Model reduction of weakly nonlinear systems

In general, model reduction techniques fall into two categories — moment —matching and Krylov techniques and balancing techniques. The present contribution is concerned with the former. The present contribution proposes the use of a perturbative representation as an alternative to the bilinear representation [4]. While for weakly nonlinear systems, either approximation is satisfactory, it will be seen that the perturbative method has several advantages over the bilinear representation. In this contribution, an improved reduction method is proposed. Illustrative examples are chosen, and the errors obtained from the different reduction strategies will be compared

The evolution of wave correlations in uniformly turbulent, weakly nonlinear systems

Evolution of wave correlations in uniformly turbulent, weakly nonlinear system

Analysis of nonlinear oscillators using volterra series in the frequency domain Part I : convergence limits

The Volterra series representation is a direct generalisation of the linear convolution integral and has been widely applied in the analysis and design of nonlinear systems, both in the time and the frequency domain. The Volterra series is associated with the so-called weakly nonlinear systems, but even within the framework of weak nonlinearity there is a convergence limit for the existence of a valid Volterra series representation for a given nonlinear differential equation. Barrett(1965) proposed a time domain criterion to prove that the Volterra series converges with a given region for a class of nonlinear systems with cubic stiffness nonlinearity. In this paper this time-domain criterion is extended to the frequency domain to accommodate the analysis of nonlinear oscillators subject to harmonic excitation

Numerical computation of nonlinear normal modes in mechanical engineering

This paper reviews the recent advances in computational methods for nonlinear normal modes (NNMs). Different algorithms for the computation of undamped and damped NNMs are presented, and their respective advantages and limitations are discussed. The methods are illustrated using various applications ranging from low-dimensional weakly nonlinear systems to strongly nonlinear industrial structures. © 2015 Elsevier Ltd

Topographically forced long waves on a sheared coastal current. Part 1. The weakly nonlinear response

The flow of a constant-vorticity current past coastal topography is investigated in the long-wave weakly nonlinear limit. In contrast to other near-critical weakly nonlinear systems this problem does not exhibit hydraulically controlled solutions. It is shown that near criticality the evolution of the vorticity interface is governed by a forced BDA (Benjamin-Davis-Acrivos) equation. The solutions of this equation are discussed and two distinct near-critical flow regimes are identified. Owing to the non-local nature of the forcing, the first of these regimes is characterized by quasi-steady solutions controlled at the topography with some blocking of the upstream rotational fluid, while in the second regime steady nonlinear wavetrains form downstream of the obstacle with no upstream influence. In the hydraulic limit the velocity band for both of these critical regimes approaches zero

Variable domain transformation for linear PAC analysis of mixed-signal systems

This paper describes a method to perform linear AC analysis on mixed-signal systems which appear strongly nonlinear in the voltage domain but are linear in other variable domains. Common circuits like phase/delay-locked loops and duty-cycle correctors fall into this category, since they are designed to be linear with respect to phases, delays, and duty-cycles of the input and output clocks, respectively. The method uses variable domain translators to change the variables to which the AC perturbation is applied and from which the AC response is measured. By utilizing the efficient periodic AC (PAC) analysis available in commercial RF simulators, the circuit’s linear transfer function in the desired variable domain can be characterized without relying on extensive transient simulations. Furthermore, the variable domain translators enable the circuits to be macromodeled as weakly-nonlinear systems in the chosen domain and then converted to voltage-domain models, instead of being modeled as strongly-nonlinear systems directly