Diaphragm structures with micron scale play a significant role in microtransducers and micro-nano devices, and the performance of these devices depends mainly on the dynamic behaviour of diaphragms. Micro-diaphragms a...Diaphragm structures with micron scale play a significant role in microtransducers and micro-nano devices, and the performance of these devices depends mainly on the dynamic behaviour of diaphragms. Micro-diaphragms are treated commonly as membranes and in some cases as plates or plates in tension (called TD plates for short), but they also show in many cases the behaviour of plates in tension and supported by air spring (called TDK plates for short). Therefore, it is necessary to perform systematic research on the dynamic behaviour of micro-diaphragms, and establish a characterized mathematical description. This paper focuses on the TDK plates since they possess universality, gives the corresponding basic equations, and then derives analytical solutions of TDK circular plates under clamped and simply supported boundary conditions. This paper also gives a 3D plot representation of characteristic curved surfaces, revealing the transition from the TDK and TD plate to the pure plate or pure membrane behaviour; and further uses the value φ to determine the property of diaphragms. Its two extreme cases, i.e. φ = 0 and φ = ∞ , correspond to pure plate or pure membrane, respectively. Thus, membrane, plate and TD plate can be treated as special cases of TDK plate. In addition, this paper reveals that the presence of air-spring not only enhances the restoring force of diaphragm such that increases its natural frequencies, but also results in the resonance of a dynamic system consisting of diaphragm and air-spring. These analytical and computational results are significant for the understanding of the operation mechanism of capacitive microtransducers and their optimized design.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60774053 and 60374044)
文摘Diaphragm structures with micron scale play a significant role in microtransducers and micro-nano devices, and the performance of these devices depends mainly on the dynamic behaviour of diaphragms. Micro-diaphragms are treated commonly as membranes and in some cases as plates or plates in tension (called TD plates for short), but they also show in many cases the behaviour of plates in tension and supported by air spring (called TDK plates for short). Therefore, it is necessary to perform systematic research on the dynamic behaviour of micro-diaphragms, and establish a characterized mathematical description. This paper focuses on the TDK plates since they possess universality, gives the corresponding basic equations, and then derives analytical solutions of TDK circular plates under clamped and simply supported boundary conditions. This paper also gives a 3D plot representation of characteristic curved surfaces, revealing the transition from the TDK and TD plate to the pure plate or pure membrane behaviour; and further uses the value φ to determine the property of diaphragms. Its two extreme cases, i.e. φ = 0 and φ = ∞ , correspond to pure plate or pure membrane, respectively. Thus, membrane, plate and TD plate can be treated as special cases of TDK plate. In addition, this paper reveals that the presence of air-spring not only enhances the restoring force of diaphragm such that increases its natural frequencies, but also results in the resonance of a dynamic system consisting of diaphragm and air-spring. These analytical and computational results are significant for the understanding of the operation mechanism of capacitive microtransducers and their optimized design.
