改进的结构振动传递矩阵法

针对传递矩阵法中状态向量一阶导数计算复杂问题,改进状态向量的选取。不据边界条件而据方程选取状态向量,可大大简化状态向量一阶导数计算过程。在状态向量与边界条件之间引入关联矩阵,使传递矩阵求解过程更加简单。以圆柱壳振动方程为例,介绍改进的传递矩阵法并证明其正确性。通过求解约束阻尼圆柱壳表明,该方法求解多自由度复杂振动方程优点更显著。     

索力振动测量的传递矩阵法

振动法测量拉索张力需要准确描述索力与自振频率的关系,在建立拉索振动的离散模型基础上应用传递矩阵法计算拉索固有频率,通过求解特征方程建立了索力与振动频率的关系;然后将计算得到的模态频率与测试得到的模态频率比较,通过修正拉索张力计算值使计算频率与实测频率误差最小,最后修正的拉索张力则为拉索实际张力。通过对实际工程的测试结果分析表明,该方法具有准确、实用和易编程的特点,完全能满足工程应用要求。     

含楔形变截面连续梁弯曲自由振动计算的传递矩阵法

本文推导了楔形变截面梁弯曲自由振动计算时的传递矩阵式，通过对含楔形变截面连续梁弯曲自由振动的实例计算，证明了本文提出了的方法是一种精确度高而且简便易行的方法。     

流体管道横向振动的频域传递矩阵法

通过Fourier变换,把经典的时域描述的流体管道横向振动4方程模型变换到频域,求解此模型,可以得到单管的频域解析解.在此基础上,结合管段节点的平衡条件,推导出多管段的传递矩阵法,把单管的频域分析扩展到多管段组成的管路,传递矩阵法可以求解多管段的任意管段和任何坐标位置的值.最后,利用Dundee大学实验管道对结果进行验证分析,并通过算例来说明本方法的应用.     

转动态薄辐齿轮振动分析的传递矩阵法

本文用截锥壳模拟薄辐齿轮，由截锥薄壳理论导出了计算转动态截锥壳振动特性及瞬态响应的传递矩阵公式。文末给出了算例。     

Timoshenko薄壁梁弯扭耦合振动的动态传递矩阵法

通过直接求解单对称均匀Timoshenko薄壁梁单元弯扭耦合振动的运动偏微分方程,导出了其自由振动时的动态传递矩阵,同时采用结合频率扫描法的二分法求解频率特征方程,并讨论了剪切变形和转动惯量对弯扭耦合Timoshenko薄壁梁的固有频率的影响.数值结果验证了本文方法在其适用范围内的精确性和有效性.     

Timoshenko薄壁湾弯扭耦合振动的动态传递矩阵法

通过直接求解单对称均匀Timoshenko薄壁梁单元弯扭耦合振动的运动偏微分方程,导出了其自由振动时的动态传递矩阵,同时采用结合频率扫描法的二分法求解频率特征方程,并讨论了剪切变形和转动惯量对弯扭耦合Timoshenko薄壁梁的固有频率的影响。数值结果验证了本文方法在其适用范围内的精确性和有效性。     

Timoshenko梁组合动力系统的精确的传递矩阵法

本文把分布质量模型的传递矩阵法和集中质量模型的传递矩阵法有机地结合起来,并将精确的传递矩阵法应用于求解包含任何支承单元、悬挂单元和Timoshenko梁单元的组合动力系统的固有特性。数值结果表明本文方法在一定范围内是完全精确的,而且编程简单。     

齿轮啮合轴系振动分析的整体传递矩阵法

分析计算了轮齿啮合综合刚度,推导了齿轮耦合单元的传递矩阵,编写了计算单对轮齿综合弹性变形(综合刚度)的通用程序,为将整体传递矩阵法推广、应用于更复杂的包含齿轮啮合效应的齿轮传动转子多轴系统的动力计算问题奠定了良好的基础.采用整体传递矩阵法对具有齿轮啮合的多转子相互耦合系统的临界转速进行了计算.计算结果表明,这是一种精确度高,简便实用的方法,适于工程技术人员在微机上应用.     

