VIBRATION AND STABILITY OF A CRACKED TRANSLATING BEAM
โ Scribed by KEVIN D. MURPHY; YIN ZHANG
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 361 KB
- Volume
- 237
- Category
- Article
- ISSN
- 0022-460X
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โฆ Synopsis
The vibration and stability characteristics of a cracked beam translating between "xed supports are investigated. Using Hamilton's principle and elementary fracture mechanics, the equations of motion for the beam are developed. Throughout this analysis it is assumed that the crack is shallow and always remains open, i.e., crack closure and the associated impact conditions are not considered. In order to restrict attention to the open crack scenario, parameter regimes corresponding to (1) a fully open crack, (2) a fully closed crack, and (3) a partly open}partly closed crack are clearly identi"ed. For parameter values in regime (1), the free vibration characteristics are studied via an eigenanalysis. This shows that the natural frequencies (Im ( )) and stability characteristics (Re ( )) #uctuate as the crack translates along with the beam between the two supports. For the shallow cracks being considered, the #uctuations are attributed primarily to the localized drop in the mass per unit length (occurring at the crack) rather than from the increased #exibility. Furthermore, the magnitudes of these #uctuations are shown to vary with both the axial transport speed and the crack depth and are mapped in the control parameter space. Implications for the free and forced vibration problems are discussed.
๐ SIMILAR VOLUMES
A continuous cracked beam vibration theory is used for the prediction of changes in transverse vibration of a simply supported beam with a breathing crack. The equation of motion and the boundary conditions of the cracked beam considered as a one-dimensional continuum were used. The eigenfrequency c
This paper addresses the problem of vibrations of a cracked beam. In general, the motion of such a beam can be very complex. This phenomenon can be attributed to the presence of the non-linearity due to the opening and closing of cracks. The focus of this paper is the modal analysis of a cantilever