Maple在结构力学教学中的应用

基于Maple强大的符号运算及图文共存功能,结合多年教学经验,就结构力学定性分析和研究型教学两个方面进行探讨,并举例说明Maple在其中所起的关键作用.实践证明,采用Maple进行结构力学教学,不仅增加了结构力学教学的趣味性,而且增强了学生对理论的理解能力、对新问题的探索能力,最终提高了学生基于力学原理的计算能力.     

各向异性弹性体光滑接触界面上的滑移脉冲波

利用Stroh公式,Fourier分析和奇异积分方程技术研究了两各向异性弹性半空间光滑接触可分离界面上滑移脉冲波的存在及其传播特性。结果表明,如果至少能在一种介质中存在Rayleigh波,且其波速小于两种介质中的最小极限速度,则滑移脉冲波就可以存在。这种脉冲波传播速度不确定,可在最小极限波速与较低的Rayleigh波速之间取值,而该取值范围又取决于无界面分离情况下的第一、第二滑移波的解。分离区大小取决于扰动的强度,界面法向力和质点速度在分离区两端有 1 /2奇异性。     

压电体光滑接触界面有局部分离时的滑移脉冲波传播

应用关于压电材料的Stroh方法以及Fourier分析和奇异积分方程技术,研究了压电体光滑接触界面有局部分离时的滑移脉冲波传播问题,分析了其存在的判据．压电体由单向压应力作用而光滑接触并处于一定强度的电场中．待求问题最终转化为含Cauchy核的奇异积分方程组,并给出其解析解．数值计算结果表明:光滑接触界面上有局部分离的滑移脉冲波普遍存在,且界面法向面力和法向电位移在局部分离区两端有奇异性;对某些特殊的材料组合,外载荷不影响滑移脉冲波的存在性．     

Propagation of slip pulse along frictionless contact interface with local separation between two piezoelectric solids

The Stroh formalism of piezoelectric materials,Fourier analysis and singular integral equation technique were used to investigate the existence of a pulse at the fric- tionless interface in presence of local separation between two contact piezoelectric solids. The two solids were combined together by uniaxial tractions and laid in the electric field. The problem was cast into a set of Cauchy singular integral equations,from which the closed-form solutions were derived.The numerical discussion on the existence of such a slip pulse was presented.The results show that such a slip pulse,which has square root singularities at both ends of the local separation zone,can propagate in most material combinations.And the existence of such a slip pulse will not be affected by the applied mechanical and electric fields in some special material combinations.     

一般各向异性单侧接触界面上波的反射和折射

研究简谐弹性波在一般各向异性介质单侧接触界面上的反射和折射问题．利用Fouier分析方法将非线性Coulomb摩擦接触边界波动问题化为一组代数方程．给出了确定局部分离、滑移和粘着区的思路和方法及各区域的解；讨论了出现界面局部分离和滑移的条件．对特定材料组合情况进行了详细数值计算，给出了界面力、相对滑移速度、张开位移、高频谐波的反射折射系数等特征参量；考察了平面和反平面波动的耦合及整体滑移等．其中关于高频谐波的结果可对已有实验结果给出很好的定性解释．在大多数情况下，即使对摩擦系数无穷大的粘滞接触界面，分离区端部也总是存在一个很小的滑移区。     

Propagation of harmonic waves through micro gap with consideration of frictional contact

Transmission of elastic waves through a micro gap between two solids with consideration of frictional contact is investigated.By using the Fourier analysis technique and the corrective solution method,the nonlinear boundary problem is reduced to a set of algebraic equations.Numerical results exhibit the locations and extents of separation, slip,and stick zones,the interface tractions,and the energy partition.The effects of gap width,frictional coefficients,and the incident angle on the wave transmission ...     

流固耦合二维声子晶体的数值模拟和实验研究

为了研究流固耦合声子晶体的特性,本文应用有限元方法进行数值模拟并通过实验进行了验证.以二维钢柱/水正方晶格声子晶体为研究对象,利用ABAQUS有限元软件计算得到了完好周期和线缺陷情况下的传输谱和声压分布.同时利用脉冲响应技术进行实验测量,得到了以上两种情况下的带隙范围.结果表明,两种方法结果吻合得很好,说明有限元方法在计算流固耦合声子晶体问题上的优越性.     

考虑摩擦接触时简谐波透过微缝隙的传播

研究了简谐波透过微缝隙的传播问题．考虑界面摩擦接触,利用Fourier分析技术和半空间解修正法,将边界非线性波动问题简化为一组代数方程并进行了详细的数值计算．给出了分离区、滑移区和粘着区的分布以及界面应力分布和能量分配;讨论了缝隙宽度、摩擦因数、入射角等因素对波动传输的影响．结果表明:由于界面发生局部接触和滑移使得反射波和透射波中含有高频谐波．缝隙宽度与各阶谐波反射、透射系数的关系可为材料及结构的无损检测提供理论依据．     

Analysis of dynamic instability of interfacial slip waves based on the surface impedance tensor

A new method relying on the Stroh formulism and the theory of the surface impedance tensor was developed to investigate the dynamic instability of interfacial slip waves. The concept of the surface impedance tensor was extended to the case where the wave speed is of a complex value, and the boundary conditions at the frictionally contacting interface were expressed by the surface impedance tensor. Then the boundary value problem was transformed to searching for zeroes of a complex polynomial in the unit circle. As an example, the steady frictional sliding of an elastic half-space in contact with a rigid flat surface was considered in details. A quartic complex characteristic equation was derived and its solution behavior in the unit circle was discussed. An explicit expression for the instability condition of the interfacial slip waves was presented.