Abstract:

Based on an equivalent rotational spring model of crack, computation methods of dynamic characteristics and dynamic responses of cracked beams were investigated. On the basis of the equivalent flexural rigidity of the cracked beam, a method for obtainingageneral solution to the dynamic governing equation of cracked beam is established. A unified explicit expression of the vibration mode of the Euler-Bernoulli beam with an arbitrary number of cracks is presented. Natural frequencies of simply-supported, cantilever and clamped-clamped cracked beams are analyzed numerically. The dynamic response of the simply-supported cracked beam subject to a concentrated harmonic load is studied. Influences of depth and number of cracks on the dynamic characteristics and dynamic response are examined, revealing that the natural frequencies decrease with increased depth and number of cracks, and influence of the crack depth on the natural frequencies is more remarkable when the crack depth is large. There is a cusp on the mode curve of the cracked beam at the crack location, and slope change of the mode curve at the crack location increases with the increase of the crack depth.The crack has no influence on the natural frequencies and the modes of the cracked beam when the bending moment of the beam at the crack location is zero. Furthermore, the mode superposition method can be usedto analyze dynamic responses of acracked beam due to orthogonality of the modes of the cracked beam.

Key words: cracked Euler-Bernoulli beam, equivalent rotational spring model, generalized function, dynamic characteristic, dynamic response