8- مراجع
                                                                                                    [1]  ANSYS User’s Manual, 9th Ed., 1996, SAS IP, Inc.
                                                                                                    [2]  Fanning, P.& Kelly O. , "Smeared Crack Models of RC beams with externally bonded CFRP plates", J. Computational Mechanics, 26, 2000, 325-332.
                                                                                                    [3]  Dirr, BO. and Schmalhorst, BK., "Crack depth analysis of a rotating shaft by vibration measurements", ASME Journal of Vibration, Acoustics, Stress and Reliability in Design, 110, 1988, 158–164
                                                                                                    [4]  Qian, GL., Gu SN, and Jiang, JS., "The dynamic behavior and crack detection of a beam with a crack", Journal of Sound and Vibration,138(2), 1990, 233–243.ICLE
                                                                                                    [5]  Narkis, Y., "Identification of crack location in vibrating simply supported beams", Journal of Sound and Vibration, 172(4), 1994, 549–558.
                                                                                                    [6]  Saavedra, PN. and Cuitino, LA., "Crack detection and vibration behavior of cracked beams", Computers and Structures, 79, 2001, 1451–1459.
                                                                                                    [7]  Dilena, M. and Morassi, A., "Identification of crack location in vibrating beams from change in mode positions", Journal of Sound and Vibration, 255(5), 2002, 915–930.
                                                                                                    [8]  Nahvi, H. and Jabbari, M., "Crack detection in beams using experimental modal data and finite element model", International Journal of Mechanical Sciences, 47, 2005, 1477–1497.
                                                                                                    [9] دانشجو، ف؛ و قاری قرآن، ع؛" شناسایی سامانه و ارزیابی دینامیکی آزمایشگاهی تیرهای بتنی خسارت دیده در پل ها"؛ پژوهشنامه حمل و نقل؛ سال سوم، شماره 2، 1385.
                                                                                                    [10]  Daneshjoo, F. & Gharighoran, A., “Experimental and theoretical dynamic system identification of damaged RC beams,” Electronic Journal of Structural Engineering, 8, 2008, 29-38.
                                                                                                    [11]  Gharighoran, A., Daneshjoo, F. & Khaji, N., “Use of Ritz method for damage detection of reinforced and post-tensioned concrete beams,” Construction and Building Materials, 23(6), 2009, 2167-2176.
                                                                                                    [12] قاری قرآن، ع؛"ارزیابی خسارت در عرشه پل ها از طریق ردیابی تغییرات در مشخصه های دینامیکی"؛ پایان نامه دکتری؛ دانشگاه تربیت مدرس؛ دانشکده فنی مهندسی تهران؛ 1386.
                                                                                                    [13]  Kachlakev, D., Miller, T., Yim, S., and Chansawat, K., “Finite Element Modeling of Reinforced Concrete Structures Strengthened with FRP Laminates,” Final Report for Oregon Department of Transportation Research Group, Internet File, 2001.
                                                                                                    [14]  Chen, W.F., “Plasticity in Reinforced Concrete,” McGraw-Hill, New York, 1982.
                                                                                                    [15]  Samman, M.M., Biswas M., and Pandey A.K., “Employing pattern recognition for detecting cracks in a bridge model,” Modal Analysis: The International Journal of Analytical and Experimental Modal Analysis, 6, 1991, 35–44.
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                    - مراجع
                                                                                                    [1]  ANSYS User’s Manual, 9th Ed., 1996, SAS IP, Inc.
                                                                                                    [2]  Fanning, P.& Kelly O. , "Smeared Crack Models of RC beams with externally bonded CFRP plates", J. Computational Mechanics, 26, 2000, 325-332.
                                                                                                    [3]  Dirr, BO. and Schmalhorst, BK., "Crack depth analysis of a rotating shaft by vibration measurements", ASME Journal of Vibration, Acoustics, Stress and Reliability in Design, 110, 1988, 158–164
                                                                                                    [4]  Qian, GL., Gu SN, and Jiang, JS., "The dynamic behavior and crack detection of a beam with a crack", Journal of Sound and Vibration,138(2), 1990, 233–243.ICLE
                                                                                                    [5]  Narkis, Y., "Identification of crack location in vibrating simply supported beams", Journal of Sound and Vibration, 172(4), 1994, 549–558.
                                                                                                    [6]  Saavedra, PN. and Cuitino, LA., "Crack detection and vibration behavior of cracked beams", Computers and Structures, 79, 2001, 1451–1459.
                                                                                                    [7]  Dilena, M. and Morassi, A., "Identification of crack location in vibrating beams from change in mode positions", Journal of Sound and Vibration, 255(5), 2002, 915–930.
                                                                                                    [8]  Nahvi, H. and Jabbari, M., "Crack detection in beams using experimental modal data and finite element model", International Journal of Mechanical Sciences, 47, 2005, 1477–1497.
