TY - JOUR
T1 - Some results on the dynamics of the linear parametric oscillator with general time-varying frequency
AU - Kourdis, Panayotis D.
AU - Vakakis, Alexander F.
PY - 2006/12/15
Y1 - 2006/12/15
N2 - The dynamics of single-degree-of-freedom linear oscillators under parametric excitation of general type (periodic or non-periodic) is considered. An analytical approach based on complexification and amplitude-phase decomposition of the response is developed leading to an (exact) set of first-order ordinary differential equations governing the amplitude and phase of the motion. Perturbation schemes for solving this set are developed and the solutions of the derived modulation equation are outlined. In addition, some results and comments on the stability of the derived solutions are provided.
AB - The dynamics of single-degree-of-freedom linear oscillators under parametric excitation of general type (periodic or non-periodic) is considered. An analytical approach based on complexification and amplitude-phase decomposition of the response is developed leading to an (exact) set of first-order ordinary differential equations governing the amplitude and phase of the motion. Perturbation schemes for solving this set are developed and the solutions of the derived modulation equation are outlined. In addition, some results and comments on the stability of the derived solutions are provided.
KW - Non-periodic parametric excitation
KW - Stability
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U2 - 10.1016/j.amc.2006.06.049
DO - 10.1016/j.amc.2006.06.049
M3 - Article
AN - SCOPUS:33845752576
SN - 0096-3003
VL - 183
SP - 1235
EP - 1248
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 2
ER -