主动约束层阻尼圆柱壳动力学分析的新传递矩阵法

基于作者最近导出的被动约束层阻尼(PCLD)圆柱壳的一阶整合矩阵微分方程,结合压电材料本构关系和比例微分负增益反馈控制策略(PD),建立了一种求解主动约束层阻尼(ACLD)圆柱壳动力学问题的新传递矩阵方法。提出的ACLD圆柱壳的一阶矩阵微分方程,采用了简化的机电耦合模型。通过对ACLD圆柱壳自由振动及其在地震激励作用下的动力学响应分析,表明ACLD圆柱壳的阻尼特性和减振效果相对于PCLD圆柱壳具有明显优势,并且发现采用周向分块敷设ACLD,且施加与结构变形中的占优模态相匹配的控制电压分布方式对地震激励的抑制效果更好。     

Free vibration analysis of arches using curved beam elements

The natural frequencies and mode shapes for the radial (in‐plane) bending vibrations of the uniform circular arches were investigated by means of the finite arch (curved beam) elements. Instead of the complicated explicit shape functions of the arch element given by the existing literature, the simple implicit shape functions associated with the tangential, radial (or normal) and rotational displacements of the arch element were derived and presented in matrix form. Based on the relationship between the nodal forces and the nodal displacements of a two‐node six‐degree‐of‐freedom arch element, the elemental stiffness matrix was derived, and based on the equation of kinetic energy and the implicit shape functions of an arch element the elemental consistent mass matrix with rotary inertia effect considered was obtained. Assembly of the foregoing elemental property matrices yields the overall stiffness and mass matrices of the complete curved beam. The standard techniques were used to determine the natural frequencies and mode shapes for the curved beam with various boundary conditions and subtended angles. In addition to the typical circular arches with constant curvatures, a hybrid beam constructed by using an arch segment connected with a straight beam segment at each of its two ends was also studied. For simplicity, a lumped mass model for the arch element was also presented. All numerical results were compared with the existing literature or those obtained from the finite element method based on the conventional straight beam element and good agreements were achieved. Copyright © 2003 John Wiley & Sons, Ltd.     

箱型吊杆的风致振动特性

该文通过风洞试验研究了箱型吊杆的风振特性,并进一步分析了紊流对吊杆气动性能的影响。箱型吊杆会发生涡振与驰振失稳,高宽比对涡振特性存在较显著影响,对改善驰振性能作用不大。紊流对箱型吊杆涡振起振风速及锁定区间有较大影响,但紊流的作用并不总是有利的。相应的数值模拟显示,紊流是通过改变结构的St数与涡脱力的大小来影响结构的涡振特性。     

An extended Layerwise method for composite laminated beams with multiple delaminations and matrix cracks

For the delamination and matrix crack prediction of composite laminated structures, the methods based on the damage mechanics and fracture mechanics are most commonly used. However, there are very few methods that can accurately simulate the delaminations together with matrix cracks, although the in‐plane matrix cracks always exist alongside the delaminations under impact loading. In this work, an extended layerwise method is developed to model the composite laminated beam with multiple delaminations and matrix cracks. In the displacement field, the nodes in the thickness direction are located at the middle surface of each single layer, the top surface and the bottom surface of the composite beams. The displacement field contains the linear Lagrange interpolation functions, the one‐dimensional weak discontinuous function and strong discontinuous function. The strong and weak discontinuous function are applied to model the displacement discontinuity induced by delaminations and the strain discontinuity induced by the interface between the layers, respectively. Because the nodes in the thickness direction are located at the middle surface of each single layer, the extended layerwise method can be conveniently employed to deal with the in‐plane matrix cracks combined with the extend FEM. Copyright © 2014 John Wiley & Sons, Ltd.     

