Acta Mechanica

, Volume 229, Issue 11, pp 4741–4751 | Cite as

Closed-form exact solutions for hysteretically damped longitudinal free and forced vibrations of tapered beams

  • Yeong-Bin Yang
  • Jae-Hoon KangEmail author


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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This research was supported by the Chung-Ang University Research Grants in 2018.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National Taiwan UniversityTaipeiTaiwan
  2. 2.School of Civil EngineeringChongqing UniversityChongqingChina
  3. 3.Chung-Ang UniversitySeoulSouth Korea

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