硬夹心矩形夹层板的整体稳定性分析

论文在Reissner型理论给出的位移模式基础上,修正其软夹心假设,考虑夹心层面内刚度,给出了硬夹心夹层板的几何方程、物理方程,建立了硬夹心夹层板结构在面内纵向载荷作用下的平衡微分方程,并对方程进行了简化,通过理论计算得到了四边简支条件下硬夹心矩形夹层板整体失稳临界载荷的解析解,并分别计算了夹心层材料的弹性模量E、厚度h、泊松比μc对硬夹心夹层板临界载荷的影响,结果证明,对于硬夹心夹层结构,夹心层面内刚度对硬夹心夹层板整体失稳临界载荷的影响较大,考虑其面内刚度是必要的.     

功能梯度简支矩形板的非线性动力响应

研究了功能梯度简支矩形板在横向简谐激励作用下的非线性动力响应问题.采用幂律分布规律描述功能梯度材料的等效材料参数,基于Galerkin法建立了系统广义坐标的常微分控制方程.利用平均法得到了系统的幅频响应特性,分析了功能梯度矩形薄板的非线性主共振特性.数值算例验证了平均化方法的正确性,揭示了功能梯度平板主共振响应中的多值性和跳跃现象;同时分析发现初始条件会改变功能梯度平板主共振的响应幅值.最后讨论了功能梯度材料的梯度指数对系统幅值响应的影响.     

正交偏振板对聚焦光斑偏振特性的影响

在间接驱动的惯性约束聚变（ICF）驱动器中,为控制靶腔入口及其附近光场的偏振特性及辐照均匀性,采用二维光谱角色散（2D-SSD）、随机相位板（RPP）和正交偏振板（OPCP）联用的束匀滑方案,数值模拟和理论分析了OPCP对焦面及离焦面处光场偏振特性以及强度均匀性的影响,并讨论了正交偏振板单元数的选取问题。结果表明,不同单元数正交偏振板对焦面及其附近光场偏振特性和强度均匀性的影响程度不同,且光场偏振特性对离焦并不敏感。此外,离焦会使强度均匀性变差,适当增加正交偏振板单元数可以在一定程度上减弱这种影响。     

核工程钢板混凝土墙防撞击贯穿实用计算方法

针对带对拉钢筋的双钢板混凝土墙,研究了双钢板混凝土墙防贯穿计算方法,建立了基于能量法的防贯穿计算公式。在已知弹体和钢板混凝土墙体材料与几何相关参数时,利用防贯穿实用计算公式可对带对拉钢筋的核工程双钢板混凝土墙体贯穿速度以及弹体剩余速度进行计算,避免了复杂的结构抗撞击反应动力时程数值分析。为验证公式的可靠性,将公式计算结果与已有刚性弹体撞击双钢板混凝土墙实验结果及其动力有限元计算结果进行对比,结果表明：防贯穿实用计算公式可以正确判断双钢板混凝土墙的贯穿状态,实用计算公式给出的弹体剩余速度与实验结果符合良好。为进一步验证公式的适用范围,将公式计算结果与共10个工况的飞机发动机撞击双钢板混凝土墙的有限元计算结果进行了对比分析,结果表明：除1个工况计算结果偏差略超10%外,其余工况的偏差均在10%以内,说明该计算方法合理可行。

     

“聚龙一号”装置上磁驱动铝飞片实验的数值模拟

采用二维磁驱动数值模拟程序MDSC2,对大电流脉冲装置聚龙一号上的151发次磁驱动370 m厚铝飞片实验、164发次磁驱动330 m厚铝飞片实验进行了数值模拟和分析。数值模拟表明：370 m厚铝飞片和330 m厚铝飞片的磁驱动过程中, VISAR测量的速度不是飞片自由面的速度,而是飞片中邻近自由面最近的固体反射面的速度。这是由于磁驱动飞片发射过程中,飞片自由面部分被烧蚀,密度低于固体密度状态,而飞片自由面和加载面中间的飞片还保持固体密度状态。VISAR测量的激光将穿过自由面的低于固体密度状态的飞片部分,到达飞片自由面最近的固体密度位置再反射回去,获得这一位置的飞片速度。数值模拟的飞片固体反射面速度历史和VISAR测量的速度历史相吻合。     

轴向变速运动局部浸液单向板的组合共振1)

论文研究了时变速度作用下局部浸液板的组合共振动力学特性。基于Von Kármán大挠度板理论,考虑流固耦合、轴向张力、轴向时变速度等因素,建立局部浸液板的非线性动力学方程,并应用Galerkin法将进行离散,获得模态坐标上的非线性方程组。分别采用多尺度法和数值方法分析了平均速度、脉动速度、张力等参数对系统非线性动力学特性的影响。结果表明：系统发生组合共振时,展现出复杂的动力学行为;第一阶模态响应幅值远大于第二阶模态响应幅值;平均速度、脉动速度幅值对系统幅频响应曲线的影响较为显著。     

TM模场入射到金属光栅的表面增强喇曼散射计算分析

以纳米量级金属履带矩形光栅为模型,研究了表面增强喇曼散射的特性.针对TM模的入射光,采用严格的耦合波原理对金属表面的衍射场进行了分析,并用数值计算方法讨论了光栅深度、光栅占空比等参量对金属表面增强的影响以及增强因子随光栅深度的变化关系.结果显示：当入射光波长为700 nm、入射角度为10°、光栅周期p=600 nm、 光栅深度d=37.5 nm、占空比为1/3时,获得最大增强,增强因子G达104倍.     

An FEM approximation for a fourth-order variational inequality of second kind

A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variational equation, and the corresponding discrete FEM variational equation is presented afterwards. Abstract error estimates and error estimates of the approximation are derived in terms of energy norm and L^2-norm.     

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.