Study of Subharmonic Response in Nonlinear System Models

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Department of Electrical Engineering, Stanford University., 1971 - Nonlinear theories - 212 pages
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The report investigates the system model G(u, u dot, . . ., u sup n, t) = F(t), where F(t) is a periodic excitation. Using an approximate solution of the form u(t) = Summation, R=0 to UH (U sub c)(R) cos R (omega sub o) t + (U sub s) (R) sin R (omega sub o) t), analytical theorems and computer results are obtained that yield information into the nature of the existence and non-existence of subharmonic components in the response. By assuming G(u, u dot ..., u sup n, t) to be a polynomial, theorems are developed that determine the conditions for the possible existence and non-existence of subharmonic response. (Author).

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Contents

INTRODUCTION
1
Figure Page
4
Figure Page
5
STABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS
13
THE THEORY OF THE EXISTENCE OF SUBHARMONIC OSCILLATIONS
19
Frequencies obtained by solving Gu ut F
35
+ Kl+00 Fcl COs V and ut UCSb1b2l
42
A FIRST ORDER NONLINEAR DIFFERENTIAL EQUATION
53
number of Fourier parameters is increased
62
A SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION
75
G k Reduction of MSE for u + u k cos 3t as the number
84
EQUATIONS WITH EXACT SOLUTIONS IN THE FORM OF SUBHARMONIC
92
APPENDIX I
98
Flow chart of ADAPT N
101
REFERENCES
105
This report investigates the system model Guu ut Ft
117

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