68 research outputs found
Tutorial of numerical continuation and bifurcation theory for systems and synthetic biology
Mathematical modelling allows us to concisely describe fundamental principles
in biology. Analysis of models can help to both explain known phenomena, and
predict the existence of new, unseen behaviours. Model analysis is often a
complex task, such that we have little choice but to approach the problem with
computational methods. Numerical continuation is a computational method for
analysing the dynamics of nonlinear models by algorithmically detecting
bifurcations. Here we aim to promote the use of numerical continuation tools by
providing an introduction to nonlinear dynamics and numerical bifurcation
analysis. Many numerical continuation packages are available, covering a wide
range of system classes; a review of these packages is provided, to help both
new and experienced practitioners in choosing the appropriate software tools
for their needs.Comment: 14 pages, 2 figures, 2 table
Nonlinear normal modes, modal interactions and isolated resonance curves
The objective of the present study is to explore the connection between the
nonlinear normal modes of an undamped and unforced nonlinear system and the
isolated resonance curves that may appear in the damped response of the forced
system. To this end, an energy balancing technique is used to predict the
amplitude of the harmonic forcing that is necessary to excite a specific
nonlinear normal mode. A cantilever beam with a nonlinear spring at its tip
serves to illustrate the developments. The practical implications of isolated
resonance curves are also discussed by computing the beam response to sine
sweep excitations of increasing amplitudes.Comment: Journal pape
Nonlinear Modal Analysis of the SmallSat Spacecraft
Non-linear elements are present in practically all spacecraft structures. When such non-linear effects are important linear modal analysis can no longer be applied. The development of a non-linear analogue of linear modal analysis is therefore an important endeavor. The objective of this paper is to show that nonlinear normal modes (NNMs) represent a useful and practical tool in this context. A full-scale spacecraft structure is considered and is modeled using the finite element method. Its NNMs are computed using advanced numerical algorithms, and the resulting dynamics is then carefully analyzed. Nonlinear phenomena with no linear counterpart including nonlinear modal interactions are also highlighted
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