Coupling dynamic behaviors of axially moving cracked cantilevered beam subjected to transverse harmonic load

Considering the existence of the opening crack, the axially motion as well as the transverse harmonic excitation, the dynamic response of the beam is studied by a structure-preserving method in this paper. With the equivalent bending stiffness introduced to describe the effect of the crack on the flexibility of the beam, the vibration model of the axially moving cracked cantilevered beam subjected to a transverse harmonic load at its free end is presented. A structure-preserving method in the generalized multi-symplectic framework is developed subsequently. Finally, the effects of the crack's parameters, the axially moving speed and the circular frequency of the transverse harmonic load on the steady vibration amplitude of the cracked beam are investigated by the structure-preserving method in detail. From numerical results, it can be found that when the beam moves with the high speed, the appearance of the crack on the beam will intensify the vibration of the beam sharply. In addition, the vibration amplitude of the cracked beam is suddenly larger in five narrow circular frequency bands. Comparing with the results of the wavelet spectral finite element method, the center circular frequencies of the narrow five circular frequency bands obtained by the generalized multi-symplectic method are highly agreed with the first five natural frequencies of the cracked beam, which illustrates the precision of the numerical results reported in this paper directly.