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Three problems in nonlinear dynamics...

Morrison, Tina Marie.

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Three problems in nonlinear dynamics with 2:1 parametric excitation.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Three problems in nonlinear dynamics with 2:1 parametric excitation./
作者:	Morrison, Tina Marie.
面頁冊數:	146 p.
附註:	Adviser: Richard H. Rand.
Contained By:	Dissertation Abstracts International67-07B.
標題:	Applied Mechanics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3227288
ISBN:	9780542789328

Three problems in nonlinear dynamics with 2:1 parametric excitation.
Morrison, Tina Marie.

Three problems in nonlinear dynamics with 2:1 parametric excitation. - 146 p.

Adviser: Richard H. Rand.

Thesis (Ph.D.)--Cornell University, 2006.

Parametric excitation is epitomized by the Mathieu equation, x¨ + (delta + epsilon cos t)x = 0, which involves the characteristic feature of 2:1 resonance. This thesis investigates three generalizations of the Mathieu equation: (1) the effect of combining 2:1 and 1:1 parametric drivers: x¨ + (delta + epsilon cos t + epsilon cos o t)x = 0; (2) the effect of combining parametric excitation near a Hopf bifurcation: x¨ + (delta + epsilon cos t)x + epsilonAx&dot; + epsilon(beta1x3 + beta 2x2x&dot; + beta 3xx&dot;2 + beta4 x&dot;3) = 0; (3) the effect of combining delay with cubic nonlinearity: x¨ + (delta + epsilon cos t)x + epsilongammax3 = epsilonbetax(t - T).

ISBN: 9780542789328Subjects--Topical Terms:

1018410
Applied Mechanics.

Three problems in nonlinear dynamics with 2:1 parametric excitation.
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020 $a 9780542789328
035 $a (UMI)AAI3227288
035 $a AAI3227288
040 $a UMI $c UMI
100 1 $a Morrison, Tina Marie. $3 1293428
245 1 0 $a Three problems in nonlinear dynamics with 2:1 parametric excitation.
300 $a 146 p.
500 $a Adviser: Richard H. Rand.
500 $a Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 4069.
502 $a Thesis (Ph.D.)--Cornell University, 2006.
520 $a Parametric excitation is epitomized by the Mathieu equation, x¨ + (delta + epsilon cos t)x = 0, which involves the characteristic feature of 2:1 resonance. This thesis investigates three generalizations of the Mathieu equation: (1) the effect of combining 2:1 and 1:1 parametric drivers: x¨ + (delta + epsilon cos t + epsilon cos o t)x = 0; (2) the effect of combining parametric excitation near a Hopf bifurcation: x¨ + (delta + epsilon cos t)x + epsilonAx&dot; + epsilon(beta1x3 + beta 2x2x&dot; + beta 3xx&dot;2 + beta4 x&dot;3) = 0; (3) the effect of combining delay with cubic nonlinearity: x¨ + (delta + epsilon cos t)x + epsilongammax3 = epsilonbetax(t - T).
520 $a Chapter 3 examines the first of these systems in the neighborhood of 2:1:1 resonance. The method of multiple time scales is used including terms of O(epsilon2) with three time scales. By comparing our results with those of a previous work on 2:2:1 resonance, we are able to approximate scaling factors which determine the size of the instability regions as we move from one resonance to another in the delta-o plane.
520 $a Chapter 4 treats the second system which involves the parametric excitation of a Hopf bifurcation. The slow flow obtained from a perturbation method is investigated analytically and numerically. A wide variety of bifurcations are observed, including pitchforks, saddle-nodes, Hopfs, limit cycle folds, symmetry-breaking, homoclinic and heteroclinic bifurcations. Approximate analytic expressions for bifurcation curves are obtained using a variety of methods, including normal forms. We show that for large positive damping, the origin is stable, whereas for large negative damping, a quasiperiodic behavior occurs. These two steady states are connected by a complicated series of bifurcations which occur as the damping is varied.
520 $a Chapter 5 examines the third system listed. Three different types of phenomenon are combined in this system: 2:1 parametric excitation, cubic nonlinearity, and delay. The method of averaging is used to obtain a slow flow which is analyzed for stability and bifurcations. We show that certain combinations of the delay parameters beta and T cause the 2:1 instability region in the delta-epsilon plane to become significantly smaller, and in some cases to disappear. We also show that the delay term behaves like effective damping, adding dissipation to a conservative system.
590 $a School code: 0058.
650 4 $a Applied Mechanics. $3 1018410
650 4 $a Engineering, Mechanical. $3 783786
690 $a 0346
690 $a 0548
710 2 0 $a Cornell University. $3 530586
773 0 $t Dissertation Abstracts International $g 67-07B.
790 $a 0058
790 1 0 $a Rand, Richard H., $e advisor
791 $a Ph.D.
792 $a 2006
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3227288