石英晶体扭转效应的仿真与优化

【作者】 郭莉；

【导师】 孙宝元；

【作者基本信息】 大连理工大学 ， 机械电子工程， 2002， 硕士

【摘要】 本文在博士学科点基金和自然科学基金的资助下，从工程实际出发，运用晶体物理学、电介质物理学、弹性理论、数值分析等交叉学科的理论成果，对石英晶体扭转效应进行了研究。应用各向异性柱体扭转理论，探讨了石英晶体在扭矩作用下内部复杂的应力场分布，给出了应力场的数值解法。联系石英晶体的压电效应，计算出内部的电极化场，并利用电场等效原理求解出等效电极化体电荷与面电荷分布。从理论与实验两个方面确定了石英晶体扭转效应的存在。建立了压电晶体扭转效应中电学量和机械量的关系。 在建立石英晶体扭转效应模型的基础上，应用多变量、无约束非线性优化方法对于晶体切型、截面形状等参数进行了优化，以获得最佳扭转灵敏度。优化结果得到了实验的有力支持。这一结果对于石英晶体扭转效应在工程中的应用有重要意义。 附录给出了基于MATLAB的仿真与优化程序。更多还原

【Abstract】 This thesis is supported by the National Natural Science Foundation of China (No.69974020) and the Scientific Research Foundation on Doctor’s Subject of the Ministry of Education (No.98014016,10010141006). From aspect of application in engineering, knowledge from different cross disciplines such as Physics of Crystals, Physics of dielectrics, Thoery of elasticity, Numerical Analysis is utilized in the investigation on the torsional effect of piezoelectric. The complicated stress distribution of piezoelectric beam under torsion is investigated first by utilizing the torsion theory of anisotropic beam. Numerical solution is approached. Affiliated with piezoelectric effect of quartz, inner nonlinear electric polarization is calculated, equivalent body bound charges and sueface bound charges under torque are approached. Existence of torsional effect is testified by theoretical and experimental anlysis. The connection between the torque and the polarized charges is established.On the base of mathematical model of torsional effect, using multivariate unrestrained nonlinear optimization method, we research cutting angles and parameters of crosssection to get best torsional sensitivity. Result of optimization is supported by experiment. This is important for application in engineering.Based on MATLABprograms of simulation and optimization of torsional effect are included in appendix.更多还原