V

7t/2

Table 11.1 Reference Quantities for Vibration Levels (Beranek and Ver, 1992)

Level (dB) Acceleration

Formula

Velocity

Displacement

vo = 10 n m / s vo = 10-8 m / s do = 10 p m do = 10-11 m

Note: Decimal multiples are 10-1 = deci (d), 10-2 = centi (c), 10-3 = milli (m), 10-6 = micro 10-9 = nano (n), and 10-12 = pico (p).

square (rms) value is the square root of the average of the square of a sine wave over a complete cycle, which is or .707 times the peak amplitude. Vibration amplitudes also can be expressed in decibels and Table 11.1 shows the preferred reference quantities.

11.2 SINGLE DEGREE OF FREEDOM SYSTEMS Free Oscillators

In its simplest form a vibrating system can be represented as a spring mass, shown in Fig. 11.2. Such a system is said to have a single degree of freedom, since its motion can be described with a knowledge of only one variable, in this case its displacement.

Figüre 11.2 Free Body Diagram of a Spring Mass System

Dynamic Force Balance

Unstretched position

Unstretched position k x

Dynamic Force Balance k x

/

•v

m

\ m

0 0

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