Page 453 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)
P. 453

440                                      Random Vibrations   Chap. 13
                                      x{f)                                        i  p(^)

                                                                    H_____
                                        Ww||wyp      f if 'n F i
                                      2.0
                                       0  ------------ 1-------                   r
                                                    I         1  '         '

                                                         Figure 13.6-8.


                              Example  13.6-2
                                  Determine the  Fourier coefficients  C„  and  the power spectral  density of the periodic
                                  function  shown  in  Fig.  13.6-9.



                                         MM                     1
                                             rr  1              1
                                1            ^0  !              1
                                                1 1          ___ 1_
                                1      0        j               1
                                [------------- 2 T------  L— r —      Figure 13.6-9.

                              Solution:  The period  is 2T  and  C„  are

                                               C  =    r^/2  f    =  f
                                                       -T /2
                                                                         sin {mr/2)
                                                                           mr/2

                                  Numerical  values  of  Q   are  computed  as  in  the  following  table  and  plotted  in  Fig.
                                  13.6-10.
                                                    riTT     /177
                                              n           Sin             - r
                                                                          2 ^ t
                                                   ~ Y
                                                                         Fn
                                              0      0       0               1 . 0 ^
                                                                          2
                                                    77
                                              1              1        (§:    0 .6 3 6 ^
                                                     2
                                              2      77      0             0
                                                   T        - 1                   T()
                                              3                              - 0 . 2 1 2 ^
                                              4     2 t7     0             0
                                                                                To
                                              5              1       (è;     0 .1 2 7 ^
   448   449   450   451   452   453   454   455   456   457   458