Moving multi-loads problem in layered cracked beams with interlayer slip

Abstract

This contribution concerns the vibration response of layered cracked uniform beams with interlayer slip under moving multiple loads. Considering a linear constitutive relation between the horizontal slip and the interlaminar shear force, the Euler-Bernoulli hypothesis is assumed to hold for each layer separately. Modeling cracks as internal elastic rotational joints, related discontinuities of the response variables are treated by the theory of generalized functions. In this manner, exact eigenfunctions are derived from a characteristic equation built as determinant of 6x6 matrix, for any number of cracks. Building pertinent orthogonality conditions for the deflection eigenfunctions, the response under moving multiple loads is built in the time domain by modal superposition. The proposed procedure is illustrated for a twolayer beam with multiple cracks, acted upon by moving multiple loads.