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

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. [ABSTRACT FROM AUTHOR]