                                                                                                    [9] دانشجو، ف؛ و قاری قرآن، ع؛" شناسایی سامانه و ارزیابی دینامیکی آزمایشگاهی تیرهای بتنی خسارت دیده در پل ها"؛ پژوهشنامه حمل و نقل؛ سال سوم، شماره 2، 1385.
                                                                                                    [10]  Daneshjoo, F. & Gharighoran, A., “Experimental and theoretical dynamic system identification of damaged RC beams,” Electronic Journal of Structural Engineering, 8, 2008, 29-38.
                                                                                                    [11]  Gharighoran, A., Daneshjoo, F. & Khaji, N., “Use of Ritz method for damage detection of reinforced and post-tensioned concrete beams,” Construction and Building Materials, 23(6), 2009, 2167-2176.
                                                                                                    [12] قاری قرآن، ع؛"ارزیابی خسارت در عرشه پل ها از طریق ردیابی تغییرات در مشخصه های دینامیکی"؛ پایان نامه دکتری؛ دانشگاه تربیت مدرس؛ دانشکده فنی مهندسی تهران؛ 1386.
                                                                                                    [13]  Kachlakev, D., Miller, T., Yim, S., and Chansawat, K., “Finite Element Modeling of Reinforced Concrete Structures Strengthened with FRP Laminates,” Final Report for Oregon Department of Transportation Research Group, Internet File, 2001.
                                                                                                    [14]  Chen, W.F., “Plasticity in Reinforced Concrete,” McGraw-Hill, New York, 1982.
                                                                                                    [15]  Samman, M.M., Biswas M., and Pandey A.K., “Employing pattern recognition for detecting cracks in a bridge model,” Modal Analysis: The International Journal of Analytical and Experimental Modal Analysis, 6, 1991, 35–44.
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                    [16] سبحانی، ج؛ "پیش بینی رفتار بتن آرمه با استفاده از شبکه های مصنوعی" ؛ پایان نامه کارشناسی ارشد؛ دانشگاه صنعتی اصفهان؛ 1380.
                                                                                                    - مراجع
                                                                                                    [1]  ANSYS User’s Manual, 9th Ed., 1996, SAS IP, Inc.
                                                                                                    [2]  Fanning, P.& Kelly O. , "Smeared Crack Models of RC beams with externally bonded CFRP plates", J. Computational Mechanics, 26, 2000, 325-332.
                                                                                                    [3]  Dirr, BO. and Schmalhorst, BK., "Crack depth analysis of a rotating shaft by vibration measurements", ASME Journal of Vibration, Acoustics, Stress and Reliability in Design, 110, 1988, 158–164
                                                                                                    [4]  Qian, GL., Gu SN, and Jiang, JS., "The dynamic behavior and crack detection of a beam with a crack", Journal of Sound and Vibration,138(2), 1990, 233–243.ICLE
                                                                                                    [5]  Narkis, Y., "Identification of crack location in vibrating simply supported beams", Journal of Sound and Vibration, 172(4), 1994, 549–558.
                                                                                                    [6]  Saavedra, PN. and Cuitino, LA., "Crack detection and vibration behavior of cracked beams", Computers and Structures, 79, 2001, 1451–1459.
                                                                                                    [7]  Dilena, M. and Morassi, A., "Identification of crack location in vibrating beams from change in mode positions", Journal of Sound and Vibration, 255(5), 2002, 915–930.
                                                                                                    [8]  Nahvi, H. and Jabbari, M., "Crack detection in beams using experimental modal data and finite element model", International Journal of Mechanical Sciences, 47, 2005, 1477–1497.
                                                                                                    [9] دانشجو، ف؛ و قاری قرآن، ع؛" شناسایی سامانه و ارزیابی دینامیکی آزمایشگاهی تیرهای بتنی خسارت دیده در پل ها"؛ پژوهشنامه حمل و نقل؛ سال سوم، شماره 2، 1385.
                                                                                                    [10]  Daneshjoo, F. & Gharighoran, A., “Experimental and theoretical dynamic system identification of damaged RC beams,” Electronic Journal of Structural Engineering, 8, 2008, 29-38.
                                                                                                    [11]  Gharighoran, A., Daneshjoo, F. & Khaji, N., “Use of Ritz method for damage detection of reinforced and post-tensioned concrete beams,” Construction and Building Materials, 23(6), 2009, 2167-2176.
                                                                                                    [12] قاری قرآن، ع؛"ارزیابی خسارت در عرشه پل ها از طریق ردیابی تغییرات در مشخصه های دینامیکی"؛ پایان نامه دکتری؛ دانشگاه تربیت مدرس؛ دانشکده فنی مهندسی تهران؛ 1386.
