Evaluation of high-order modes and damage effects of multi-crack beams using enhanced spectral element method

Abstract

Exact evaluation of high-order modes of a multi-crack Euler–Bernoulli beam using the conventional spectral element method (SEM) suffers from the deficiency of numerical ill-conditioning, mainly due to round-off errors in floating-point computations involved in evaluating the spectral element stiffness matrix, therefore, the modeling of the multiple cracks intensively increases the complexity of the matrix. To address this limitation, an enhanced SEM with the spectral element stiffness matrix constructed in a set of local coordinate systems is developed. With the method, two sets of local coordinate systems are created to derive two types of spectral element stiffness matrices for a multi-crack beam. The proposed spectral element stiffness matrices are of improved capacities to characterize the high-order modes of a multi-crack beam by largely eliminating the round-off errors involved in the conventional SEM. Moreover, the function of evaluating high-order modes endows the enhanced SEM with distinctive capability to reveal the effect of multiple cracks on the modal property of a multi-crack beam. The effectiveness of the proposed method in evaluating high-order modes and revealing the effects of multiple cracks on the modal property of a beam is investigated on various damage cases.

Accurate Modeling and Wave Propagation Analysis of Cracked Slender Structural Members by the Spectral Element Method

“…Krawczuk et al [26] studied the propagation of fexural wave in a cracked Timoshenko beam with rectangular cross section by modeling the crack as a dimensionless and massless spring with bending and shear fexibilities. Xu et al [27] established the SEM model of Euler-Bernoulli beam with multiple cracks by modeling the crack as a massless spring with bending fexibility. Izadifard et al [28] modelled the crack as massless rotational and translational springs and established the dynamic model of cracked frame structure by the SEM.…”

Identification of Multiple Cracks in Composite Laminated Beams Using Perturbation to Dynamic Equilibrium

“…Initial cracks in beam-type structural components can develop to significant extents subject to long-term transverse loads, jeopardizing local stiffness against bending moments, by which structural failures can be induced [ 1 ]. Thereby, approaches for identifying cracks in beam-type structural components are worth investigating, especially multiple crack identification, which is more challengeable compared with single crack identification [ 2 ]. Compared with approaches relying on natural frequencies [ 3 , 4 , 5 , 6 , 7 , 8 , 9 ], approaches relying on mode shapes are naturally capable of locating cracks because they contain spatial locations of structural elements.…”