Vibrational energy estimation of cracked composite beams using radiative energy transfer method

Abstract

An energy flow model based on the radiative energy transfer method (RETM) is established for the high-frequency response prediction of finite composite beams with edge cracks. The Timoshenko beam theory is applied to derive the motion governing equations of the beam. The composite beam is divided into several components in line with its multiple cracks. Cracks and boundary conditions are modeled as elastic springs. Spring stiffnesses at the cracks are obtained by the inverse of the flexibility coefficients from the fracture mechanics theory. Power reflection and transmission coefficients through the cracks are derived through wave propagation analysis. The response of the beam loaded by a high-frequency point force is described by vibrational energy density and intensity. The energy response of each part of the beam is contributed by the rays emitted from the actual source set at load point and then, reflected or transmitted through the fictitious sources at cracks. Fictitious sources are determined by the energy balance equations at cracks and boundaries. Numerical examples show that the energy distributions of the multi-cracked composite beams are well predicted by the proposed approach.