Post-critical Behavior of Three-dimensional Composite Beams Near the Autoparametric Resonance under Flapwise Excitation

The bifurcation analysis of a symmetrically composite beam subjected to harmonic flapwise baseexcitation is studied when the ratio of flapwise and chordwise internal resonances is 1:2. Results areobtained by the numerical solution of modulation equations. In previous works, the modulationequations did not exhibit any symmetric properties. Therefore, modified equations with symmetricproperties are studied in this paper. Chracteristics of the response are investigated in terms of timehistory, phase portraits diagrams and bifurcation diagram of poincare maps. It is observed that periodicand multi-periodic motions, jump and stable motion are appeared near the internal and external tunnigfrequency parameters.