                                                                                                    [13]  Kachlakev, D., Miller, T., Yim, S., and Chansawat, K., “Finite Element Modeling of Reinforced Concrete Structures Strengthened with FRP Laminates,” Final Report for Oregon Department of Transportation Research Group, Internet File, 2001.
                                                                                                    [14]  Chen, W.F., “Plasticity in Reinforced Concrete,” McGraw-Hill, New York, 1982.
                                                                                                    [15]  Samman, M.M., Biswas M., and Pandey A.K., “Employing pattern recognition for detecting cracks in a bridge model,” Modal Analysis: The International Journal of Analytical and Experimental Modal Analysis, 6, 1991, 35–44.
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                    - مراجع
                                                                                                    [1]  ANSYS User’s Manual, 9th Ed., 1996, SAS IP, Inc.
                                                                                                    [2]  Fanning, P.& Kelly O. , "Smeared Crack Models of RC beams with externally bonded CFRP plates", J. Computational Mechanics, 26, 2000, 325-332.
                                                                                                    [3]  Dirr, BO. and Schmalhorst, BK., "Crack depth analysis of a rotating shaft by vibration measurements", ASME Journal of Vibration, Acoustics, Stress and Reliability in Design, 110, 1988, 158–164
                                                                                                    [4]  Qian, GL., Gu SN, and Jiang, JS., "The dynamic behavior and crack detection of a beam with a crack", Journal of Sound and Vibration,138(2), 1990, 233–243.ICLE
                                                                                                    [5]  Narkis, Y., "Identification of crack location in vibrating simply supported beams", Journal of Sound and Vibration, 172(4), 1994, 549–558.
                                                                                                    [6]  Saavedra, PN. and Cuitino, LA., "Crack detection and vibration behavior of cracked beams", Computers and Structures, 79, 2001, 1451–1459.
                                                                                                    [7]  Dilena, M. and Morassi, A., "Identification of crack location in vibrating beams from change in mode positions", Journal of Sound and Vibration, 255(5), 2002, 915–930.
                                                                                                    [8]  Nahvi, H. and Jabbari, M., "Crack detection in beams using experimental modal data and finite element model", International Journal of Mechanical Sciences, 47, 2005, 1477–1497.
                                                                                                    [9] دانشجو، ف؛ و قاری قرآن، ع؛" شناسایی سامانه و ارزیابی دینامیکی آزمایشگاهی تیرهای بتنی خسارت دیده در پل ها"؛ پژوهشنامه حمل و نقل؛ سال سوم، شماره 2، 1385.
                                                                                                    [10]  Daneshjoo, F. & Gharighoran, A., “Experimental and theoretical dynamic system identification of damaged RC beams,” Electronic Journal of Structural Engineering, 8, 2008, 29-38.
                                                                                                    [11]  Gharighoran, A., Daneshjoo, F. & Khaji, N., “Use of Ritz method for damage detection of reinforced and post-tensioned concrete beams,” Construction and Building Materials, 23(6), 2009, 2167-2176.
                                                                                                    [12] قاری قرآن، ع؛"ارزیابی خسارت در عرشه پل ها از طریق ردیابی تغییرات در مشخصه های دینامیکی"؛ پایان نامه دکتری؛ دانشگاه تربیت مدرس؛ دانشکده فنی مهندسی تهران؛ 1386.
                                                                                                    [13]  Kachlakev, D., Miller, T., Yim, S., and Chansawat, K., “Finite Element Modeling of Reinforced Concrete Structures Strengthened with FRP Laminates,” Final Report for Oregon Department of Transportation Research Group, Internet File, 2001.
                                                                                                    [14]  Chen, W.F., “Plasticity in Reinforced Concrete,” McGraw-Hill, New York, 1982.
                                                                                                    [15]  Samman, M.M., Biswas M., and Pandey A.K., “Employing pattern recognition for detecting cracks in a bridge model,” Modal Analysis: The International Journal of Analytical and Experimental Modal Analysis, 6, 1991, 35–44.
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                    [16] سبحانی، ج؛ "پیش بینی رفتار بتن آرمه با استفاده از شبکه های مصنوعی" ؛ پایان نامه کارشناسی ارشد؛ دانشگاه صنعتی اصفهان؛ 1380.
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                    [16] سبحانی، ج؛ "پیش بینی رفتار بتن آرمه با استفاده از شبکه های مصنوعی" ؛ پایان نامه کارشناسی ارشد؛ دانشگاه صنعتی اصفهان؛ 1380.
                                                                                                     
                                                                                                    [16] سبحانی، ج؛ "پیش بینی رفتار بتن آرمه با استفاده از شبکه های مصنوعی" ؛ پایان نامه کارشناسی ارشد؛ دانشگاه صنعتی اصفهان؛ 1380.