By John G. Webster (Editor)
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Additional info for 30.Instrumentation and Measurement
In periodic vibrations, the motion of an object repeats itself in an oscillatory manner. This can be represented by a sinusoidal waveform x(t) = Xpeak sin(ωt) u(t) = dx/dt = ωXpeak cos(ωt) = Upeak sin(ωt + π/2) This section is concerned with applications of accelerometers to measure physical properties such as acceleration, vibration and shock, and motions associated with inertial navigation. A full understanding of accelerometer dynamics is necessary in relation to characteristics of acceleration, vibration, and (39) where u(t) is the time-dependent velocity, and Upeak ϭ ͶXpeak is the maximum velocity.
The second type of impedance is the specific acoustic impedance, Zs, defined as the quotient of the sound pressure and Compliance Displ. ratio Mobility Vel. ratio Accel. ratio the particle velocity: Zs = p u (8) The unit is the rayl, equal to Pa и s и mϪ1. The third type of impedance, called the mechanical impedance, Zm, is defined as the quotient of the force exerted on a given area and the resulting particle velocity: Zm = pS u (9) The unit of Zm is the mechanical ohm, equal to N и s/m. Each type of impedance has certain advantages in the solution of specific problems.
Accelerometers are designed to have different characteristics by suitable selection of these parameters. Once the response is expressed in the form of Eqs. (44) and (45), analysis can be taken further either in the time domain or in the frequency domain. The time response of a typical second-order system for a unit-step input is given in Fig. 18. The Bode plot gain phase responses are depicted in Fig. 19. Detailed discussions about frequency response, damping, damping ratio, and linearity are made in relevant sections, and further information can be obtained in the references.
30.Instrumentation and Measurement by John G. Webster (Editor)