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Meccanica

, Volume 51, Issue 11, pp 2589–2606 | Cite as

A comprehensive analysis of hardening/softening behaviour of shearable planar beams with whatever axial boundary constraint

  • S. Lenci
  • F. Clementi
  • G. Rega
Nonlinear Dynamics, Identification and Monitoring of Structures

Abstract

The free nonlinear oscillations of a planar elastic beam are investigated based on a comprehensive asymptotic treatment of the exact equations of motion. With the aim of investigating the behaviour also for low slenderness, shear deformations and rotational inertia are taken into account. Attention is payed to the influence of the geometrical and mechanical parameters, and of the boundary conditions in changing the nonlinear behaviour from softening to hardening. An axial linear spring is added to one end of the beam, and it is shown how the behaviour changes qualitatively on passing from the hinged-hinged (commonly hardening) to the hinged-supported (commonly softening) case. Some interesting, and partially unexpected, results are obtained also for values of the slenderness moderately low but still in the realm of practical applications.

Keywords

Geometrically exact beam model Asymptotic analysis  Nonlinear free vibrations Axially restrained/unrestrained beams High/low slenderness Hardening/softening behaviour 

Notes

Acknowledgments

This work has been partially supported by the Italian Ministry of Education, University and Research (MIUR) by the PRIN funded program 2010/11 N.2010MBJK5B “Dynamics, stability and control of flexible structures”.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Civil and Buildings Engineering, and ArchitecturePolytechnic University of MarcheAnconaItaly
  2. 2.Department of Structural and Geotechnical EngineeringSapienza University of RomeRomeItaly

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