微穿孔板传递矩阵计算方法的改进及实验

传统的声电类比法对双层微穿孔板吸声结构进行计算时,忽略了空腔声质量的影响,对于空腔距离比较短,频率比较低时是适用的,但是当空腔距离比较大或频率比较高时,则存在误差。用传递矩阵法对微穿孔板吸声结构进行分析：解决了空腔声阻抗的近似计算带来的误差;对于微孔部分传递矩阵中的声阻抗计算仍然采用马大猷教授的理论,不需要引入修正参数δx。通过上述工作,进行了微穿孔板吸声结构的吸声系数的计算和相应的实验验证,理论计算结果与实验数据吻合良好。     

Direct differentiation method for sensitivity analysis based on transfer matrix method for multibody systems

On one hand, the new version of transfer matrix method for multibody systems (NV‐MSTMM), has been proposed by formulating transfer equations of elements in acceleration level instead of position level as in the original discrete time transfer matrix method of multibody systems to study multibody system dynamics. This new formulation avoids local linearization and allows using any integration algorithms. On the other hand, sensitivity analysis is an important way to improve the optimization efficiency of multibody system dynamics. In this paper, a totally novel direct differentiation method based on NV‐MSTMM for sensitivity analysis of multibody systems is developed. Based on direct differentiation method, sensitivity analysis matrix for each kind of element is established. By assembling transfer matrices and sensitivity analysis matrices based on differentiation law of multiplication, the sensitivity analysis equation of overall transfer equation is deduced. The computing procedure of the proposed method is also presented. All these improvements as well as three numerical examples show that the direct differentiation method based on NV‐MSTMM is suitable for optimizing the dynamic sensitivity in multi–rigid‐body systems.     

A mixed stress model for linear elastodynamics of arbitrarily curved beams

This work presents a mixed stress finite element for linear elastodynamics of arbitrarily curved beams based on a modified Hellinger–Reissner functional. A rational approach to choose the stress approximation is proposed. In particular, the self‐equilibrated stress is augmented by some stress modes obtained from the lower‐order displacement approximation using the equilibrium equations, in such a way that the total number of stress modes is equal to the number of strain modes. The rationale is to preserve all the interactions among the stresses, proper of a curved structure without compromising the flexibility of the element. An arbitrarily curved geometry is described using a parametric Hermitian interpolation scheme tuned by minimizing the initial curvature of the arch. The effectiveness of the present approach is numerically demonstrated. Copyright © 2007 John Wiley & Sons, Ltd.     

用传递矩阵法分析微穿孔板的声学特性

微穿孔板吸声结构以其众多的优点,在噪声控制领域得到越来越广泛的应用。因微穿孔板结构中涉及大量的参数,在穿孔板层数较多时,用声电类比法或试验的方法研究微穿孔板结构的吸声性能将变得非常复杂。传递矩阵法尤其适于多层结构的分析,且易于用计算机编程实现。文章推导了用传递矩阵法计算微穿孔板结构声学性能的计算公式,并与用声电类比法计算的结果、试验测定数据进行了对比,结果显示,传递矩阵法是可以作为微穿孔板结构设计的一种简单而有效的参考方法。     

变截面梁横向振动特性的半解析法

提出一种计算变截面梁横向振动特性的半解析法。基于欧拉-伯努利梁理论给出的弯曲刚度、质量分布沿梁轴线连续或非连续变化的变截面梁横向振动方程;将该变截面梁等效为多段均匀梁,并基于相邻两段连接处的位移(位移、转角)和力(弯矩、剪力)的连续条件,建立了两相邻均匀段之间模态函数的关系;针对简支边界条件给出了计算变截面梁横向振动固有频率的特征方程和模态函数,并用Newton-Raphson方法计算其固有频率。通过与有限元法的数值结果比较说明半解析解的高精度和有效性。