1、 displacement, velocity, and acceleration; and the operating principles of the sensors that detect and measure these properties.Vibration is oscillatory motion resulting from the application of oscillatory or varying forces to a structure. Oscillatory motion reverses direction. As we shall see, the
2、oscillation may be continuous during some time period of interest or it may be intermittent. It may be periodic or nonperiodic, i.e., it may or may not exhibit a regular period of repetition. The nature of the oscillation depends on the nature of the force driving it and on the structure being drive
3、n. Motion is a vector quantity, exhibiting a direction as well as a magnitude. The direction of vibration is usually described in terms of some arbitrary coordinate system (typically Cartesian or orthogonal) whose directions are called axes. The origin for the orthogonal coordinate system of axes is
4、 arbitrarily defined at some convenient location.Most vibratory responses of structures can be modeled as single-degree-of-freedom spring mass systems, and many vibration sensors use a spring mass system as the mechanical part of their transduction mechanism. In addition to physical dimensions, a sp
5、ring mass system can be characterized by the stiffness of the spring, K, and the mass, M, or weight, W, of the mass. These characteristics determine not only the static behavior (static deflection, d) of the structure, but also its dynamic characteristics. If g is the acceleration of gravity:F = MAW
6、 = MgK = F/d = W/dd = F/K = W/K = Mg/KDynamics of a Spring Mass System The dynamics of a spring mass system can be expressed by the systems behavior in free vibration and/or in forced vibration. Free Vibration. Free vibration is the case where the spring is deflected and then released and allowed to
7、 vibrate freely. Examples include a diving board, a bungee jumper, and a pendulum or swing deflected and left to freely oscillate.Two characteristic behaviors should be noted. First, damping in the system causes the amplitude of the oscillations to decrease over time. The greater the damping, the fa
8、ster the amplitude decreases. Second, the frequency or period of the oscillation is independent of the magnitude of the original deflection (as long as elastic limits are not exceeded). The naturally occurring frequency of the free oscillations is called the natural frequency, fn: (1) Forced Vibrati
9、on. Forced vibration is the case when energy is continuously added to the spring mass system by applying oscillatory force at some forcing frequency, ff. Two examples are continuously pushing a child on a swing and an unbalanced rotating machine element. If enough energy to overcome the damping is a
10、pplid, the motion will continue as long as the excitation continues. Forced vibration may take the form of self-excited or externally excited vibration. Self-excited vibration occurs when the excitation force is generated in or on the suspended mass; externally excited vibration occurs when the exci
11、tation force is applied to the spring. This is the case, for example, when the foundation to which the spring is attached is moving. Transmissibility. When the foundation is oscillating, and force is transmitted through the spring to the suspended mass, the motion of the mass will be different from
12、the motion of the foundation. We will call the motion of the foundation the input, I, and the motion of the mass the response, R. The ratio R/I is defined as the transmissibility, Tr:Tr = R/I Resonance. At forcing frequencies well below the systems natural frequency, RI, and Tr1. As the forcing freq
13、uency approaches the natural frequency, transmissibility increases due to resonance. Resonance is the storage of energy in the mechanical system. At forcing frequencies near the natural frequency, energy is stored and builds up, resulting in increasing response amplitude. Damping also increases with
14、 increasing response amplitude, however, and eventually the energy absorbed by damping, per cycle, equals the energy added by the exciting force, and equilibrium is reached. We find the peak transmissibility occurring when fffn. This condition is called resonance. Isolation. If the forcing frequency
15、 is increased above fn, R decreases. When ff = 1.414 fn, R = I and Tr = 1; at higher frequencies R I and Tr 1. At frequencies when R 0.1 in., to make them practical.The change in intensity or angle of a light beam directed onto a reflective surface can be used as an indication of its distance from t
16、he source. If the detection apparatus is fast enough, changes of distance can be detected as well.The most sensitive, accurate, and precise optical device for measuring distance or displacement is the laser interferometer. With this apparatus, a reflected laser beam is mixed with the original incide
17、nt beam. The interference patterns formed by the phase differences can measure displacement down to 100 nm. NIST and other national primary calibration agencies use laser interferometers for primary calibration of vibration measurement instruments at frequencies up to 25 kHz.Electromagnetic and Capacitive Sensors. Another important class of noncontact, special-purpose di
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