Levinson 矩形微板谐振器热弹性阻尼解析解

基于 Levinson 高阶剪切板理论,给出了四边简支微板谐振器热弹性耦合自由振动的复频率以及板内变温场的精确解析解;由复频率法给出了表征微板热弹性阻尼的逆品质因子;通过数值结果分析了 Levinson 微板的热弹性阻尼随几何尺寸和振动模态变化的规律,并与一阶剪切变形理论和经典板理论的预测结果进行了比较,分析了剪切变形对热弹性阻尼的影响程度。数值结果表明,对于中厚板和厚板谐振器,经典板理论预测的热弹性阻尼值明显大于剪切变形板理论的预测值。这是由于经典板理论忽略了横向剪切变形,从而过高地估计了微板的抗弯刚度。另外,在四边简支条件下,还给出了 Mindlin 微板和 Levinson 微板热弹性阻尼预测值之间的比较。结果表明,Levinson高阶剪切变形理论能够更好地预测厚板谐振器的热弹性阻尼。这是因为 Levinson 理论下的位移场能够精确满足上下表面应力为零的条件,温度场包含了厚度方向坐标的高阶项。     

简支Mindlin板的振动与声辐射研究

建立基于Mindlin厚板理论的简支矩形板振动及声辐射数学计算模型。通过Rayleigh积分公式计算出板结构与声场交界面的声压,进而获得求解结构表面振速的方程。利用振动模态正交性获得结构振动与声辐射的特性参数以及声辐射阻抗与模态声辐射系数。由于Mindlin厚板模型考虑了板的横向剪切变形和转动惯量,其动力学计算结果比经典薄板理论更精确,在高频时更可靠。但由于声辐射只跟板的横向振动相关,两种模型计算出来的平均辐射效率没有明显区别。     

药品包衣厚度测量系统晶振频率分析及实验研究

为提高药品包衣效果和包衣质量,针对包衣厚度在线监测问题,提出基于石英晶体谐振原理的包衣厚度测量方法。利用石英晶体的压电效应原理分析石英晶体谐振片厚度剪切振动的谐振频率与包衣厚度之间的函数关系,使用等效密度法建立有限元模型并分析石英晶体谐振器在不同膜厚情况下的模态和谐振频率,理论和有限元分析结果均表明晶片的谐振频率随薄膜厚度的增加而降低,且呈近似的线性关系,检测灵敏度约为12 k Hz/μm。使用石英晶体微天平系统进行包衣厚度的测量实验,实测厚度和分析结果具有很好的一致性。研究结果表明基于石英晶体谐振的膜厚测量法可以应用于制药包衣厚度的实时测量。     

厚度振动换能器降耦合结构优化与工程应用

厚度振动是高频换能器的常用振动模态。对压电圆片而言,横向方向的耦合总是存在的,不存在理想的厚度振动模态。若压电圆片的尺寸比例合适,横向耦合较弱,若尺寸比例不合适,横向耦合会很强。耦合会使振子表面振动位移反相,频响曲线出现多个难以区分的谐振峰,对换能器的发送电压响应、指向性等产生负面影响,对某军用型号工程中利用该振动模态工作的换能器的生产质量有较大影响。通过对压电振子的振动模态、耦合振动频率等理论和仿真计算,开展频率优化研究,降耦合对换能器的影响分析以及试验验证,仿真分析和试验结果表明:中心孔对圆片高频换能器模态振动具有明显的降耦合作用,可提高圆片换能器的发射能力,改善指向性特性,解决了该类换能器生产质量不高、成品率低等问题。     

