysis of annular plates by letting α=π/2. Illustrative examples are given to demonstrate the performance of the present DQ method for the analysis of various structures (annular plates, cylindrical shells and conical shells). The discrepancies between the analyses of laminated conical shells considering the constant stiffness and the variable stiffness are mainly concerned.     

Dynamic finite element method for generally laminated composite beams

A dynamic finite element method for free vibration analysis of generally laminated composite beams is introduced on the basis of first-order shear deformation theory. The influences of Poisson effect, couplings among extensional, bending and torsional deformations, shear deformation and rotary inertia are incorporated in the formulation. The dynamic stiffness matrix is formulated based on the exact solutions of the differential equations of motion governing the free vibration of generally laminated composite beam. The effects of Poisson effect, material anisotropy, slender ratio, shear deformation and boundary condition on the natural frequencies of the composite beams are studied in detail by particular carefully selected examples. The numerical results of natural frequencies and mode shapes are presented and, whenever possible, compared to those previously published solutions in order to demonstrate the correctness and accuracy of the present method.     

Exact dynamic stiffness matrix of a Timoshenko three-beam system

An exact dynamic stiffness matrix is established for an elastically connected three-beam system, which is composed of three parallel beams of uniform properties with uniformly distributed-connecting springs among them. The formulation includes the effects of shear deformation and rotary inertia of the beams. The dynamic stiffness matrix is derived by rigorous use of the analytical solutions of the governing differential equations of motion of the three-beam system in free vibration. The use of the dynamic stiffness matrix to study the free vibration characteristics of the three-beam system is demonstrated by applying the Muller root search algorithm. Numerical results for the natural frequencies and mode shapes of the illustrative examples are discussed for 10 interesting boundary conditions and three different stiffness constants of springs.     

Effect of train carbody’s parameters on vertical bending stiffness performance

Finite element analysis(FEA) and modal test are main methods to give the first-order vertical bending vibration frequency of train carbody at present, but they are inefficiency and waste plenty of time. Based on Timoshenko beam theory, the bending deformation, moment of inertia and shear deformation are considered. Carbody is divided into some parts with the same length, and it’s stiffness is calculated with series principle, it’s cross section area, moment of inertia and shear shape coefficient is equivalent by segment length, and the fimal corrected first-order vertical bending vibration frequency analytical formula is deduced. There are 6 simple carbodies and 1 real carbody as examples to test the formula, all analysis frequencies are very close to their FEA frequencies, and especially for the real carbody, the error between analysis and experiment frequency is 0.75%. Based on the analytic formula, sensitivity analysis of the real carbody’s design parameters is done, and some main parameters are found. The series principle of carbody stiffness is introduced into Timoshenko beam theory to deduce a formula, which can estimate the first-order vertical bending vibration frequency of carbody quickly without traditional FEA method and provide a reference to design engineers.     

热应力对机翼结构固有频率的影响分析

研究了热应力对飞行器机翼结构固有频率的影响。用ANSYS建立机翼结构有限元模型,计算了均匀温度场、非均匀温度场和非均匀可变温度场条件下的结构热应力分布和振动模态。根据固有振动的结构变形,分析了热应力对固有频率的影响效应。研究结果表明,热环境下机翼结构因材料属性的退化导致固有频率下降,但对于振型节线处于翼面内部的振动模态,附加热应力刚度矩阵在结构总刚度矩阵变化中起主导作用,使该阶固有频率增大。     

Coupled bending and torsional vibration of axially loaded thin-walled Timoshenko beams

A dynamic transfer matrix method of determining the natural frequencies and mode shapes of axially loaded thin-walled Timoshenko beams has been presented. In the analysis the effects of axial force, warping stiffness, shear deformation and rotary inertia are taken into account and a continuous model is used. The bending vibration is restricted to one direction. The dynamic transfer matrix is derived by directly solving the governing differential equations of motion for coupled bending and torsional vibration of axially loaded thin-walled Timoshenko beams. Two illustrative examples are worked out to show the effects of axial force, warping stiffness, shear deformation and rotary inertia on the natural frequencies and mode shapes of the thin-walled beams. Numerical results demonstrate the satisfactory accuracy and effectiveness of the presented method.     

摩擦式双级分段变刚度汽车双质量飞轮设计理论研究及应用

提出基于摩擦的双级分段变刚度汽车双质量飞轮的设计理论,实现了兼顾低转速、低转矩小扭转角下具有小刚度的柔性和大扭转角时具有高反抗转矩和大刚度的设计要求。分析所提出的摩擦式双级分段变刚度双质量飞轮结构及工作原理;对所能实现的二级过载保护的结构实现进行剖析;导出摩擦式双级分段变刚度双质量飞轮转矩特性的数学力学模型;试验表明,转矩特性的测试结果与所构建模型的仿真分析基本一致;研究扭转刚度对传动系一、二阶共振转速的影响;将利用摩擦实现增大转矩和过载保护的理念引入双质量飞轮的设计,为高性能双质量飞轮产品的开发提供了设计思路,揭示出引入摩擦的双级分段变刚度双质量飞轮减振器优良减震的内在本质。