Vibration Analysis of Non-Uniform Beams with an Arbitrary Number of Cracks
In this paper, a method is presented to facilitate the computation of dynamic properties of non-uniform beams with any number of cracks. Based on the Frobenius method, an analytical solution of vibration equation of non-uniform beams is obtained. In combination with the line spring model of crack, the transfer matrices for non-uniform beam element and crack are established respectively. Then the global transfer matrix can be simply formulated, from which the frequency equation in the form of 2×2 determinant is derived. Due to the decrease in the determinant order as compared with previously developed procedures, significant savings in the computational task would be achieved by the present method.
M.H. Aliabadi, Qingfen Li, Li Li and F.-G. Buchholz
Z. G. Yu et al., "Vibration Analysis of Non-Uniform Beams with an Arbitrary Number of Cracks ", Key Engineering Materials, Vols. 324-325, pp. 303-306, 2006