变弯曲

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

I noticed her back was now mysteriously rid of its deformity and her straggling hair suddenly became radiantly beautiful.

我注意到她背部上的弯曲神奇地消失了，她散乱的头发忽然变得十分美丽，光彩照人。

I noticed her back was now mysteriously rid of its deformity and her straggling* hair suddenly became radiantly* beautiful.

我注意到她背部上的弯曲神气地消失了，她散乱的头发忽然变得十分美丽，光彩照人。

Using the same method, we can know that the fractal character exists for Lianyungang's coastline and Yancheng's, Nantong's, the fractal value of each is 1.0531, 1.0693, 1.1495. The values of fractal show that the extension of sinuation of coastline change complex, and so the distributing space is larger gradually from north to south.

采用相同的方法和标度，江苏省沿海三个地级市连云港、盐城、南通的海岸线在1：50000地形图上同样具有分形的特征，分维值分别是1.0531、1.0693、1.1495，由北向南逐渐增大，反映了江苏省海岸线的弯曲程度由北向南逐渐变复杂的趋势，相应的海岸线在平面上展布的空间由北向南也是愈来越大。

The research indicates there is a large left-lateral movement trend in the eastern China, which covers nearly a half of the area of Chinese mainland and affects the crustal movement in the entire eastern China and its adjacent areas. It is considered that the present-day coastline of China seas is just resulted from such a left-lateral movement, and Stype coastline will be more curved in the future.

研究表明：中国东部的地壳运动存在着一个大的左旋运动态势，其范围覆盖近一半的中国陆地面积，影响着中国整个东部和周边区域的地壳运动，中国东部现今的海岸线形态可能很大程度上归因于这种地壳运动，而且中国海岸线的"S"形曲线将会随着地壳运动变得更加弯曲。

With the application of the Pro-Hellinger-Reissner variational principle, dual equations in the symplectic space are yielded to present an analytical method for the bending of annular sector plates.

然后应用类 Hellinger-Reissner变分原理，导出了辛几何空间的对偶方程，从而将环扇形薄板弯曲问题导入到辛对偶求解体系。

We have studied the variational pattern of track geometrical form due to wheel/rail forces under the quasi-static for operating of rolling stock, and also have studied the actions on elastic displacements of constraint rail due to the thickness and stiffness of track pad.

由轮轨力所引起的线路几何形态的变化规律；在假定轮轨力不变的情况下，又研究了轨底垫层的厚度和刚度对于约束钢轨弹性位移所起的作用；为确定轮轴的弯曲变形对轮轨关系的影响，同时建立了轮对有限元模型，计算了轮对承载状态所发生的弹性变形。

The effect of undissolved ferrite amount on contact, impact and bending fatigue properties were studied. The stress relaxation and grain refinement due to occurring of plastic deformation are main reasons of improving the fatigue life.

就未溶铁素体含量对接触疲劳、多冲疲劳及弯曲疲劳性能的影响机理进行研究，局部的应力集中因铁素体发生塑变而得到松弛和细化晶粒是提高疲劳寿命的主要原因。

Maleic rosin has been added to the surface of wood flour in the form of monoester, i.e., the formation of esterified wood flour bearing a pendent carboxylic group. The rheological study showed that the complex viscosity η(superscript *, storage modulus and loss modulus of WF-HDPE composites decreased firstly and increased afterward and declined lastly as the dosage of maleic rosin increased, however, the viscosity of the composite melts decreased as a whole. After the modification of wood flour, the rheological properties of composite melts were improved markedly. According to the mechanical test it was indicated that, by proper treatment of wood flour with maleic rosin, the tensile strength and flexural strength of WF-HDPE increased obviously.

WF-HDPE流变学研究表明：复合材料的复合黏度η(上标*、储能模量和损耗模量随马来松香用量的增加先减小后增大最后减小，但体系的黏度和模量总体呈下降趋势，木粉经马来松香改性后复合熔体的流变性能显著改善，这不仅有利于提高复合材料的成型加工效率，而且适当的马来松香处理也能够提高复合材料的拉伸强度和弯曲强度，后者被静态力学试验结果所证实。

Spikelets 3–4 mm, brown; callus hairs a little shorter than spikelet, brown; lower glume oblong-lanceolate, papery becoming herbaceous toward apex, back brown-hirsute, apex narrowly truncate; lower lemma 3/4 length of glumes; upper lemma oblong, obtuse and awnless or minutely mucronate, varying to shortly 2-toothed and awned from sinus; awn twisted, bent, up to 6 mm.

小穗3-4毫米，棕色；胼胝体毛一小短于小穗，棕色；狭的更低的颖片长圆状披针形，纸质的变得的草质的向先端，背面棕色具粗毛，先端截形；更低的外稃3/4段颖片；上面外稃长圆形，短尖的钝和awnless或微小的，变化随着短2齿和从那里凹缺；芒扭曲，弯曲，可达6毫米花粉囊3，1.6-2.2毫米。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。