Nonlinear Dynamics

Abstract Indirect reduced-order models (ROMs) aim to dramatically reduce the cost of simulating nonlinear dynamic behaviour in large nonlinear finite element systems. Applied force based methods, most notably implicit condensation and expansion, are a classical approach. This work summarises and critiques the past 25 years of development whilst making the case for the continued relevance of the m…

Abstract Reduced-order modelling describes a powerful set of techniques for dramatically reducing the cost of dynamic simulations in complex engineering systems, with broad application for designing and understanding nonlinearity. For Reduced-Order Models (ROMs) to be useful in an industrial context, an analyst must have a high degree of confidence that the results reported by the ROM are reflect…

Abstract We introduce Extrema-Segmented Entropy (ExSEnt), a feature-decomposed framework for quantifying time-series complexity that separates temporal from amplitude contributions. The method partitions a signal into monotonic segments by detecting sign changes in the first-order increments. For each segment, it extracts the interval duration and the net amplitude change, generating two sequence…

Abstract In this work the free vibration response of the anisotropic pendulum is analyzed. The spherical pendulum has three primary periodic motions of free vibration, but two are degenerate and have the same frequency, and therefore all three are stable. In contrast, the anisotropic pendulum has three distinct primary periodic motions of free vibration, but only if the level of energy is above a…