By Farzad Ebrahimi

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As the composite beam element is of a one-element-one-member configuration, modeling with this type of element would not need to take into account the discontinuity between different parts of the beam. The accuracy of this new composite element has been compared satisfactorily with existing results. One advantage of the 30 Advances in Vibration Analysis Research method proposed is that it can be extended easily to deal with beams consisting of an arbitrary number of non-uniform segments. Regarding the free and forced vibration analysis for cracked beam using composite element, modelling with this type of element would allow the automatic inclusion of interaction effect between adjacent local damages in the finite element model.

2007), where all three layers are modeled as Timoshenko beams. However, increasing the complexity of the model also significantly increases the amount of numerical and symbolic computation in order to achieve the complete formulation. Classical FEM method has a proven track record and is the most commonly used method for structural analysis. It is a systematic approach, leading to element stiffness and mass matrices, easily adaptable to a wide range of problems. The polynomial shape functions are used to approximate the displacement fields, resulting in a linear eigenproblem, whose solutions are the natural frequencies of the system.

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.

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