296 F. Tubino and G. Piccardo VΩ 0 2 4 6 a b c jnorm,max Ωm = 0.9 Ωm = 0.925 Ωm = 0.95 Ωm = 0.975 Ωm = 1 Ωm = 1.025 Ωm = 1.05 Ωm = 1.075 Ωm = 1.1 ESM ESM ESM ESM ESM ESM ESM ESM ESM VΩ 0 2 4 6 jnorm,max Ωm = 0.9 Ωm = 0.925 Ωm = 0.95 Ωm = 0.975 Ωm = 1 Ωm = 1.025 Ωm = 1.05 Ωm = 1.075 Ωm = 1.1 ESM ESM ESM ESM ESM ESM ESM ESM ESM 0.06 0.07 0.08 0.09 0.1 0.06 0.07 0.08 0.09 0.1 0.06 0.07 0.08 0.09 0.1 VΩ 0 2 4 6 pjnorm,max Ωm = 0.9 Ωm = 0.925 Ωm = 0.95 Ωm = 0.975 Ωm = 1 Ωm = 1.025 Ωm = 1.05 Ωm = 1.075 Ωm = 1.1 EURL Setra EURL BSI EMRL ISO (Ωcm=0.005) EMRL ISO (Ωcm=0.003) EMRL ISO (Ωcm=0.001) p p Fig. 28.1 Mean value of the normalized maximum non-dimensional acceleration: comparison among Monte Carlo simulations (symbols) and ESM with peak factor by Vanmarcke (a) and by Davenport (b), EURL and EMRL (c) approximately one and the coefficient of variation V˝ is small: in this case, the dynamic response is a narrow band random process and Vanmarcke theory provides very good results. On the other hand, the Davenport formulation provides a better approximation of the numerical results when the non-dimensional mean step frequency is lower than 0.95 or higher than 1.05, especially for large values of V˝, when the dynamic response is not really a narrow band random process. In any case, ESM based on Davenport formulation provides conservative estimates of the maximum dynamic response. Figure 28.1c clearly shows that EURL and EMRL do not allow to take into account the probability distribution of the step frequency and they provide a maximum values of the structural response independent of V˝ and Q m. However, SETRA model provides a normalized maximum non-dimensional acceleration that is in perfect accordance with numerical
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