Mindlin板弯曲和振动分析的高阶杂交应力三角形单元

现有的Mindlin板单元只能通过零剪力分片检验,而不能通过非零常剪力分片检验。该文根据Reissner- Mindlin一阶剪切变形理论,基于余能原理,提出了一种高阶杂交应力六节点三角形Mindlin板单元。该单元特点是不仅能通过零剪力分片检验,而且能通过严格的非零常剪力增强型分片检验。构造单元时特别注意了单元边界位移以及域内应力的插值函数的选取。采用任意阶Timoshenko梁函数作为边界位移插值函数,应力插值函数选取为满足平衡方程的多项式。对不同厚度不同边界条件的方板进行弯曲和自由振动分析,质量矩阵采用集中质量阵。数值结果表明无论对薄板还是中厚板,该单元均是准确有效的。     

功能梯度Levinson圆板弯曲解的均匀化和经典化表示

基于Levinson三阶剪切变形理论,研究了材料性质沿厚度任意连续变化的功能梯度材料圆板的轴对称弯曲问题。首先,建立了功能梯度材料圆板在Levinson板理论下轴对称弯曲问题位移形式的控制微分方程,其中考虑了拉-弯耦合和三阶剪切变形效应。然后,利用载荷等效关系以及均匀板的经典理论控制微分方程,导出功能梯度圆板在Levinson剪切变形理论下弯曲解与经典理论下均匀圆板的挠度之间的解析转换关系,给出了转换系数的计算公式。由此,可将功能梯度材料圆板在Levinson三阶剪切理论下的弯曲问题转化为相应均匀薄圆板在经典理论下的弯曲问题求解,以及转换系数的计算问题。     

多环盘组合结构的横向弯曲耦合振动建模与求解

超声谐振系统是旋转超声加工的核心设备,而多环盘结构是超声谐振系统中一种典型的负载结构,其横向弯曲耦合振动分析对于超声谐振系统设计具有重要意义。基于Mindlin厚板动力学理论,利用环盘的位移、转角、剪力和弯矩的连续条件和边界条件,建立了多环盘组合结构的横向弯曲耦合振动分析模型,推导了频率求解方程,并基于MATLAB设计了多环盘横向弯曲耦合振动频率的计算软件。通过理论模型求解、有限元模态分析和齿轮模态实验之间的对比分析,验证了该求解模型的准确性和程序的实用性,为旋转超声加工系统的设计提供了技术参考。     

硅酸镓镧单晶材料的声表面波标签研究

声表面波射频识别标签在射频标签领域获得广泛关注,其中对标签基底材料的研究也成了研究热点。文章旨在研究使用硅酸镓镧单晶材料为压电基底的声表面波标签的标签特性。对使用硅酸镓镧单晶材料为压电基底的声表面波标签进行频域和时域分析,并结合有限元分析方法,对标签的特征频率、叉指换能器(Interdigital Transducer, IDT)的反射系数、叉指电极金属化比、金属电极厚度以及标签回波特性进行研究分析,提取了耦合模COM(Coupled-mode)模型参数。分析结果表明了压电效应是声表面波的谐振与反谐振频率存在的根源,验证了脉冲幅度编码方式,并为使用硅酸镓镧材料作为压电基底的声表面波标签的制作提供了仿真实验依据。     

考虑芯层横向变形的粘弹性复合材料夹层板结构的声振特性分析

夹层板结构具有很高的比强度和比刚度。若芯层采用粘弹性阻尼材料，夹层板结构还具有良好的隔振和隔声特性，因此在工程结构中得到广泛应用。以往的夹层板理论大多忽略了芯层的横向正应变和横向正应力，在分析芯层较厚的夹层板或者夹层结构的高频振动问题时由于不能体现芯层的横向压缩变形，往往显得不够合理。针对这一不足，构造了一个复合材料夹层板单元：夹层板的上下面板采用基于一阶剪切变形理论的Mindlin假定以及层合板理论进行分析；采用文献[6，7]中提出的Timoshenko层合厚梁理论构造了单元每边的转角和剪应变场，消除了Mindlin板单元当板厚变小时的剪切锁死问题；假定芯层的位移沿厚度方向线性变化，并用上下面板的自由度表示，最终形成以上下面板自由度表示的系统总的运动方程。该单元不仅考虑了芯层的横向剪切变形，还考虑了芯层的横向压缩变形。数值计算结果表明：无论对于静力问题、动力问题还是声辐射等问题，考虑芯层的横向压缩变形是合理的，也是有必要的。     

