Experimental continuation in nonlinear dynamics: recent advances and future challenges
arXiv:2408.00138 · doi:10.1007/s11071-024-10543-9
Abstract
Experimental continuation encompasses a set of methods that combine control and continuation to obtain the full bifurcation diagram of a nonlinear system experimentally, including responses that would be unstable in the system without feedback control. Such control-based methods thus allow the experimenter to directly and exhaustively explore the dynamics of the system without the need for a good mathematical model. The objective of this paper is twofold, namely (i) to review and present the state-of-the-art methods in a unified manner and (ii) to introduce a novel experimental derivative-free arclength continuation procedure, termed arclength control-based continuation. These methods are also demonstrated and compared on an electronic Duffing oscillator and a clamped thin plate featuring geometrical nonlinearity. Finally, the current state of the art is reflected upon, and the challenges lying ahead for this growing field are discussed.
References in corpus (26)
- The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems
- A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions
- Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds
- How to Compute Invariant Manifolds and their Reduced Dynamics in High-Dimensional Finite-Element Models
- Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures
- Experimental continuation of periodic orbits through a fold
- A Phase Resonance Approach for Modal Testing of Structures with Nonlinear Dissipation
- Systematic experimental exploration of bifurcations with non-invasive control
- Application of control-based continuation to a nonlinear structure with harmonically coupled modes
- Control-based continuation: bifurcation and stability analysis for physical experiments
- Shape Control for Experimental Continuation
- Methods of Continuation and their Implementation in the COCO Software Platform with Application to Delay Differential Equations
- How do Conservative Backbone Curves Perturb into Forced Responses? A Melnikov Function Analysis
- Numerical Continuation in Nonlinear Experiments using Local Gaussian Process Regression
- Coarse Bifurcation Diagrams via Microscopic Simulators: A State-Feedback Control-Based Approach
- Experimental assessment of polynomial nonlinear state-space and nonlinear-mode models for near-resonant vibrations
- Nonlinear damping quantification from phase-resonant tests under base excitation
- Challenging an experimental nonlinear modal analysis method with a new strongly friction-damped structure
- Fast Computation of Steady-State Response for Nonlinear Vibrations of High-Degree-of-Freedom Systems
- Robust and fast backbone tracking via phase-locked loops
- A Virtual Acoustic Black Hole on a Cantilever Beam
- Nonlinear modal testing of damped structures: Velocity feedback vs. phase resonance
- Modelling of physical systems with a Hopf bifurcation using mechanistic models and machine learning
- Fast computation and characterization of forced response surfaces via spectral submanifolds and parameter continuation
- Experimental analysis of the TRC benchmark system
- Model-free Continuation of Periodic Orbits in Certain Nonlinear Systems Using Continuous-Time Adaptive Control