13-6] VIBRATION AND SHOCK 



acceleration density. The quantity is defined by 



G = limit -p 



697 



(13-8) 



^here G = acceleration density; the usual units for acceleration density 

 are g^ per cycle per second 



a"^ = mean square acceleration within a specified bandwidth 



B = the bandwidth within which the acceleration a occurs. 



In this chapter, the acceleration 

 density function is defined for posi- 

 tive frequencies only. Thus, it 

 differs slightly from the power 

 density functions of Chapter 5. It is 

 evident from the defining equation 

 that for a given random motion this 

 property is a function of frequency. 

 A plot of the acceleration density of 

 Gaussian noise as a function of 

 frequency, known as an acceleration 

 density spectrum, defines a steady- 

 state random motion as completely 

 as it can be known. Two such plots 



;:x 



< FREQUENCY, cps 



Fig. 13-6 Acceleration Density Spectra. 



are shown in Fig. 13-6. The solid curve shows an acceleration density 

 spectrum which might be measured in a random environment. The dashed 

 curve represents a special case called a flat random motion spectrum or a 

 white random ^notion spectrum. Such a curve is often chosen for a test speci- 

 fication, being a convenient compromise between many different actual 

 environments. 



If the acceleration density spectrum is known, the rms acceleration may 

 be calculated for any frequency band. For the band lying between fre- 

 quencies/i and/2, the rms acceleration may be calculated by Equation 13-9a 



a-yliy^f- 



(13-9a) 



For the case of white random motion spectrum, this expression simplifies 

 to the following: 



a = V^- (13-9b) 



Before considering the response of a system to random excitation, it is 

 helpful to review briefly the case of sinusoidal vibration. If a sinusoidal 



