开孔变截面微悬臂梁传感器的等效刚度和固有频率

研究新型开孔变截面微悬臂梁传感器的等效法向刚度及其对固有频率的影响.首先,考虑微梁纵截面孔洞结构引起的弯扭耦合效应,利用二次积分法获得在自由端集中载荷作用下悬臂梁的挠度,基于弹性材料的Hooke定律建立了微梁等效法向刚度分析的解析模型.然后,采用Rayleigh法获得了微梁的固有频率.最后,通过比对实验结果和有限元结果对解析模型进行了验证.研究表明:解析模型对于开孔变截面微梁刚度和频率的预测和标定具有较好的精度;微梁的等效刚度和固有频率与跨宽比负相关,却与内外宽度比正相关.有关结论可为新型变截面微纳机械传感器的设计提供理论依据和参考.

Equivalent Stiffness and Natural Frequency of a Variable Cross-section Microcantilever Sensor with a Hole

This paper focuses on the equivalent normal stiffness of a new-type variable cross-section microcantilever biosensor with a hole and its effect on the natural frequency. First,considering the bending-torsion coupling effect induced by the cavity structure in the longitudinal cross-section of the micro-beam,the cantilever deflection subjec-ted to a concentrated load at the free-end is obtained by the quadratic integral method. Based on the Hooke's law of elastic material,an analytic model is established for the equivalent normal stiffness of the micro-beam. Thereafter, the natural frequency of the micro-beam is obtained by the Rayleigh's method. Finally,the analytical model is veri-fied by comparing with the relevant experimental results and finite element results. The study show that the analyti-cal model has a good accuracy for predicting and calibrating the stiffness,as well as the frequency of the variable cross-section micro-beam with a hole,and the equivalent stiffness and the natural frequency are negatively correlated with the span-to-width ratio,whereas,positively correlated with the inner-to-outer-width ratio. The relevant conclu-sions can provide a theoretical basis and reference for the design of new-type micro-/nano-mechanical sensors with variable cross-sections.