Coupled bending and torsional vibration of nonsymmetrical axially loaded thin-walled Bernoulli–Euler beams

Elasticity-based free vibration of anisotropic thin-walled beams

“…These numerical values are the same to four significant figures with those computed by Friberg using the Vlasov beam theory [44]. The frequencies computed using the Timoshenko model of Jun [45] are in very good agreement with the values obtained using the assumption of zero Poisson ratio. There is some discrepancy with the results of Petrolo and co-workers [48], which is mildly surprising given that their approach uses similar powerseries approximations over the cross-section, albeit via forms incorporated into finite element approximations.…”

“…The results for the simply supported beam are given in Table 3, for which the main comparative study is the work of Jun [45,46]. As before, the Rayleigh theory results can be computed using the methodology of Han for the simply supported beam [35] and these results are in good agreement with the Timoshenko results of Jun and the results of de Borbon and Ambrosini [47] with somewhat less agreement with the work of Petrolo and co-workers [48].…”

“…2 using Vlasov beam theory. Since that time numerous researchers have also studied this particular crosssection, including Jun [45,46], de Borbon and Ambrosini [47], and Petrolo and co-workers [48]. This beam section has some advantages over the previous section in that the vibrational modes for isotropic beams can be split into groups that reflect symmetry or asymmetry about the vertical axis that bisects the section.…”

“…Two types of support conditions were considered: the fixedfree beam originally studied by Friberg [44] and the simply supported beam of the same cross-section considered by Jun [45,46] and de Borbon and Ambrosini [47]. In the present model, 3 terms were used in the x and y directions for the three variables (these terms include only those represented by the appropriate symmetry group) and 8 axial terms for the fixed-free beam.…”

Computations and evaluations of higher-order theories for free vibration analysis of beams

“…The radius, r, is equal to 0.0245 m, the thickness, t, is equal to 0.004 m, and the length, L, is equal to 0.82 m. The material was assumed isotropic with the Young modulus equal to 68.9 GPa, the Poisson ratio equal to 0.3 and the density equal to 2700 Kg/m 3 . The first two uncoupled frequencies are reported in Table 4 where results from different models are compared with those by Jun et al [54]. A more detailed comparison between 1D CUF models and beam models from open literature can be found in Carrera et al [37].…”