DYNAMICS OF A SLENDER BEAM WITH AN ATTACHED MASS UNDER COMBINATION PARAMETRIC AND INTERNAL RESONANCES, PART II: PERIODIC AND CHAOTIC RESPONSES

✍ Scribed by S.K. Dwivedy; R.C. Kar

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 364 KB
• Volume: 222
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1998.2063

✦ Synopsis

The governing second order temporal dierential equation of a slender beam with an attached mass at an arbitrary position under vertical base excitation which retains the cubic non-linearities of geometric and inertial type is reduced to a set of ®rst order dierential equations by the method of normal forms for combination parametric and internal resonances of 3:1. These equations are used to ®nd the periodic, quasi-periodic and chaotic responses of the system for various bifurcating parameters, namely, damping, amplitude and frequency of base motion, attached mass and its location. Bifurcation set, mixed-mode oscillation, period-doubling, quasi-periodic orbits and dierent routes to chaos, namely, alternate periodic-chaotic transition, torus breakdown and intermittency have been studied for the above mentioned bifurcating parameters using phase portrait, Poincare section, time and power spectra.