ELECTRICALLY FORCED THICKNESS-SHEAR VIBRATIONS OF QUARTZ PLATE WITH NONLINEAR COUPLING TO EXTENSION

We study electrically forced nonlinear thickness-shear vibrations of a quartz plate resonator with relatively large amplitude. It is shown that thickness-shear is nonlinearly coupled to extension due to the well-known Poynting effect in nonlinear elasticity. This coupling is relatively strong when the resonant frequency of the extensional mode is about twice the resonant frequency of the thickness-shear mode. This happens when the plate length/thickness ratio assumes certain values. With this nonlinear coupling, the thickness-shear motion is no longer sinusoidal. Coupling to extension also affects energy trapping which is related to device mounting. When damping is 0.01, nonlinear coupling causes a frequency shift of the order of 10^-6 which is not insignificant,and an amplitude change of the order of 10^-8. The effects are expected to be stronger under real damping of 10^-5 or larger. To avoid nonlinear coupling to extension, certain values of the aspect ratio of the plate should be avoided.     

PARALLEL FINITE ELEMENT ANALYSIS OF HIGH FREQUENCY VIBRATIONS OF QUARTZ CRYSTAL RESONATORS ON LINUX CLUSTER

Quartz crystal resonators are typical piezoelectric acoustic wave devices for frequency control applications with mechanical vibration frequency at the radio-frequency （RF） range. Precise analyses of the vibration and deformation are generally required in the resonator design and improvement process. The considerations include the presence of electrodes, mountings, bias fields such as temperature, initial stresses, and acceleration. Naturally, the finite element method is the only effective tool for such a coupled problem with multi-physics nature. The main challenge is the extremely large size of resulted linear equations. For this reason, we have been employing the Mindlin plate equations to reduce the computational difficulty. In addition, we have to utilize the parallel computing techniques on Linux clusters, which are widely available for academic and industrial applications nowadays, to improve the computing efficiency. The general principle of our research is to use open source software components and public domain technology to reduce cost for developers and users on a Linux cluster. We start with a mesh generator specifically for quartz crystal resonators of rectangular and circular types, and the Mindlin plate equations are implemented for the finite element analysis. Computing techniques like parallel processing, sparse matrix handling, and the latest eigenvalue extraction package are integrated into the program. It is clear from our computation that the combination of these algorithms and methods on a cluster can meet the memory requirement and reduce computing time significantly.     

飞秒激光冲击AZ31B镁合金过程的数值模拟

采用有限元分析法对飞秒激光冲击AZ31B镁合金进行数值模拟,研究了激光冲击处理对镁合金变形过程的影响,分析了单脉冲激光冲击下材料内部的位移、动能、应力和应变的分布情况,得到了材料的瞬态速度和应变率变化过程.仿真结果表明,单脉冲飞秒激光冲击镁合金产生的塑性变形,可在材料表面形成微米级凹坑,中心点处最大位移为34μm,最大变形速度390m/s;在冲击初期,材料表面的应力和应变主要分布在冲击区域中心节点和边缘附近,并且得到镁合金的最大应力和最大应变率分别为955 MPa和1.8×106 s-1.研究结果能够为深入分析飞秒激光与镁合金作用时材料变形参量的变化规律提供数值理论依据.     

基于透光性能分析的微藻光生物反应器构筑板材选型

利用配备人工光源的光生物反应器(AL-PBR)培养微藻是实现微藻快速增殖,进而满足相关产业需求的重要手段。为指导AL-PBR的构筑材质选型,完善了现有方法,比选了7种市售透明板材。考虑到微藻在不同入射光波段的光生态学,应综合分析板材在光合有效辐射波段(400~700nm)、红光波段(630~700nm)、蓝光波段(430~480nm)和中波紫外线波段(UV-B,280~320nm)的透光性能。前三波段的平均透射率越高越好,UV-B波段反之。测定结果表明:如果AL-PBR以太阳光作为外部光源,现阶段宜采用进口聚碳酸酯板和普通玻璃板作为构筑材质,且前者更佳;如果以单色LEDs灯或荧光灯作为外部光源,宜选用聚甲基丙烯酸甲酯板。     

