Modelling of the dynamics of Euler’s beam by ϕ6 potential

We derive in this paper the mathematical model, describing the single mode dynamics of a beam subjected to external loads. Taking into account the geometrical nonlinearities and considering the second order approximation of the deflected length of the beam, we show that the single mode dynamics of a simply supported (hinged–hinged) beam can be described by a ϕ6 potential with various configurations.

► Modeling of the dynamics of hinged–hinged beam.
► Duffing and extended Duffing oscillator.
► Bonded and unbounded potential configurations.
► ϕ6 can lead to catastrophic motion.
► Failure on mechanical on nonlinear beam structure.