20 Natural Frequencies of Layered Beams Using a Continuous Variation Model 195 Fig. 20.9 Pin-pin beam deflections as a function of – three-cell beam Fig. 20.10 Clamp-clamp beam deflections as a function of – three-cell beam The forced motion approach gives the first frequency for this case as D1.28. This can be seen in Fig. 20.9. Using the assumed mode approach, with the same initial polynomial given before and ten orthogonal polynomials, the method produces a first frequency D1.63, which is larger than the one given by the forced motion by 27.3 %. Differences start to increase as the assumed polynomial for the deflection and the actual deflection shapes become more distinct. For clamp-clamp boundary conditions and using the forced motion, the deflections can be seen in Fig. 20.10. Resonance is observed at D2.48. For this case the assumed mode gives: D3.02. The difference here is 21.8 %. A summary of the results is given in Table 20.1.
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