Abstract
Abstract This article reports the results of an investigation on the effects of internal moments on the vibration behavior of thin-walled steel members. The analyses are based on the Generalized Beam Theory (GBT), a thin-walled bar theory accounting for cross-section in-plane deformations - its main distinctive feature is the representation of the member deformed configuration by means of a linear combination of cross-section deformation modes, multiplied by their longitudinal amplitude functions. The study concerns a simply supported T-section (with unequal flanges) members exhibiting a wide range of lengths and subjected to uniform internal moment diagrams - their magnitudes are specified as percentages of the corresponding critical buckling values. After providing a brief overview of the main concepts and procedures involved in performing a GBT-based structural analysis, the vibration behavior of load-free and loaded T-section members is addressed - the influence of the applied loadings is assessed in terms of (i) the fundamental frequency difference and (ii) the change in the corresponding vibration mode shape. For validation purposes, some GBT results are compared with values yielded by shell finite element analysis performed in the code ABAQUS (Simulia, 2008).
Highlights
Vibration behavior of thin-walled steel members subjected to uniform bending AbstractThis article reports the results of an investigation on the effects of internal moments on the vibration behavior of thin-walled steel members
The results presented and discussed are validated by means of values and mode shapes provided by numerical analyses performed with the code ABAQUS (Simulia, 2008), adopting fine meshes of four-node isoparametric shell (S4) elements to discretize the columns
J., Ouro Preto, 71(3), 349-359, jul. sep. | 2018. The observation of these results leads to the following conclusions: (i) First of all, there is a fairly good correlation between the fundamental frequency values and vibration mode shapes obtained through ABAQUS shell finite element and Generalized Beam Theory (GBT)-based analyses, which fully validates the latter − the differences on the fundamental frequency values increase with α: (i1) they are minor for small applied moments (less than 4% for −0.50 ≤ α ≤ 0.50, (i2) increases to 7% for −0.90 ≤ α ≤ 0.90, and (i3) reaches 10% for higher applied moments
Summary
The GBT is a one-dimensional bar theory that expresses/discretizes the member deformed configuration as a linear combination of cross-section deformation modes multiplied by the corresponding (modal) amplitude functions. The solution to buckling or vibration problem yields on determining the corresponding eigenvalues (buckling loads or natural frequencies) and eigenvectors (buckling or vibration mode shapes) − the latter provide the coefficients of the modal amplitude functions With this purpose, if one makes (i) aB = 1 and aν = 0, (ii) aB = 0 and aν = 1 or (iii) aB = ψ (0 ≤ ψ ≤ 1) and aν = 1, Eqs. 3. Load-free vibration behavior and loaded T-section members with (i) the cross-section depicted, (ii) the discretization shown in Fig. 1(b) and (iii) the particular dimensions of bw = 150 mm (web width), bs = 150 mm (top flange width), bi = 50 mm (bottom flange width), s = 20 mm (stiffener width) and e = 3 mm (wall thickness) – the influence of the applied loadings (uniform major-axis bending moment) is assessed in terms of (i) the fundamental frequency variation and (ii) the change in the corresponding vibration mode shape. The supported beam buckling behavior is first analyzed, since his knowledge is indispensable to assess the loaded member vibration behavior
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