Free Vibration of Damaged Frame Structures Considering the Effects of Axial Extension, Shear Deformation and Rotatory Inertia: Exact Solution

Abstract

In this paper, a procedure based on the transfer matrix method for obtaining the exact solution to the equations of free vibration of damaged frame structures, considering the effects of axial extension, shear deformation, rotatory inertia, and all compliance components arising due to the presence of a crack, is presented. The crack is modeled by a rotational and/or translational spring based on the concept of linear elastic fracture mechanics. Only the in-plane motion of planar structures is considered. The formulation is validated through some examples existing in the literature. Additionally, the mode shapes and natural frequencies of a frame with pitched roof are provided. The variation of natural frequencies with respect to the crack location is presented. It is concluded that considering the axial compliance, and axial-bending coupling due to the presence of a crack results in different dynamic characteristics, which should be considered for problems where high precision is required, such as for the crack identification problems.

On Damage Identification in Planar Frames of Arbitrary Size

“…In principle, all the natural frequencies of all the possible configurations of damaged frames can be calculated, and the correct location of the damage can be identified, maximizing the fitness functions (7) and (8). e numerical applications will show that, in order to identify the two damage parameters, that is, location and intensity, it is enough to take into account only a few numbers of natural frequencies.…”

“…A great number of studies are based on the comparison of the static or dynamic response of models of damaged structures with respect to the undamaged configuration [1][2][3][4][5][6][7][8][9] and propose damage identification techniques. e latter often require the measurement of different kind of data on the existing structure; these, for example, may concern the variation of dynamic characteristics, such as natural frequencies [10][11][12][13][14][15][16][17][18][19][20], mode shapes [21,22], modal curvature [23,24], and time-frequency features [25], or static quantities, such as displacements or strains induced by applied loads [26][27][28].…”

Vibration of locally cracked pre-loaded parabolic arches

“…In a linear setting, this is represented by a matrix, originally introduced by Dimarag-onas and co-workers [8,9,10,11,3,12,13,14,14,15,16]. As for later studies, without pretending to be exhaustive, we may quote [17,18,19,20,21,22]. We may refer the interested readers to the early review article by Doebling et al [1] and to the recent review by Hou and Xia [23].…”

Free vibrations of spatial frame structures: Analytical modelling and solution

“…Beams usually have predictable mechanical characteristics due to their geometric simplicity, which allows certain assumptions to be made. These assumptions typically depend on many parameters like the deformations the beam undergoes, cross-sectional properties of the beam as well as the geometry of the beam axis (Eroglu and Tufekci, 2017; Freund and Karakoç, 2016; Tüfekçi and Arpaci, 1998; Tüfekci et al, 2020a). Therefore, the assumptions must be made carefully considering the properties of the beam.…”