By Farzad Ebrahimi
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Extra info for Advances in Vibration Analysis Research
30- Elem. 40-Elem. 20-Elem. 40-Elem. 61 FEM; 4-DOF/node 20-Elem. 40-Elem. 02 Table 1. 88rad/s Fig. 3. 53% for the fifth natural frequency for 20-element models 46 Advances in Vibration Analysis Research when comparing the DFE and the 4-DOF FEM. 51% again for the fifth mode when comparing the DFE and 4-DOF FEM. Also, the first four normalized modes were computed using DFE model for the cantilevered curved sandwich beam and are shown in the Figure 3 below, generated using a 40-element DFE model. The curved beam has a large radius of curvature compared to its span, so the mode shapes of a straight beam can be used as a rough guideline to gauge the acceptability of the current modes.
5 -2 Fig. 12. Free vibration modes of CS rod ( variable cross section uniform rod). 1 20 Advances in Vibration Analysis Research 3. Conclusion In this article, some analytical approximation techniques were employed in the transverse vibration analysis of beams. In a variety of such techniques, the most used ones, namely ADM, VIM and HPM were chosen for use in the computations. First, a brief theoretical knowledge was given in the text and then all of the methods were applied to selected cases. Since the exact values for the free vibration of a uniform beam was available, the analyses were started for that case.
The simplest sandwich beam model utilizes Euler-Bernoulli theory for the face layers and only allows the core to deform only in shear. This assumption has been widely used in several DSM and FEM studies such as those by Banerjee (2003), Ahmed (1971,1972), Mead and Markus (1968), Fasana and Marchesiello (2001), Baber et al. , Adique & Hashemi (2007), and Hashemi & Adique (2009). In more recent publications, Banerjee derived two new DSM models which exploit more complex displacement fields. In the first and simpler of the two (Banerjee & Sobey, 2005), the core bending is governed by Timoshenko beam theory, whereas the face plates are modeled as Rayleigh beams.