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Acta Mech 221, 7997 (2011)
DOI 10.1007/s00707-011-0495-x
Received: 7 December 2010 / Published online: 4 May 2011 Springer-Verlag 2011
Abstract An analytical approach for evaluating the forced vibration response of uniform beams with an arbitrary number of open edge cracks excited by a concentrated moving load is developed in this research. For this purpose, the cracked beam is modeled using beam segments connected by rotational massless linear elastic springs with sectional exibility, and each segment of the continuous beam is assumed to satisfy Timoshenko beam theory. In this method, the equivalent spring stiffness does not depend on the frequency of vibration and is obtained from fracture mechanics. Considering suitable compatibility requirements at cracked sections and corresponding boundary conditions, characteristic equations of free vibration response are derived. Then, forced vibration response is treated under a moving load with a constant velocity. Using the determined eigenfunctions, the forced vibration response may be obtained by the modal superposition method. Finally, some parametric studies are presented to show the effects of crack parameters and moving load velocity.
1 Introduction
One of the key issues of evaluation of the structural systems is evaluating the response of the structures under service loads. Some structures such as bridges may experience fatigue phenomena or overloading, which may result in some cracks in these structures. These cracks may cause changes in the structural parameters (e.g., the stiffness of a structural member such as beam elements), which can change the dynamic properties (such as natural frequencies and mode shapes) [1,2]. Obviously, the response of structures under dynamic loads depends on the mentioned structural parameters. Consequently, cracks may significantly affect the behavior of these structures. Various analytical methods have been used to illustrate the dynamic behavior of damaged beams among which various approaches were employed to model the cracks in beams. One method models the crack by reducing the suitable section modulus [3], while another method tries to evaluate a local exibility for the cracked section [4]. Neglecting the shear effects in bending, some models have been proposed, in which the cracked sections are replaced by a rotational massless spring [57]. Using the theory of fracture mechanics to describe the local exibility of cracked section, the complete vibration behavior of a cracked EulerBernoulli beam faced with...