JOURNAL OF SOUND AND VIBRATION Journal of Sound and Vibration 311 (2008) 328–352 Analytical predictions of natural frequencies of cracked simply supported beams with a stationary roving mass Shuncong Zhong, S. Olutunde Oyadiji à Dynamics and Aeroelasticity Research Group, School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester M13 9PL, UK Received 10 March 2006; received in revised form 2 September 2007; accepted 12 September 2007 Available online 21 December 2007 Abstract Natural frequencies of a damaged simply supported beam with a stationary roving mass are studied theoretically. The transverse deflection of the cracked beam is constructed by adding a polynomial function, which represents the effects of a crack, to the polynomial function which represents the response of the intact beam [J. Ferna´ndez-Sa´ez, L. Rubio, C. Navarro, Approximate calculation of the fundamental frequencies for bending vibrations of cracked beams, Journal of Sound and Vibration 225 (1999) 345–352]. By means of the boundary and kinematics conditions, approximate closed-form analytical expressions are derived for the natural frequencies of an arbitrary mode of transverse vibration of a cracked simply supported beam with a roving mass using the Rayleigh’s method. The natural frequencies change due to the roving of the mass along the cracked beam. Therefore the roving mass can provide additional spatial information for damage detection of the beam. That is, the roving mass can be used to probe the dynamic characteristics of the beam by roving the mass from one end of the beam to the other. The presence of a crack causes the local stiffness of the beam to decrease which, in turn, causes a marked decrease in natural frequency of the beam when the roving mass is located in the vicinity of the crack. The magnitude of the roving mass used varied between 0% and 50% of the mass of the beam. The predicted frequencies are shown to compare very well with those obtained using the finite element method and the experimental results. Finally, the effects of crack depth, crack location and roving mass on the natural frequency of the beam are investigated. It is shown that the natural frequencies of the cracked beam decrease as the crack depth increases and as the roving mass is traversed closer to the crack location. r 2007 Elsevier Ltd. All rights reserved. 1. Introduction Inspection of structural components for damage is vital for making decisions about their repair or retirement. A crack may cause serious failure of a structure; therefore it must be detected in the early state when it is small. In practice, it is difficult to recognize most cracks by using visual inspection techniques; generally, they may be detected by non-destructive techniques. System identification is an important tool for such purpose. ARTICLE IN PRESS www.elsevier.com/locate/jsvi 0022-460X/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsv.2007.09.009 à Corresponding author. Tel.: +44 161 275 4348; fax: +44 161 275 3844. E-mail address: s.o.oyadiji@manchester.ac.uk (S.O. Oyadiji).