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On the resonance properties of quasi-linear second-order differential-difference equations Anderson, Robert Allan

Abstract

Since very little has appeared in the literature regarding solutions of driven nonlinear differential-difference equations, it has been the purpose of this investigation to obtain approximate solutions to these equations and to investigate their resonance properties. The equations considered are second-order quasi-linear differential-difference equations. Stability criteria are presented for equations having delayed damping and for equations having a delayed restoring force. Application of the Ritz method leads to general equations which determine the constants in the assumed solution. The general equations for systems with odd nonlinearities are used to obtain the resonance properties for several specific examples. Unusual jump resonance phenomena are obtained when the input frequency is varied. Regions of the response curve occur which are not connected to each other. The approximate solution is verified by an analog computer simulation employing track and store techniques to enable automatic plotting of the response curves. The Ritz-method results compare favourably with the analog-simulation results.

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