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微米尺度的膜片结构在电容型微传感器和微纳器件中具有重要作用,而器件的性能主要取决于膜片的动力学行为.微膜片通常处理为膜,某些场合处理为板或张力板(Plate in tension,简称为TD板),但许多场合还显示出空气弹簧支承的张力板(Plate in tension and supported by air-spring,简称为TDK板)的行为.因此,必需对膜片的动力学行为作系统的研究,建立一个特征化的数学描述.该文集中对具一般性的TDK板进行研究,给出其基本方程,并导出四周固定和简支两种边界条件下的TDK圆板的分析解.该文还给出特征曲面的三维图表示,揭示出TDK板和TD板向纯板和纯膜行为过渡的情形,并用φ值判定膜片的性质,其极端情形,即φ=0和φ=∞,分别对应纯板和纯膜.这样,膜、板和TD板可作为TDK板的特例处理.该文还揭示了空气弹簧的存在不仅增强了膜片的恢复力从而提高膜片的固有频率,而且导致膜片与空气弹簧构成的动力学系统的共振.这些分析和计算的结果对电容微传感器的工作机理的理解及其优化设计具有重要意义.
Micrometer-scale diaphragm structure plays an important role in capacitive micro-sensors and micro-nano devices, and the performance of the device mainly depends on the dynamic behavior of the membrane.Micro-diaphragm is usually treated as a membrane, in some cases as a plate or tension Plate (Plate in tension, referred to as the TD plate), but in many cases also shows the air spring-supported tension plate (Plate in tension, supported by air-spring, referred to as TDK plate) behavior. Kinematics behavior of the system to establish a characterization of the mathematical description of the paper focused on the general TDK board to study its basic equations are given and derived four fixed and simple support boundary conditions TDK round two The analytical solution of the plate is also given.The 3D representation of the characteristic surface is also given, which reveals the transition of the TDK and TD plates to the pure plate and the pure membrane behavior, and the value of φ is used to determine the properties of the diaphragm. In its extreme case, φ = 0 and φ = ∞, corresponding to the pure and pure films, respectively. Thus, the films, plates and TD plates can be treated as special cases of TDK plates. The natural frequency of the diaphragm, but also the diaphragm Resonance dynamics of the system configuration of the air spring. The results of these calculations and analysis and understanding of the optimization design of the working principle of the capacitive micro-sensor is important.