车轨桥中高频耦合振动分析的功率流方法及模型

轮轨滚动激励引起的桥梁振动响应和输入功率是计算桥梁结构辐射噪声的重要参数。时域车轨桥耦合振动分析常用于低频振动分析,但在中高频分析时效率较低。为此,提出一种基于力法原理的频域功率流方法解决这一问题。采用无限长Euler梁或Timoshenko梁建立钢轨部件,采用无限大Kirchhoff板、Mindlin板或有限元模型建立桥梁部件,采用弹簧元件模拟钢轨与桥梁之间的连接扣件,并以弹簧力为未知量建立力法基本方程。对比计算了不同轨桥模型对U梁和箱梁桥振动功率的影响。结果表明:U梁桥面板的剪切效应对桥梁振动功率计算结果影响很大,采用传统的无限大Kirchhoff板模型将导致功率级计算误差达到15 dB,而采用Mindlin板模型可获得良好的计算精度与效率。相对于箱梁实体有限元模型而言,采用Mindlin板模型的误差仍然较大。     

The determination of the optimal length of crystal blanks in quartz crystal resonators

It is well understood that the strong coupling of thickness-shear and flexural vibrations in piezoelectric crystal plates only occurs at specific length at which the vibration mode conversion, like the flexural mode gradually converting to thickness-shear mode while the thickness-shear mode converting to higher-order flexural mode, happens. It is important to avoid the strong coupling of modes in a crystal resonator that uses thickness-shear vibrations to enhance the energy trapping. To achieve such a design goal, the length of a crystal blank should be carefully chosen such that the coupling is at its weakest, which usually is in the middle of two strong coupling points. Through a closer examination of the frequency spectra, or the frequency-length relationship in this study, we can see that the strong coupling points appear periodically. This implies that we can find exact locations with the plate theory that predicts the resonance frequency. Based on this observation, we first use the first-order Mindlin plate theory with the precise thickness-shear frequency, which is normalized to one, to find corresponding wavenumbers. Then the length as a variable is solved from the coupled frequency equation for exact coupling points in a crystal plate of AT-cut quartz. The optimal length of a crystal blank in the simplest resonator model is calculated for the coupled thickness-shear, flexural, and extensional vibrations. The solutions and the method will be important in the determination of optimal length of a crystal blank in the resonator design process.     

An analysis of nonlinear vibrations of coupled thickness-shear and flexural modes of quartz crystal plates with the homotopy analysis method

We investigated the nonlinear vibrations of the coupled thickness-shear and flexural modes of quartz crystal plates with the nonlinear Mindlin plate equations, taking into consideration the kinematic and material nonlinearities. The nonlinear Mindlin plate equations for strongly coupled thickness- shear and flexural modes have been established by following Mindlin with the nonlinear constitutive relations and approximation procedures. Based on the long thickness-shear wave approximation and aided by corresponding linear solutions, the nonlinear equation of thickness-shear vibrations of quartz crystal plate has been solved by the combination of the Galerkin and homotopy analysis methods. The amplitude frequency relation we obtained showed that the nonlinear frequency of thickness-shear vibrations depends on the vibration amplitude, thickness, and length of plate, which is significantly different from the linear case. Numerical results from this study also indicated that neither kinematic nor material nonlinearities are the main factors in frequency shifts and performance fluctuation of the quartz crystal resonators we have observed. These efforts will result in applicable solution techniques for further studies of nonlinear effects of quartz plates under bias fields for the precise analysis and design of quartz crystal resonators.     

