This survey paper presents a comprehensive review of work in the field of non-linear oscillations. A brief discussion of second-order systems is followed by a presentation of exact criteria, approximate analytical methods and computational techniques for limit cycles in single variable systems. Multivariate systems are then covered from an analogous viewpoint which allows the reader to clearly identify both how single variable methods have been extended and the possibilities for further research. Particular emphasis is placed on describing function methods since it is believed that, where exact solutions are not possible, the approach may not only give approximate solutions but provides good insight for further computational or simulation studies. The coverage is essentially restricted to continuous lumped parameter systems and includes both free and forced oscillations. Several applications of the theories in various fields of engineering and science are discussed and indicate the broad interest in non-l...

A survey on non-linear oscillations

Algebraic expressions are given for some critical jump-resonance curves in feedback systems containing one nonlinearity. The usual describing-function approximation is employed, and the following nonlinearities are considered: a) linear plus (2n + 1)th power, b) saturation with hysteresis, c) dead zone, d) backlash.

Some Analytically Determined Critical Jump-Resonance Curves

An expression is derived for the incremental describing function of a nonlinearity whose first-harmonic output has a phase shift with respect to the input. Its application in predicting jump resonance in feedback systems containing certain multidimensional nonlinearities is demonstrated by three typical examples.

R. Balasubramanian

Papers

Prediction of jump resonance in systems containing certain multidimensional nonlinearities