Abstract
Exact solutions for hysteretically damped free vibrations of tapered longitudinal beams are obtained instead of undamped free vibrations. Also forced vibrations of tapered longitudinal beams with hysteretical damping are studied by a closed-form exact method. The hysteretically damped natural frequency equations are exactly derived. Accurate longitudinal amplitude versus forcing frequency curves showing the forced response due to distributed loading are plotted with various hysteretical damping parameters. The present method is capable to be applied to a tapered tall building with hysteretic damping subjected to longitudinal harmonic loads like earthquake loads.
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