Dynamic behavior of micro-diaphragms and its characterized description
Tóm tắt
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.
Tài liệu tham khảo
Rayleigh L. The Theory of Sound. London: Macmillan. 1st ed: Vol. I, 1877, Vol. II. 1878; 2nd ed: Vol. I, 1894, Vol. II. 1896
Wente E C. A condenser transmitter as a uniformly sensitive instrument for the absolute measurement of sound intensity. Phys Rev, 1917, 10(1): 39–63
Mason W P. Electromechanical Transducers and Wave Filters. Nev York: Van Nostrand D Company Inc, 1st ed, 1942; 2nd ed, 1948
Haller M I, Khuri-Yakub B T. A surface micromachined electrostatic ultrasonic air transducer. IEEE Trans Ultrason Ferroelect Freq Contr, 1996, 43(1): 1–6
Ladabaum I, Jin X, Soh H, et al. Surface micromachined capacitive ultrasonic transducers. IEEE Trans Ultrason Ferroelect Freq Contr, 1998, 45(3): 678–690
Ge L F. Modeling of electrostatic ultrasonic transducers with micro air-gap structure. In: Proceedings of 16th ICA and 135th ASA Meeting. New York: Acoust Soc Am, 1998. 1081–1082
Ge L F. Electrostatic airborne ultrasonic transducer: Modeling and characterization. IEEE Trans Ultrason Ferroelect Freq Contr, 1999, 46(5): 1120–1127
Kupnik M, Wygant I O, Khuri-Yakub B T. Finite element analysis of stress stiffening effects in CMUTs. In: Proceedings of 2008 IEEE International Ultrasonic Symposium, 2008, 4E-1
Wygant I O, Kupnik M, Khuri-Yakub B T. Analytically calculating membrane displacement and the equivalent circuit model of a circular CMUT cell. In: Proceedings of 2008 IEEE International Ultrasonic Symposium, 2008. P3F069-06
Ge L F. Response of capacitive micromachined ultrasonic transducers. In: Proceedings of 7th Int Symp Instrumentation and Control Tech. SPIE, 2008, No. 7127, 71270B-2
Ge L F. A novel design of micromachined capacitive Lamb wave transducer. In: Proceedings of 6th Intl Symp Instrumentation and Control Tech. SPIE, 2006, No. 6358, 63581I-1
Ge L F. A design of high-sensitivity micromachined capacitive ultrasonic mass resonators. In: Proceedings of 2008 IEEE International Ultrasonic Symposium, 2008. 5J-6
Wah T. Vibration of circular plates. J Acoust Soc Am, 1962, 34(3): 275–281
Leissa A. Vibration of Plates. Washington D. C.: NASA, 1969 (originally published); New York: Acoust Soc Am, 1993