Affiliations: Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil | Sapienza University of Rome, Rome, Italy | Federal University of Goiás, Goiânia, GO, Brazil
Note: [] Corresponding author: Paulo B. Gonçalves, Pontifical
Catholic University of Rio de Janeiro, Rua Marquês de São Vicente
225, Rio de Janeiro, RJ, Brazil. Tel.: +55 21 3527 1189; E-mail:
paulo@puc-rio.br
Abstract: In this paper an inextensible cantilever beam subject to a
concentrated axial load and a lateral harmonic excitation is investigated.
Special attention is given to the effect of the axial load on the
frequency-amplitude relation, bifurcations and instabilities of the beam. To
this aim, the nonlinear integro-differential equations describing the
flexural-flexural-torsional coupling of the beam are used, together with the
Galerkin method, to obtain a set of discretized equations of motion, which are
in turn solved by using the Runge-Kutta method. Both inertial and geometric
nonlinearities are considered in the present analysis. Due to symmetries of the
beam cross section, the beam exhibits a 1:1 internal resonance which has an
important role on the nonlinear oscillations and bifurcation scenario. The
results show that the axial load influences the stiffness of the beam changing
its nonlinear behavior from hardening to softening. A detailed parametric
analysis using several tools of nonlinear dynamics unveils the complex dynamic
behavior of the beam in the parametric and external resonance regions.
Bifurcations leading to multiple coexisting solutions are observed.
