Dynamic analysis of tapered symmetrically layered beams with interlayer slip

Abstract

In the present contribution, for the first time the dynamic analysis of slender three-layer beams with interlayer slip, whose cross-section is tapered, is carried out. The cross-section of the middle layer is constant along the beam span, while the cross-section of the two outer layers, which varies along the beam span, is identical. The beam axis may have a small initial deflection due to intentional or unintentional imperfection. The layers are elastically bonded, resulting in an interlayer slip under load. The equations of motion and boundary conditions under planar transverse loading are derived, assuming the Euler-Bernoulli hypothesis for each layer separately. In numerous examples, the natural frequencies, eigenfunctions and the forced vibration response is computed, and the effect of different boundary conditions, initial deflection and variable cross-section is investigated. To validate this beam theory, a finite element (FE) analysis assuming a plane stress state is performed in parallel for all examples. It is demonstrated that the results of the proposed beam theory show excellent agreement with the much more computationally expensive FE analyses in all cases.