By Farzad Ebrahimi
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Extra resources for Advances in Vibration Analysis Research
In the this Chapter, we derive a DFE formulation for the free vibration analysis of curved sandwich beams and test it against FEM and DSM to show that DFE is another viable tool for structural vibration analysis. The face layers are assumed to behave according to EulerBernoulli theory and the core deforms in shear only, as was also studied by Ahmed (1971,1972). The authors have previously developed DFE models for two straight, 3-layered, sandwich beam configurations; a symmetric sandwich beam, where the face layers are assumed to follow Euler-Bernoulli theory and core is allowed to deform in shear only (Adique & Hashemi, 2007, and Hashemi & Adique, 2009), and a more general nonsymmetric model, where the core layer of the beam behaves according to Timoshenko theory while the faces adhere to Rayleigh beam theory (Adique & Hashemi, 2008, 2009).
B. Z. T. Atay, Homotopy perturbation method for free vibration analysis of beams on elastic foundations, IOP Conf. : Mater. Sci. , Volume: 10, Number:1, 9th World Congress on Computational Mechanics and 4th Asian Pasific Congress on Computational Mechanics, Sydney, Australia (2010). R. Lu, M. K. R. China 1. Introduction Beams are fundamental models for the structural elements of many engineering applications and have been studied extensively. There are many examples of structures that may be modeled with beam-like elements, for instance, long span bridges, tall buildings, and robot arms.
225 m) would make the beam appear nearly straight). 2 Clamped-Clamped (C-C) end conditions The next test case uses the same beam properties as the previous example, with clampedclamped end conditions. The results of the DFE, and 3- and 4-DOF/node FEM formulations along with those reported by Ahmed (1971,1972) are listed in Table 2 below. For the first set of results from Ahmed (1971), shown in the second column of Table 2 below, each node has 4-DOFs. The 10-element FEM model developed employs similar polynomial Hermite shape functions such as those found in equations (10) and (11) for the approximation space of the field variables v, v’, w and w’, respectively.