Topics in Modal Analysis, Volume 7

460 N.T. Khiem et al. to conduct the time history response by using the FFT procedure. The proposed herein approach that can be called spectral method allows for avoiding the moving singularity phenomenon and time consumable tracking current position of the load. Moreover, this method is capable to expose the effect of high frequency components overall beam length that is typically caused by cracks appeared in the beam. The spectral method can be further developed to use for crack detection of beam based on the dynamic signal measured at vehicle moving on the beam. Acknowledgements This work has been completed under support from the NAFOSTED of Vietnam to whom the authors are much thankful. References 1. Fryba L (1972) Vibration of solids and structures under moving loads. Noordhoff International Publishing, Prague 2. Olsson M (1991) On the fundamental moving load problem. J Sound Vib 145(2):299–307 3. Rao GV (2000) Linear dynamics of an elastic beam under moving loads. J Vib Acoust 122:281–289 4. Pesterev AV et al (2001) Response of elastic continuum carrying multiple moving oscillators. J Eng Mech 127(3):260–265 5. Garinei A (2006) Vibration of simple beam-like modeled bridge under harmonic moving loads. Int J Eng Sci 44:778–787 6. Zehsaz M, Sadeghi MH, Ziaei Asl A (2009) Dynamics response of railway under a moving load. J Appl Sci 9(8):1474–1481 7. Mahmoud MA, Abou Zaid MA (2002) Dynamic response of a beam with a crack subject to a moving mass. J Sound Vib 256(4):591–603 8. Bilello C, Bergman LA (2004) Vibration of damaged beams under a moving mass: theory and experimental validation. J Sound Vib 274:567–582 9. Lin H-P, Chang S-C (2006) Forced response of cracked cantilever beams subjected to a concentrated load. Int J Mech Sci 48:1456–1463 10. Yang J et al (2008) Free and forced vibration of cracked inhomogeneous beams under an axial force and moving load. J Sound Vib 312:166–181 11. Shafiei M, Khaji M (2011) Analytical solution for free and forced vibrations of multiple cracked Timoshenko beam subject to a concentrated moving load. Acta Mech 22:79–97 doi:10.1007/s00707-011-0495-x 12. Li J, Law SS (2012) Damage identification of a target substructure with moving load excitation. Mech Syst Signal Process 30:78–90 13. Zhang Y, Wang L, Xiang Z (2012) Damage detection by mode shape squares extracted from a passing vehicle. J Sound Vib 331:291–307 14. Pesterev AV, Tan CA, Bergman LA (2001) A new method for calculating bending moment and shear force in moving load problems. Trans ASME: J Appl Mech 68:252–259 15. Wu JJ, Whittaker AR, Cartmell MP (2000) The use of finite element techniques for calculating the dynamic response of structures to moving loads. Comput Struct 78:789–799 16. Martinez-Castro AE, Museros P, Castillo-Linares A (2006) Semi-analytic solution in the time domain for non-uniform multi-span BernoulliEuler beams traversed by moving load. J Sound Vib 294:278–297 17. Anderson L, Nielsen SRK, Krenk S (2007) Numerical methods for analysis of structure and ground vibration from moving load. Comput Struct 85:43–58 18. Henchi K et al (1997) Dynamic behavior of multi-span beams under moving load. J Sound Vib 199(1):33–50 19. Azizi N, Saadatpour MM, Mahzoon M (2011) Using spectral element method for analyzing continuous beams and bridges subjected to a moving load. Appl Math Model 36:3580–3592. doi:10.1016/j.apm.2011.10.019 20. Chondros TG, Dimaroganas AD (1998) A continuous cracked beam theory. J Sound Vib 215:17–34

RkJQdWJsaXNoZXIy MTMzNzEzMQ==