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Volume : V, Issue : II, March - 2015

DYNAMIC ANALYSIS OF A MONORAIL BEAM FOR AN OVERHEAD CRANE

Naba Raj Gairhe, K.V. Ramana, D.V.A Ramasastry

By : Laxmi Book Publication

Abstract :

A monorail beam is subjected to dynamic load. The design engineer is more concerned with its vibration behavior under undamped, no load condition to avoid resonance, which may lead to a catastrophic failure. One of the major failure reasons is formation of crack and its propagation, over a time. Emphasis is to be given to the investigation of the natural frequency and corresponding natural modes of the beam material which will furnish useful data, for prevention of crack. This paper addresses estimation of vibration displacement and natural frequencies of a standard I- Section, selecting 3 commercial grade steels and subsequently suggesting the appropriate material for a monorail beam.

Keywords :


Article :


Cite This Article :

Naba Raj Gairhe, K.V. Ramana, D.V.A Ramasastry (2015). DYNAMIC ANALYSIS OF A MONORAIL BEAM FOR AN OVERHEAD CRANE. Indian Streams Research Journal, Vol. V, Issue. II, http://isrj.org/UploadedData/6347.pdf

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  35. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  36. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  37. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  38. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  39. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  40. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  41. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  42. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  43. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  44. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  45. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  46. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  47. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  48. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  49. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  50. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  51. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  52. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  53. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  54. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  55. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  56. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
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  58. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
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  60. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  61. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
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  73. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  74. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
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  76. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  77. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  78. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
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  85. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  86. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
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  89. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  90. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  91. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  92. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
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  94. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  95. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  96. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
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  98. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  99. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  100. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
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  102. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
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  104. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  105. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  106. P.K. Jena et al “ Effect of damage parameters on vibration signatures of a cantilever beam” Procedia Engineerings 38(2012)3318-3330
  107. P.K. Jena et al “ Effect of damage parameters on vibration signatures of a cantilever beam” Procedia Engineerings 38(2012)3318-3330
  108. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  109. P.K. Jena et al “ Effect of damage parameters on vibration signatures of a cantilever beam” Procedia Engineerings 38(2012)3318-3330
  110. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  111. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  112. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
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  114. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  115. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
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  120. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  121. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  122. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  123. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  124. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  125. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  126. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  127. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  128. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  129. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  130. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  131. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  132. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  133. P.K. Jena et al “ Effect of damage parameters on vibration signatures of a cantilever beam” Procedia Engineerings 38(2012)3318-3330
  134. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  135. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  136. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  137. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  138. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  139. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  140. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  141. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  142. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  143. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  144. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  145. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  146. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  147. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  148. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  149. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  150. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  151. P.K. Jena et al “ Effect of damage parameters on vibration signatures of a cantilever beam” Procedia Engineerings 38(2012)3318-3330
  152. P.K. Jena et al “ Effect of damage parameters on vibration signatures of a cantilever beam” Procedia Engineerings 38(2012)3318-3330
  153. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  154. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  155. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  156. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  157. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  158. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  159. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  160. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  161. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  162. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  163. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  164. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  165. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  166. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  167. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  168. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  169. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  170. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  171. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  172. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  173. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  174. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  175. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  176. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  177. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  178. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  179. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  180. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  181. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  182. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  183. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  184. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  185. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  186. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  187. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  188. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  189. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  190. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  191. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  192. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  193. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  194. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  195. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  196. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  197. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  198. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  199. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  200. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  201. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  202. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  203. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  204. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  205. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  206. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  207. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  208. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  209. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  210. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  211. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  212. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  213. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  214. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  215. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  216. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  217. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  218. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  219. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  220. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  221. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  222. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  223. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  224. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  225. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  226. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  227. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  228. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  229. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  230. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  231. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  232. P.K. Jena et al “ Effect of damage parameters on vibration signatures of a cantilever beam” Procedia Engineerings 38(2012)3318-3330
  233. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  234. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  235. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  236. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  237. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  238. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  239. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  240. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  241. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  242. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  243. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  244. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  245. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  246. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  247. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  248. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  249. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  250. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  251. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  252. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  253. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  254. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  255. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  256. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  257. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  258. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  259. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  260. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  261. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  262. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  263. P.K. Jena et al “ Effect of damage parameters on vibration signatures of a cantilever beam” Procedia Engineerings 38(2012)3318-3330
  264. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  265. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  266. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  267. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  268. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  269. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  270. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  271. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  272. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  273. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  274. P.K. Jena et al “ Effect of damage parameters on vibration signatures of a cantilever beam” Procedia Engineerings 38(2012)3318-3330
  275. P.K. Jena et al “ Effect of damage parameters on vibration signatures of a cantilever beam” Procedia Engineerings 38(2012)3318-3330
  276. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  277. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  278. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  279. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  280. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  281. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  282. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  283. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  284. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.
  285. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  286. O. Kerem Murat and C. Topkaya “Lateral buckling of overhanging crane trolley monorails” Engineering structure 28(2006) 1162-1172
  287. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  288. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  289. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  290. P.K. Jena et al “ Effect of damage parameters on vibration signatures of a cantilever beam” Procedia Engineerings 38(2012)3318-3330
  291. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  292. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  293. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  294. Stifrin E.I and Ruotolo R “ Natural frequencies of a beam with an arbitrary no of cracks” Journal of Sound and vibration; 1999; 223(3): 409-23
  295. Z.A. Jassim et al.“A review on the vibration Analusis for a damage occurance of a cantilever beam” Engineering Failure Analysis 31(2013)442-461.www.elsevier.com/locate/engfailand.
  296. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  297. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  298. P.K. Jena et al “ Effect of damage parameters on vibration signatures of a cantilever beam” Procedia Engineerings 38(2012)3318-3330
  299. N.S. Trahair “ Lateral Buckling of monorail beams” Engineering Structures 32( 2010) 982-987
  300. Hai-Ping Lim “ Force response of cracked cantilever beams subjected to a concentrated moving load” Internal Journal of mechanical sciences 48(2006) 1456-1463
  301. T. Yan and Y Yang “ Foced Vibration of Edge- cracked functionally graded beams due to a transverse moving load. “ Procedia Engineering 14(2011)3293-3300
  302. C.H. Lee et al “ Dynamic response of a monorail steel bridge under a moving train “ Journal of sound vibration 294(2006) 562-579
  303. N.S. Trahair “Distortional buckling of overhanging monorail beams” Engineering Structures 32(2008) 3213-3218.
  304. Sadettin Orhan “Analysis of force and forced vibration of a cracked cantilever beam” NDT & E International 40(2007)443-50.

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