THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

612 20. Vibration and Vibration Controlpiezoelectric elements against which rest a mass that is preloaded by a stiff spring.When an accelerometer becomes subject to acceleration imparted by the vibrationbeing measured, the mass exerts a force on the piezoelectric element that is proportionalto the acceleration. The charge developed in the piezoelectric elementis, in turn, proportional to the force. The accelerometer may be designed so thatthe piezoelectric element is stressed in compression or in shear. The piezoelectricelements are usually quartz crystals or specially processed ceramic materials.There is more than one type of sensitivity of interest in accelerometer specifications.The charge sensitivity, measured in picocoulombs/g, and voltage sensitivity,measured in terms of mV/g, are important, depending whether the accelerometer isused with charge measuring or voltage measuring equipment. Also, the transversesensitivity, which is the sensitivity to acceleration in a plane normal to the axis tothe principal accelerometer axis should be a low value, preferably less than 3% ofthe main axis sensitivity at low frequencies.The preamplifier, which constitutes the second stage in signal processing, servestwo purposes: one is to amplify the vibration pickup signal that is generally quiteweak and the other purpose is to serve as an impedance transformer between theaccelerometer and the subsequent chain of equipment. A preamplifier may be designedto function as a voltage amplifier in which case the output voltage is directlyproportional to the input voltage or it may function as a charge amplifier in whichcase the output voltage is proportional to the input charge. Each type of amplifierhas its own advantages and disadvantages. When a charge amplifier is used,changes in cable length (which modifies the cable capacitance) have negligibleeffects on the measurements. When a voltage amplifier is employed, the systemwill be extremely sensitive to changes in cable capacitance. Because the input resistanceof a voltage amplifier cannot be disregarded, the extremely low-frequencyresponse of the system may be affected. But voltage amplifiers are usually lessexpensive and may be more reliable because they contain fewer components.20.9 Random VibrationsMost of the vibration problems discussed earlier in this chapter are deterministic,i.e., the forcing function can be described as a function of time. An example ofa deterministic problem is the imbalance of a shaft operating at a known speed.Random vibrations, on the other hand, result from excitation that can be onlydescribed statistically. Structural excitation of an aircraft fuselage due to jet enginenoise or turbulent flow is considered to be a random process. Both frequency andamplitude vary and they do not establish a deterministic pattern.Probability DensityBecause the amplitude or acceleration of random vibration cannot be determinedas a function of time, it is described in terms of its probability density. Onemodel widely used is the Gaussian distribution or normal probability density curve