Vibrational power flow analysis of cracked functionally graded beams

Vibrational power flow analysis of Timoshenko microbeams with a crack

“…Fig. 4 compares the present results of the input power flow with the results obtained by Zhu et al [17]. It shows a perfect agreement between Zhu et al's results and the present results.…”

“…2, the crack position is modeled as a rotational spring. For beam structures with transverse bending vibration, the bending moment dominates the vibrational behavior, therefore the bending stiffness at the crack section can be approximated by the stiffness of the rotating spring [17]. The premises of this spring modelling approach are that the crack does not propagate, always remains open and is perpendicular to the upper surface of the beam.…”

“…It had been well known that the change of the excitation frequency will lead to the fluctuation of the input power flow for macroscale cracked beams [17]. This is because the crack can interrupt the original wave propagation path, that is, a part of traveling waves will be reflected when they meet the crack.…”

“…Xu et al [16] adopted the vibrational power flow to study nonlinear dynamic behaviors of the rotating blade with a breathing crack. Zhu et al [17] analyzed the vibrational power flow of cracked functionally graded beams and highlighted the influence of crack location, crack depth and gradient index to the power flow. Zheng et al [18] analyzed the dynamic response of the cracked fluid-filled cylindrical shell and presented a damage detection method based on the energy flow.…”

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

“…On the other hand, many researches have examined the case of a cracked FGB subjected to external loadings in the form of moving loads or axial forces [10][11][12][13][14][15][16]. Lately, Lin-Feng Zhu et al [17] analysed the vibrational power flow of a cracked FG Timoshenko beam under a concentrated transverse harmonic force using the wave propagation approach to obtain the input power flow and transmitted power flow and applying the continuous wavelet transform to deal with the inverse problem of crack identification. It should be pointed out that all of the aforementioned investigations were limited to linear analysis.…”