On the accuracy of Mindlin plate predictions for the frequency-temperature behavior of resonant modes in AT- and SC-cut quartz plates

The frequency spectra of resonant modes in AT- and SC-cut quartz plates and their frequency-temperature behavior were studied using Mindlin first- and third-order plate equations. Both straight-crested wave solutions and two-dimensional plate solutions were studied. The first-order Mindlin plate theory with shear correction factors was previously found to yield inaccurate frequency spectra of the modes in the vicinity of the fundamental thickness-shear frequency. The third-order Mindlin plate equations without correction factors, on the other hand, predict well the frequency spectrum in the same vicinity. In general, the frequency-temperature curves of the fundamental thickness-shear obtained from the first-order Mindlin plate theory are sufficiently different from those of the third-order Mindlin plate theory that they raise concerns. The least accurately predicted mode of vibration is the flexure mode, which results in discrepancies in its frequency-temperature behavior. The accuracy of other modes of vibrations depends on the degree of couplings with the flexure mode. Mindlin first-order plate theory with only the shear correction factors is not sufficiently accurate for high frequency crystal vibrations at the fundamental thickness-shear frequency. Comparison with measured resonant frequencies and frequency-temperature results on an AT-cut quartz plate shows that the third-order plate theory is more accurate than the first-order plate theory; this is especially true for the technically important fundamental thickness shear mode in the AT-cut quartz plate.     

Synthesis of a novel langanite-type compound La3Al5.5Nb0.5O14 by the sol-gel process

Langanite (La₃Ga_5.5Nb_0.5O₁₄, LGN) and its isomorphs are a few piezoelectric materials which have the unique temperature compensation and piezoelectric properties. But the high Ga₂O₃ content makes them very expensive and limits their applications. We reported a new langanite-type compound La₃Al_5.5Nb_0.5O₁₄ (LAN) which has the advantage of no Ga₂O₃ content. Chemically homogeneous La₃Al_5.5Nb_0.5O₁₄ sol was synthesized using La (NO₃)₃·6H₂O, Al (NO₃)₃·9H₂O and niobium citrate as starting materials. Single-phased LAN powder was prepared by decomposition of a citrate polymer precursor and subsequent reactions at high temperatures. TG-DTA, XRD and FTIR were employed to investigate the transformation process of gel to LAN powder. The results showed that, after calcination at 900 °C, pure La₃Al_5.5Nb_0.5O₁₄ polycrystalline powder with a narrow particle size distribution was obtained, which has the same structure with La₃Ga_5.5Nb_0.5O₁₄.     

Time-resolved spectroscopy of intrinsic luminescence of Y3Ga5O12 and (LaLu)3Lu2Ga3O12 single crystals

The nature of intrinsic luminescence of Y₃Ga₅O₁₂ (YGG) and (LaLu)₃Lu₂Ga₃O₁₂ (LLGG) single crystals grown from a melt was determined. In the case of a YGG single crystal containing Y_Ga antisite defects with a concentration of 0.25–0.275 at.% the intrinsic luminescence was considered as a superposition of luminescence of self-trapped excitons (STE), luminescence of excitons localized near antisite defects (LE(AD) centers) and luminescence caused by a recombination of an electron with a hole captured at Y_Ga antisite defects. Due to a large (2–3%) concentration of Lu_La antisite defects in LLGG single crystals the intrinsic luminescence was a superposition mainly of the LE(AD) center emission and the recombination luminescence of Lu_La antisite defects. The energy structure of the mentioned centers in YGG and LGGG hosts was determined from the excitation spectra of their luminescence under excitation by synchrotron radiation in the range of the fundamental absorption edge of these garnets.     

The frequency-temperature analysis equations of piezoelectric plates with Lee plate theory

Frequency-temperature analysis theory of crystal plates based on the incremental field theory (IFT) and the Mindlin plate theory have been widely used in the vibration analysis of crystal resonators subject to temperature change. As one of the two major plate theories for the resonator analysis, the Lee plate theory based on the trigonometric series expansion of displacements has been extensively used for both analytical and numerical analyses of quartz resonators, and efforts have also been made in correcting and perfecting the theory for much broader applications. In this paper, the earlier frequency-temperature analysis equations based on the IFT is further extended to the trigonometric series expansion in a systematic manner. By incorporating the frequency-temperature analysis into the Lee plate theory, the complete analysis of crystal resonators can be made in a consistent way. The thickness-shear and flexural vibration equations have been compared with the Mindlin plate theory to demonstrate the similarity and consistency.     

