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  «2 
  ] 
  

  

  LIU. 
  On 
  the 
  Lateral 
  Deflexion 
  and 
  Vibration 
  of 
  '''Clamped- 
  

   Directed 
  " 
  Bars. 
  By 
  John 
  Morrow, 
  J/. 
  ^c. 
  ( 
  Vict.), 
  I). 
  Eng. 
  

   i^Upool), 
  Lecturer 
  in 
  Engineering, 
  Armstrong 
  College 
  (Uni- 
  

   versity 
  of 
  Durham) 
  *. 
  

  

  Section 
  I. 
  — 
  Lntroduct'ion 
  and 
  Contents. 
  

  

  § 
  1. 
  The 
  vibrations 
  o£ 
  a 
  bar 
  under 
  the 
  terminal 
  conditions 
  

   ^vhich 
  are 
  probably 
  most 
  frequent 
  in 
  engineering 
  practice, 
  

   appear 
  to 
  have 
  hitherto 
  attracted 
  but 
  little 
  attention. 
  These 
  

   conditions 
  occur 
  when 
  one 
  end 
  o£ 
  the 
  bar 
  is 
  clamped, 
  and 
  

   the 
  other 
  is 
  constrained 
  to 
  retain 
  its 
  original 
  direction. 
  

   Such 
  conditions 
  may 
  be 
  realized 
  by 
  having 
  two 
  initially 
  parallel 
  

   bars, 
  CA 
  and 
  DB 
  (fig. 
  1), 
  each 
  clamped 
  at 
  one 
  end, 
  with 
  the 
  

   otherwise 
  free 
  ends 
  connected 
  by 
  a 
  rigid 
  bar 
  AB. 
  

  

  Figs. 
  1 
  and 
  2 
  show 
  two 
  distinct 
  ways 
  in 
  which 
  such 
  a 
  

  

  Fi-. 
  1. 
  

  

  Fiir. 
  2. 
  

  

  '<k 
  

  

  

  system 
  may 
  vibrate. 
  In 
  the 
  former 
  case 
  we 
  have 
  pure 
  

   lateral 
  vibration, 
  whereas 
  in 
  the 
  latter 
  there 
  is 
  a 
  necessary 
  

   accompaniment 
  of 
  longitudinal 
  vibrations 
  in 
  each 
  bar. 
  The 
  

   former 
  case 
  is 
  the 
  more 
  important 
  since 
  in 
  it 
  the 
  frequency 
  

   of 
  the 
  fundamental 
  type 
  will, 
  in 
  general, 
  be 
  the 
  lower. 
  

  

  I 
  propose 
  to 
  refer 
  to 
  a 
  bar 
  under 
  the 
  end 
  conditions 
  of 
  

   fig. 
  1 
  as 
  a 
  " 
  Clamped-Directed 
  " 
  bar. 
  

  

  Although 
  there 
  exists 
  a 
  considerable 
  literature 
  on 
  the 
  theory 
  

   of 
  the 
  lateral 
  vibration 
  of 
  thin 
  rods, 
  the 
  practical 
  application 
  

   of 
  the 
  results 
  is 
  extremely 
  limited. 
  The 
  explanation 
  of 
  this 
  

   is 
  to 
  be 
  sought, 
  not 
  in 
  any 
  lack 
  of 
  enterprise 
  on 
  the 
  part 
  of 
  

  

  * 
  Commimicated 
  by 
  tlie 
  Physical 
  Society 
  : 
  read 
  June 
  12, 
  1908. 
  

  

  