Nonstationary processes: Decreasing forcing frequency
Abbreviated Journal Title
Mech. Res. Commun.
SOFTENING DUFFING OSCILLATOR; RESPONSES; Mechanics
Nonstationary (NS) processes or NS dynamical systems (DS) are characterized by the appearance of the process (p) on the Control Parameters (CP) in the governing operators. That is, CP(NS) or CP(p) where p is arbitrary processes: deterministic or random, and by the evolution paths (phi) traced by CPs within the bifurcation regions. Kryolov and Bogolyubov, Russian mathematicians, made first step in introducing NS processes. They also introduced asymptotic method for solution of nonlinear equations. Next, Mitropolskii , head of the Ukrainian School of mathematics and dynamics, expanded the asymptotic method. Evan-Iwanowski , Syracuse NY and his school, expanded the concept of nonstationarity and the asymptotic method to include the multiple-resonance (combination resonance) systems. Extensive experimental work showed excellent agreement with the analysis. Next, the authors dealt with the NS topics related to the precursors to chaos and NS period doubling applications to structural mechanics [3-8]. The new method of NS bifurcation maps allowed determining the dynamical contents of the response within time ranges or cycles for extended time-flow sample . In that, the method is more effective than the well known Poincare maps by eliminating overlapping responses. This paper presents the study of the effects of decreasing forcing frequency Omega(NS) = Omega(o)(1+ alpha(v)t) in the Duffing nonlinear oscillator, where alpha(v) is a negative number. The new dynamic responses appear which are not encountered for the increasing forcing frequency. The authors are convinced that the new physical, chemical and biodynamic nonstationary interpretation eventually will show up based on this study.
Mechanics Research Communications
"Nonstationary processes: Decreasing forcing frequency" (2000). Faculty Bibliography 2000s. 7840.