Lee plate equations for electroded quartz crystal plates with the consideration of electrode density and stiffness

Lee plate equations for high-frequency vibrations of piezoelectric plates have been established and improved over the last decades with the sole objective of obtaining the accurate prediction of frequency and mode shapes to aid crystal resonator design. The latest improvement includes extra terms related to derivatives of the flexural displacement to adjust the accuracy and consider electrodes for practical applications. As part of the efforts to make the equations applicable for resonator design with the improved frequency accuracy and consideration of electrodes, we derived Lee plate equations for electroded plates by changing the integration limits in the dimension reduction procedure to signify the dominant role of the crystal plate. By modifying the density terms in plate equations to include the contribution of both electrode stiffness and density, the accuracy of the thickness-shear vibration frequency of electroded plates is improved for commonly used electrode materials.     

Sol-gel synthesis of yellow-emitting La4Ca(SiO4)3O:Ce phosphors for white-light emitting diodes

Ce³⁺ doped La₄Ca(SiO₄)₃O phosphors with silicate oxyapatite structure were synthesized by the sol-gel process. The X-ray diffraction (XRD) patterns showed that a pure phase was formed when sintering temperature was higher than 1300°C. The optical properties of La₄Ca(SiO₄)₃O:Ce³⁺ phosphors with varying sintering temperature and concentration were investigated by examining their excitation and emission spectroscopy. The phosphors exhibited a broad emission band centered at 550nm which could be attributed to the 5d-4f transition of Ce³⁺ and a stronger excitation peak around 467nm as well as several shoulder bands, nicely matching with the widely applied blue LED chips. Higher emission intensity was observed when firing temperature above 1300°C, due to increasing crystallinity of the powders. When Ce³⁺ concentration was equal to 5 at%, the sample exhibited the optimum excitation and emission efficiency. The results indicate that La₄Ca(SiO₄)₃O:Ce³⁺ is a promising candidate in the application of blue chip excited white light emitting diodes (LEDs).     

Ga2O3 nanowires grown on GaN-Ga2O3 core-shell nanoparticles using a new method: Structure, morphology, and composition

Ga₂O₃ nanowires grown on GaN-Ga₂O₃ core-shell nanoparticles were prepared through heat-treating GaN powder method which comprises a pre-nitridation process in the flow of N₂ gas and a post-oxidation process in the air at 1200 °C. XRD and EDS patterns indicated that the heat-treated GaN powders were a powder mixture of GaN and Ga₂O₃. SEM, TEM, HRTEM and SAED images revealed that some nanowires that grow out from the edge of the GaN-Ga₂O₃ core-shell nanostructures with atomically smooth interfaces were monoclinic Ga₂O₃. Large blue-shifts in vibration frequency of Ga-N bonds observed in the FTIR spectrum could be contributed to size confinement effect and internal strains in GaN nanoparticles.     

Improved dielectric properties of CaCu3Ti4O12 thin films on oxide bottom electrode of La0.5Sr0.5CoO3

We report on the effect of La_0.5Sr_0.5CoO₃ (LSCO) bottom electrode to the dielectric properties of CaCu₃Ti₄O₁₂ (CCTO) thin films grown on Ir/Ti/SiO₂/Si substrates. Compared with the films grown directly on Ir/Ti/SiO₂/Si substrates, the dielectric constant has been increased greatly about 100%, and the dielectric loss decreased to lower than 0.2 in the frequency range of 1-100 kHz. The origin has been discussed in details based on the analysis of the X-ray diffraction and impedance spectra measurements. Results of the impedance spectra suggest that the absence of undesired interfacial layer between Ir/CCTO thin films might be one of the major reasons of the improvement of the dielectric properties when the LSCO was introduced as the bottom electrode.