ANALYSIS OF SYMMETRIC LAMINATED RECTANGULAR PLATES IN PLANE STRESS

Symmetric laminated plates used usually are anisotropic plates. Based on the fundamental equation for anisotropic rectangular plates in plane stress problem, a general analytical solution is established accurately by method of stress function. Therefore the general formula of stress and displacement in plane is given. The integral constants in general formula can be determined by boundary conditions. This general solution is composed of solutions made by trigonometric function and hyperbolic function, which can satisfy the problem of arbitrary boundary conditions along four edges, and the algebraic polynomial solutions which can satisfy the problem of boundary conditions at four corners. Consequently this general solution can be used to solve the plane stress problem with arbitrary boundary conditions. For example, a symmetric laminated square plate acted with uniform normal load, tangential load and nonuniform normal load on four edges is calculated and analyzed.     

板材冲压翻边的解析理论模型

基于全量塑性理论及膜应变假设,给出两种新的冲压板材内曲拉伸／外曲收缩翻边坯料尺寸预示解析数学模型。引入板材冲压成形性分析软件KMAS系统中,对铁路客车牵引架实际冲压件的翻边成形坯料尺寸进行了预示,并与其它解析模型的预示结果以及实验及实测数据进行了对比。讨论了板材的面内各向异性对翻边高度的影响。     

板材冲压成形有限元数值模拟界面摩擦约束处理方法

基于弹塑性大变形板材冲压成形增量有限元法,采用线性弹簧单元提出一种空间三维板材冲压成形等效界面摩擦力的处理方法.这种方法的优点是可以反映界面摩擦力的同步、被动产生效果,同时它还可以保证约束后刚度矩阵的对称性.将提出的摩擦约束处理算法引入自主开发的板材成形模拟软件FASTAMP,计算了汽车油底壳的成形过程,计算结果的厚度分布与实际冲压件吻合比较好,验证了等效界面摩擦力约束处理方法的有效性.     

微孔洞生长对板材拉伸过程中变形局部化的影响

本文在作者提出的含孔洞材料下限本构方程的基础上，采用了初始缺陷带模型对微孔洞生长及分布对板材拉伸过程中变形局部影响进行了，分析着重研究了细观损演化规律对变形局部化模式及临界应变的影响，并成功预测了ＡＩＳＩ４３４０钢板材拉伸试件变形局部化换稳为及失稳方向。     

区域集群下板材订单配置模型及算法研究

针对集群企业板材资源滞留、无法共享、加工旺季材料短缺等问题,依据区域板材特性和区域企业集群地理相关优势,建立以减少需求方板材订单采购费用最小化为目标的板材订单分配模型,采用以粒子群、免疫算法相结合的混合调度算法。计算过程中,将订单分配对应企业编号作为免疫系统的抗体基因,通过比较适应度函数解与订单预算成本的关系,将抗体群区分为支配解与非支配解,提高算法对抗原的免疫能力和最优解的选择概率。最后以板材订单分配实例进行试验仿真,分别采用PSO算法与IA-PSO算法进行试验对比,对平台上6家订单发布企业寻找合适地理位置相近和价格相对低廉的供应商。试验结果表明,IA-PSO算法能够有效地解决区域集群内板材订单的匹配问题,并且在寻找价格更低和位置更合适的供应商上更有优势。     

金属板材冲压成型过程的有限单元法模拟

用有限单元法模拟了金属板材的冲压成型过程。在模拟过程中，应用了同时考虑了薄膜力和弯矩的板壳大变形理论，考虑了板材在塑性阶段各向异性的强化性质，考虑了模具和工件的接触和摩擦条件，分析了金属板在冲压过程中的屈曲现象，建立了增量形式的变分原理。弹塑性薄壳单元被引入，它的位移模式在变分的意义上满足单元边界上一阶导数连续的条件，并有足够的秩来适应单元的有限拉伸、转动和弯曲，计算中采用了罚函数方法，即在模具和工件的接触面上，模具的表面被假设为文克尔地基，采用了修正的库伦摩擦定律，迭代法被用来决定模具与工件的接触条件和金属板的塑性行为。本文最后提供了一个算例。