Direct Mechanical Determination of the Dynamic Response of Diaphragms

Abstract

The freefield resonant frequency and the deflection under given static pressure of a thin, circular, clamped-edge diaphragm may be calculated theoretically by well-known equations. Also, experimental means exist for a determination of these quantities. No satisfactory theoretical or experimental method has appeared, however, by which it is possible to obtain, for a complicated physical system, the diaphragm deflection as a function of the frequency of an applied sinusoidal pressure, over a frequency range that includes the natural diaphragm resonance. An experimental method is described by which a piezoelectric driver is employed to generate a sinusoidal pressure of variable frequency in a confined gas, to which one side of a test diaphragm may be exposed. Equations are derived describing the gas-coupling medium and the piezoelectric driver. By use of these equations, it is possible to predict the characteristics of the apparatus. A study is made of the dynamic response of a series of thin, circular, clamped-edge diaphragms. Since the diaphragm geometry is simple, the resonant frequency may be calculated theoretically. A shock-excitation technique is also employed to determine the resonant frequency. Comparison is then made between the latter two methods and the result given by the apparatus. The static-pressure dependence of the resonant amplitude and resonant frequency of the diaphragms is studied and discussed. The magnitude of the dynamic-pressure amplitude is determined, employing a calibrated commercial pressure gauge below its own resonance. Modifications of the apparatus are reported that extend the dynamic-pressure amplitude and the useful frequency range, and the possibility of utilizing the apparatus for dynamic calibration of pressure gauges is noted.