An Analysis of Thickness-shear Vibrations of an Annular Plate with the Mindlin Plate Equations

The Mindlin plate equations with the consideration of thickness-shear deformation as an independent variable have been used for the analysis of vibrations of quartz crystal resonators of both rectangular and circular types. The Mindlin or Lee plate theories that treat thickness-shear deformation as an independent higher-order vibration mode in a coupled system of two-dimensional variables are the choice of theory for analysis. For circular plates, we derived the Mindlin plate equations in a systematic manner as demonstrated by Mindlin and others and obtained the truncated two-dimensional equations of closely coupled modes in polar coordinates. We simplified the equations for vibration modes in the vicinity of fundamental thickness-shear frequency and validated the equations and method. To explore newer structures of quartz crystal resonators, we utilized the Mindlin plate equations for the analysis of annular plates with fixed inner and free outer edges for frequency spectra. The detailed analysis of vibrations of circular plates for the normalized frequency versus dimensional parameters provide references for optimal selection of parameters based on the principle of strong thickness-shear mode and minimal presence of other modes to enhance energy trapping through maintaining the strong and pure thickness-shear vibrations insensitive to some complication factors such as thermal and initial stresses.Comment: Paper to be presented to the 2015 IEEE International Frequency Control Symposium and European Frequency and Time Forum, Denver, CO, USA. April 12-16, 201

Multi-color optical monitoring of the quasar 3C 273 from 2005 to 2016

We have monitored the quasar 3C 273 in optical $V$, $R$ and $I$ bands from 2005 to 2016. Intraday variability (IDV) is detected on seven nights. The variability amplitudes for most of nights are less than 10\% and four nights more than 20\%. When considering the nights with time spans $>4$ hours, the value of duty cycle (DC) is 14.17 per cent. Over the twelve years, the overall magnitude and color index variabilities are $\bigtriangleup I=0^{\rm m}.67$, $\bigtriangleup R=0^{\rm m}.72$, $\bigtriangleup V=0^{\rm m}.68$, and $\bigtriangleup (V-R)=0^{\rm m}.25$ respectively. The largest clear IDV has an amplitude of 42% over just 5.8 minutes and the weakest detected IDV is 5.4% over 175 minutes. The BWB (bluer when brighter) chromatic trend is dominant for 3C 273 and appears at different flux levels on intraday timescales. The BWB trend exists for short-term timescales and intermediate-term timescales but different timescales have different correlations. There is no BWB trend for our whole time-series data sets. A significant anti-correlation between BWB trend and length of timescales is found. Combining with $V$-band data from previous works, we find a possible quasi-periodicity of $P=3918\pm1112$ days. The possible explanations for the observed variability, BWB chromatic trend and periodicity are discussed.Comment: 63 pages, 11 figures, 6 tables. Accepted for publication in ApJ

Thickness-shear Vibration Frequencies of an Infinite Plate with a Generalized Material Property Grading along the Thickness

For quartz crystal resonators of thickness-shear type, the vibration frequency and mode shapes, which are key features of resonators in circuit applications, reflect the basic material and structural properties of the quartz plate and its variation with time under various factors such as erosive gases and liquids that can cause surface and internal damages and degradation of crystal blanks. The accumulated effects eventually will change the surface conditions in terms of elastic constants and stiffness and more importantly, the gradient of such properties along the thickness. This is a typical functionally graded materials (FGM) structure and has been studied extensively for structural applications under multiple loadings such as thermal and electromagnetic fields in recent years. For acoustic wave resonators, such studies are equally important and the wave propagation in FGM structures can be used in the evaluation and assessment of performance, reliability, and life of sensors based on acoustic waves such as the quartz crystal microbalances (QCM). Now we studied the thickness-shear vibrations of FGM plates with properties of AT-cut quartz crystal varying along the thickness in a general pattern represented by a trigonometric function with both sine and cosine functions of the thickness coordinate. The solutions are obtained by using Fourier expansion of the plate deformation. We also obtained the frequency changes of the fundamental and overtone modes which are strongly coupled for the evaluation of resonator structures with property variation or design to take advantages of FGM in novel applications.Comment: Paper for the proceedings of the 2015 IEEE International Frequency Control Symposium and the European Frequency and Time Forum, Denver, CO, USA. April 12-16, 201

Effects of Surgery on Prognosis of Young Women With Operable Breast Cancer in Different Marital Statuses: A Population-Based Cohort Study

BackgroundThe influence of surgical approaches [including mastectomy, breast-conserving therapy (BCT) and post-mastectomy breast reconstruction (PMBR) on prognosis of young women (<40 years old) with operable breast cancer has not been determined yet, and this might vary in patients with different marital statuses. Therefore, we aimed to investigate the effect of surgery on survival outcomes for young women with operable breast cancer in different marital statuses.MethodsWe used the Surveillance, Epidemiology, and End Results (SEER) database to identify young women with operable breast cancer between 2004 and 2016, who underwent mastectomy, BCT or PMBR. We assessed overall survival (OS) and breast cancer-specific survival (BCSS) using the Kaplan–Meier method and hazard ratios using multivariate Cox proportional hazard regression.ResultsCompared to mastectomy, both of BCT and PMBR conferred better OS (BCT: HR = 0.79, 95%CI: 0.69–0.90, p <0.001; PMBR: HR = 0.70, 95%CI: 0.63–0.78, p <0.001) and BCSS (BCT: HR = 0.79, 95%CI: 0.69–0.91, p = 0.001; PMBR: HR = 0.73, 95%CI: 0.65–0.81, p <0.001), but there was no significant difference of survival between BCT and PMBR group. The survival benefit of BCT compared to mastectomy remained significant in unmarried young women (OS: HR = 0.68, 95%CI: 0.55–0.83, p <0.001; BCSS: HR = 0.69, 95%CI: 0.56–0.86, p = 0.001) but not in the married (OS: HR = 0.89, 95%CI: 0.75–1.05, p = 0.177; BCSS: HR = 0.89, 95%CI: 0.75–1.05, p = 0.161), while no matter married or not, PMBR group had better OS and BCSS than mastectomy group but not BCT group.ConclusionBoth of BCT and PMBR had improved survival compared to mastectomy for young women with operable breast cancer. The survival benefit of BCT compared to mastectomy remained significant in unmarried patients but not in married patients

The Connection between Buddhist Temples, the Landscape, and Monarchical Power: A Comparison between Tuoba Hong (471–499) from the Northern Wei Dynasty and Li Shimin (626–649) from the Tang Dynasty

Since the Western Jin period, Buddhism has confronted bureaucratic power within the architectural landscape. In this study, historical records and archaeological reports of two Buddhist temples—the Siyuan Temple 思遠佛寺 built during the reign of Tuoba Hong 拓跋宏 and Emperor Xiaowen 孝文帝 of the Northern Wei dynasty, and the Zhaoren Temple 昭仁寺, built during the reign of Li Shimin 李世民 and Emperor Taizong 唐太宗 of the Tang dynasty—were examined. A comparison was made of the two temples’ geographic locations in relation to cities while considering period-specific phenomena. This study also considers mountains, water, and topographical features. The geographic information reflects differences in the ideas of the ruling class and monarchs of the two historical periods. The findings are that both Buddhist temples were close to the capital and both emperors demonstrated the supremacy of their power by building them. Therefore, the religious landscape owes its formation, development, and underlying significance to emperors and social groups