Abstract
For chaotic vibrations involving dynamic through generated in a post-buckled beam, influences of an axial displacement on dynamic properties in chaos are clarified by numerical analysis. Especially, the chaotic vibrations bifurcated from 1/2 subharmonic resonance are focused on. The beam is constrained by an axial elastic support and both ends of the beam are clamped. Applying Galerkin method to the basic equation of the buckled beam in consideration with geometric non-linearity, nonlinear cubic simultaneous equations in multi-degrees of freedom are reduced. Further, the equations are transformed into nonlinear ordinary differential equations using normal coordinates corresponding to linear natural modes. By integrating the equations numerically, time histories and Poincare sections are calculated. Moreover, Lyapunov dimension can be obtained using the evolution equations. According to the calculated results, initial axial displacements increase the number of governing modes in the chaos including dynamic snap-through.
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