Page 451 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)
P. 451

438                                      Random Vibrations   Chap. 13


                                               k -
                                                 k
                                                 1                         ¿(f-Q
                                                 Af
                                                 1


                                                Figure 13.6-4.       = 0 ( / - / „ )


                                        F{t)







                                        Sin
                                                                     Figure 13.6-5.  Wide-band record
                                                                  f   and  its spectral  density.













                                                                     Figure  13.6-6.  Narrow-band  record
                                                                  -f  and its spectral  density.

                                  Typical  spectral  density functions  for  two  common  types  of random  records
                              are shown in Figs.  13.6-5  and  13.6-6.  The first is a wide-band  noise-type of record
                              that  has  a  broad  spectral  density  function.  The  second  is  a  narrow-band  random
                              record  that  is  typical  of  a  response  of  a  sharply  resonant  system  to  a  wide-band
                              input.  Its  spectral  density  function  is  concentrated  around  the  frequency  of  the
                              instantaneous variation within the  envelope.
                                  The spectral  density of a given record can be measured electronically by the
                              circuit of Fig.  13.6-7.  Here  the  spectral  density is noted  as the contribution of the
                              mean  square value  in the frequency interval  A /  which  is divided by A/.

                                                      S( f )  =  lim  A m                (13.6-7)
                                                             A/^O  A/
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