, Volume 50, Issue 3, pp 675–688 | Cite as

Nonlinear free dynamics of a two-layer composite beam with different boundary conditions

  • Stefano Lenci
  • Francesco Clementi
  • Jerzy Warminski
Advances in Dynamics, Stability and Control of Mechanical Systems


The nonlinear free vibrations of a two-layer elastic composite beam are investigated. Different boundary conditions, both symmetric and not symmetric with respect to the beam midpoint, equal on both layers and different on each layers, are considered. The analysis is developed by means of the multiple time scale method, and at each order of the asymptotic development, we obtain different information. The first order terms provide the linear natural frequencies. The first, the second and the third natural frequencies are computed explicitly. The next order terms, on the other hand, provide the nonlinearity coefficients measuring the nonlinear amplitude dependence of the natural frequencies, i.e. the curvature of the backbone curve. Both the linear frequencies and the nonlinear coefficients are found to be dependent on two dimensionless parameters only and, for boundary conditions different on each layer, also of the ratio between the axial stiffnesses of each layer.


Two-layer beam Nonlinear interface Different boundary conditions Free vibrations 



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”. A preliminary version of this work is presented in [28].


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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Stefano Lenci
    • 1
  • Francesco Clementi
    • 1
  • Jerzy Warminski
    • 2
  1. 1.Department of Civil and Buildings Engineering, and ArchitecturePolytechnic University of MarcheAnconaItaly
  2. 2.Department of Applied MechanicsLublin University of TechnologyLublinPoland

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