A nonlinear analysis of the response of a simply supported buckled beam to a harmonic axial load is presented'
The method of multiple scales is used to determine to second order the amplitude- and phase-modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the
governing equation using both digital analog computers. For small excitation amplitudes, the analytical results are in
good agreement with the numerical solutions, The large-amplitude responses are investigated by using a digital computer
and are compared with those obtained via an analog computer simulation. The complicated dynamic behaviors that were
found include period-multiplying and period-demultiplying biturcations, period-three and period-six motions. jump
phenomena, and chaos. ln some cases, multiple periodic attracters coexist, and a chaotic attractor coexists with a periodic
attractor. Phase portraits, spectra of the responses, and a bifurcation set of the many solutions are presented |
