Abstract
The dynamic behavior of a bridge-erecting machine, carrying a moving mass suspended by a wire rope, is investigated. The bridge-erecting machine is modelled by a simply supported uniform beam, and a massless equivalent “spring-damper” system with an effective spring constant and an effective damping coefficient is used to model the moving mass suspended by the wire rope. The suddenly applied load is represented by a unitary Dirac Delta function. With the expansion method, a simple closed-form solution for the equation of motion with the replaced spring-damper-mass system is formulated. The characters of the rope are included in the derivation of the differential equation of motion for the system. The numerical examples show that the effects of the damping coefficient and the spring constant of the rope on the deflection have significant variations with the loading frequency. The effects of the damping coefficient and the spring constant under different beam lengths are also examined. The obtained results validate the presented approach, and provide significant references in the design process of bridgeerecting machines.
Similar content being viewed by others
References
Ding, H. J., Chen, W. Q., and Xu, R, On the bending, vibration and stability of laminated rectangular plates with transversely isotropic layers. On the bending, vibration and stability of laminated rectangular plates with transversely isotropic layers 22 1, 17–24 (2001) DOI10.1007/BF02437941
Greco, A. and Santini, A, Dynamic response of a flexural non-classically damped continuous beam under moving loadings. Dynamic response of a flexural non-classically damped continuous beam under moving loadings 80, 1945–1953 (2002)
Yanmeni, A. N., Tchoukuegno, R., and Woafo, P, Non-linear dynamics of an elastic beam under moving loads. Non-linear dynamics of an elastic beam under moving loads 273, 1101–1108 (2004)
Martínez-Castro, A. E. Museros, P., and Castillo-Linares, A, Semi-analytic solution in the time domain for non-uniform multi-span Bernoulli-Euler beams traversed by moving loads. Semi-analytic solution in the time domain for non-uniform multi-span Bernoulli-Euler beams traversed by moving loads 294, 278–297 (2006)
Simsek, M. and Kocatürk, T, Nonlinear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load. Nonlinear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load 320, 235–253 (2009)
Garinei, A, Vibrations of simple beam-like modelled bridge under harmonic moving loads. Vibrations of simple beam-like modelled bridge under harmonic moving loads 44, 778–787 (2006)
Sudheesh, C. P., Sujatha, C., and Shankar, K, Vibration of simply supported beams under a single moving load: a detailed study of cancellation phenomenon. Vibration of simply supported beams under a single moving load: a detailed study of cancellation phenomenon 99, 40–47 (2015)
Majumder, L. and Manohar, C. S. A time-domain approach for damage detection in beam structures using vibration data with a moving oscillator as an excitation source. Journal of Sound and Vibration, 268, 699–716 (2003)
Zrnić, N. D., Gašić, V. M., and Bosnjak, S. M, Dynamic responses of a gantry crane system due to a moving body considered as moving oscillator. Dynamic responses of a gantry crane system due to a moving body considered as moving oscillator 15, 243–250 (2015)
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (No. 11472179)
Rights and permissions
About this article
Cite this article
Yang, S., Fang, X., Zhang, J. et al. Dynamic behavior of bridge-erecting machine subjected to moving mass suspended by wire ropes. Appl. Math. Mech.-Engl. Ed. 37, 741–748 (2016). https://doi.org/10.1007/s10483-016-2087-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-016-2087-6