T1-5 1.5    Principles of Noise Reduction A  good  vibration  isolation  system  is  reducing  vibration  transmission  through  structures  and  thus,  radiation  of  these vibration into air, thereby reducing noise. There are many ways to reduce noise. One of the most practical and effective may be the use of vibration mounts. As a general rule, a well-designed vibration isolator will also help reduce noise. In the case of panel flutter, for example, a well- designed vibration mount could reduce or eliminate the noise. This can be achieved by eliminating the flutter of the panel itself, or by preventing its transmission to ground, or by a combination of the two. The range of audible frequencies is so high that the natural frequencies of a vibration mount can usually be designed to be well below the noise-producing frequency. In order to reduce noise, try to identify its sources; e.g., transformer hum, panel flutter, gear tooth engagement, rotor unbalance, etc. Next, identify the noise frequencies. Vibration isolators for these sources designed in accordance with the guidelines for vibration and shock control may then act as barriers either in not conducting the sound, or in attenuating the vibration which is the source of the noise. 2.0    BASIC DEFINITIONS AND CONCEPTS IN VIBRATION AND SHOCK ANALYSIS 2.1    Kinematic Characteristics COORDINATE — A quantity, such as a length or an angle, which defines the position of a moving part. In Figure 1, x is a coordinate, which defines the position of the weight, W. DISPLACEMENT — A change in position. It is a vector measured relative to a specified position, or frame of reference. The change in x (Figure 1) measured upward, say, from the bottom position, is a displacement. A displacement can be positive or negative, depending on the sign convention, translational or rotational. For example, an upward displacement may be positive, and a downward displacement negative. Similarly, a clockwise rotation may be positive and a counterclock- wise rotation negative. Units: inches, feet, meters (m), millimeters (mm), or, in the case of rotations: degrees, radians, etc. VELOCITY — The rate of change of displacement. Units: in/sec, mph., m/sec, etc. Velocity is a vector whose magnitude is the SPEED. Angular velocity might be measured in radians/sec or deg/sec, clockwise or counterclockwise. ACCELERATION — The rate of change of velocity. Units: in/sec², m/sec², etc. It is a vector and has a magnitude and direction. Angular acceleration might be measured in rad/sec² or deg/sec², clockwise or counterclockwise. VIBRATORY MOTION — An oscillating motion; such as, that of the weight W, in Figure 1. SIMPLE VIBRATORY MOTION — A form of vibratory motion, which as a function of the time is of the form x = a sin 3t, where  a  and  3  are  constants. The  maximum  displacement,  a,  from  the  mean  position  (x  =  0)  is  the  AMPLITUDE;  the FREQUENCY (rate at which the motion repeats itself) is f = 3/23 cycles/sec, where ANGULAR FREQUENCY 3 has the dimensions of rad/sec, and frequency f has the dimensions of reciprocal time; e.g. reciprocal seconds 1/sec. Such motion is also called harmonic or sinusoidal motion. PERIOD, CYCLE — The interval of time within which the motion repeats itself. In Figure 5, this is T seconds. The term cycle tends to refer also to the sequence of events within one period. AMPLITUDE — Figure 5 shows time history of a vibratory motion, which repeats itself every T seconds. The maximum values of the displacement, x, from the reference position (x = 0) are called PEAKS. These are (a₁, a₂...). The largest of these is called the PEAK AMPLITUDE. STEADY-STATE MOTION — A periodic motion of a mechanical system; e.g., a continuously swinging pendulum of constant amplitude. STOCHASTIC or RANDOM MOTION — A motion which changes with time in a nonperiodic, possibly very complex, manner. Figure 5    Periodic Motion 0 x T 2T 3T Time, t, secs a₁ a₂ a₅ a₆ a₃ a₄