1 Nonlinear Vibrations of a Beam with a Breathing Edge Crack Using Multiple Trial Functions 9 0 200 400 600 800 1000 1200 1400 1600 1800 2000 10-15 10-10 10-5 Frequency, w, [rad/s] Frequency, w, [rad/s] Fifth Harmonic, aj5 [m] a 15 , L c =0.2 a 15 , L c =0.4 a 25 , L c =0.2 a 25 , L c =0.4 a 35 , L c =0.2 a 35 , L c =0.4 0 200 400 600 800 1000 1200 1400 1600 1800 2000 10-16 10-14 10-12 10-10 10-8 10-6 Fifth Harmonic, aj5 [m] a 15 , a=0.2 a 15 , a=0.5 a 25 , a=0.2 a 25 , a=0.5 a 35 , a=0.2 a 35 , a=0.5 a b Fig. 1.8 Fifth harmonic of each modal coefficient vs. frequency. (a) For ˛ D0:5 and different crack location. (b) For Lc D0:2 m and different crack ratio Table 1.1 Ratio of maximum amplitudes of even harmonics of each modal coefficient for different crack location ˛ D0:5 Lc a12/a12 a22/a12 a32/a12 a14/a14 a24/a14 a34/a14 0.2 1 0.00128 0.01438 1 0.00141 0.0151 0.4 1 0.18786 0.05545 1 0.22663 0.04163 Table 1.2 Ratio of maximum amplitudes of even harmonics of each modal coefficient for different crack depth Lc D0:2 ˛ a12/a12 a22/a12 a32/a12 a14/a14 a24/a14 a34/a14 0.2 1 0.00132 0.01327 1 0.00147 0.01385 0.5 1 0.00128 0.01437 1 0.00141 0.01507 References 1. Dimarogonas, A.D.: Vibration of cracked structures: a state of the art review. Eng. Fract. Mech. 55(5), 831–857 (1996) 2. Aydın, K.: Vibratory characteristics of Euler-Bernoulli beams with arbitrary number of cracks subjected to axial load. J. Vib. Control. 14(4), 485–510 (2008) 3. Khiem, N.T., Lien, T.V.: A simplified method for natural frequency analysis of multiple cracked beam. J. Sound Vib. 254(4), 737–751 (2001) 4. Mermertas¸, V., Erol, H.: Effect of mass attachment on the free vibration of cracked beam. In: The 8th International Congress on Sound and Vibration (2001) 5. Zhong, S., Oyadiji, S.O.: Analytical predictions of natural frequencies of cracked simply supported beam with stationary roving mass. J. Sound Vib. 311, 328–352 (2008) 6. Mazanog˘lu, K., Yes¸ilyurt, I., Sabuncu, M.: Vibration analysis of multiple cracked non-uniform beams. J. Sound Vib. 320, 977–989 (2009) 7. Chondros, T.G., Dimarogonas, A.D., Yao, J.: A continuous cracked beam vibration theory. J. Sound Vib. 215(1), 17–34 (1998) 8. Chondros, T.G., Dimarogonas, A.D., Yao, J.: Vibration of a beam with a breathing crack. J. Sound Vib. 239(1), 57–67 (2001) 9. Cheng, S.M., Wu, X.J., Wallace, W.: Vibrational response of a beam with a breathing crack. J. Sound Vib. 225(1), 201–208 (1999) 10. Chati, M., Rand, R., Mukherjee, S.: Modal analysis of a cracked beam. J. Sound Vib. 207(2), 249–270 (1997) 11. Giannini, O., Casini, P., Vestroni, F.: Nonlinear harmonic identification of breathing cracks in beams. Comput. Struct. 129, 166–177 (2013) 12. Baeza, L., Ouyang, H.: Modal approach for forced vibration of beams with a breathing crack. Key Eng. Mater. 413–414, 39–46 (2009) 13. Batihan, A.C., Cigeroglu, E.: Nonlinear vibrations of a beam with a breathing edge crack. In: IMAC XXXIII (2015) 14. Batihan, A.C.: Vibration analysis of cracked beams on elastic foundation using Timoshenko beam theory. Master Thesis, Middle East Technical University (2011)
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