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

Clinical Studies on conformal radiotherapy combined with epidermal growth factor receptor-tyrosine kinase inhibitor in second-line treatment of non-small cell lung cancer

Purpose: To study the effect of conformal radiotherapy combined with epidermal growth factor receptor-tyrosine kinase inhibitor (EGFR-TKI) in the second-line treatment of non-small cell lung cancer (NSCLC).Methods: A total of 316 patients attending Shanghai Pulmonary Hospital affiliated to Tongji University, were divided into two groups: 106 patients were treated with conformal radiotherapy combined with EGFR-TKI (gefitinib, 250 mg/day; or erlotinib, 150 mg/day), while 210 patients were treated with EGFRTKI alone. Some factors, including adverse reactions (AR), disease control rate (DCR), progression-free survival (PFS), overall survival (OS), and one-year and two-year survival rate, were evaluated.Results: No obvious difference was observed in AR between the two groups (p > 0.05). In the combination therapy group, complete response (CR) was 5 cases, partial response (PR) 43 cases, and stable disease (SD) 47 cases, progressive disease (PD) was 11 cases, response rate (RR) was 45.3 %, and DCR 89.6 %. Median PFS in the combination therapy group and targeted therapy group was 6.5 and 5.0 months, respectively. On the other hand, median OS in the combination therapy group and targeted group was 14.1 and 12.6 months, respectively. One-year survival rate of the combination therapy group and EGFR-TKI group was 60.3 and 50.0 %, respectively, while the two-year survival rate was 26.3 and 19.0 %, respectively.Conclusion: Conformal radiotherapy combined with EGFR-TKI can be used as an effective second-line treatment for NSCLC.Keywords: Non-small cell lung cancer, Epidermal growth factor receptor tyrosine kinase inhibitor, Conformal radiotherapy, Targeted therapy, Survival rat