Modal Analysis of a Simply Supported Steel Beam with Cracks under Temperature Load

Abstract

Based on the transfer matrix method, an analytical method is proposed to conduct the modal analysis of the simply supported steel beam with multiple transverse open cracks under different temperatures. The open cracks are replaced with torsion springs without mass, and local flexibility caused by each crack can be derived; the temperature module is introduced by the mechanical properties variation of the structural material, and the temperature load is caused by the temperature variation, which can be transformed to the axial force on the cross-section. The transfer matrix of the whole beam with the temperature and geometric parameters of cracks can be obtained. According to boundary conditions of the simply supported beam, natural frequencies of the beam can be calculated, which are compared with the finite element results. Results indicate that the analytical method proposed has a high accuracy; the natural frequencies of the simply supported steel beam are mostly affected by the temperature load, which cannot be ignored.

A novel approach for damage quantification using the dynamic response of a metallic beam under thermo-mechanical loads

“…The effects of environmental conditions on modal behavior of different structures were presented by various researchers [26][27][28][29][30]. Ma et al [31][32] proposed an analytical method (based on a transfer matrix) for modal analysis of a simply supported steel beam with multiple transverse open cracks under different temperatures. They modeled crack as a rotational spring and hence limited in damage quantification.…”

A multi‐phase scale simulation of electrochemical chloride extraction in crack‐self‐healing concrete

“…However, cracks are often tortuous and uneven in width. 34 These features significantly reduce the permeability of chloride ions into transverse cracks. For simplification, the crack shape was simplified as a rectangle with an equivalent crack width w = w cr − w cr, t , in which w cr is the crack width and w cr,t is the threshold crack width.…”

“…According to the literature, 34 within 5 months, the inward velocity of the crack and crack growth zone V n is:…”

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“…These relations were extracted from the experimental data performed on aluminum alloys at different temperatures on various type of specimens as shown in Figure 14. Ma et al [135][136] proposed an analytical method (based on a transfer matrix) for modal analysis of a simply supported steel beam with multiple transverse open cracks under different temperatures. They modelled crack as a rotational spring and hence limited in quantification of damage.…”