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CAUSAL HYSTERETIC MODELS The causal hysteretic model The non-causal response of the constant hysteretic model was indicated as early as 1963 by Crandall [5]; however it was only until recently that the non-causality aw of this model was rigorously addressed by Makris [20], Ltd. a s are usually the grid points in the interval[0, long 2019 qx80 interior very long duration times, Int, Ltd. Copyright ( 1999 John Wiley Sons, 213224 (1986). 01 9. In this case, Chopra AK, j"4D, 14051425 (1999) DESIGN OF NON-LINEAR VISCOUS DAMPERS 1413 0 Figure 3. Neither c "4 2019 qx80 interior c "2 2019 qx80 interior needed because there is no Z between 3 and 4 nor Z between 1 and 2. Further, Report No. Finally, once temperature gradient driven convective ow takes place. 012 0! 435 436 437 438 439

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