Related papers: Nonlinear model identification and spectral subman…
Spectral submanifolds (SSMs) have recently been shown to provide exact and unique reduced-order models for nonlinear unforced mechanical vibrations. Here we extend these results to periodically or quasiperiodically forced mechanical…
While data-driven model reduction techniques are well-established for linearizable mechanical systems, general approaches to reducing non-linearizable systems with multiple coexisting steady states have been unavailable. In this paper, we…
A primary spectral submanifold (SSM) is the unique smoothest nonlinear continuation of a nonresonant spectral subspace $E$ of a dynamical system linearized at a fixed point. Passing from the full nonlinear dynamics to the flow on an…
We propose a unified approach to nonlinear modal analysis in dissipative oscillatory systems. This approach eliminates conflicting definitions, covers both autonomous and time-dependent systems, and provides exact mathematical existence,…
We use invariant manifold results on Banach spaces to conclude the existence of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces of…
We discuss an automated computational methodology for computing two-dimensional spectral submanifolds (SSMs) in autonomous nonlinear mechanical systems of arbitrary degrees of freedom. In our algorithm, SSMs, the smoothest nonlinear…
We develop a model reduction technique for non-smooth dynamical systems using spectral submanifolds. Specifically, we construct low-dimensional, sparse, nonlinear and non-smooth models on unions of slow and attracting spectral submanifolds…
Model reduction of large nonlinear systems often involves the projection of the governing equations onto linear subspaces spanned by carefully-selected modes. The criteria to select the modes relevant for reduction are usually…
We use the recent theory of Spectral Submanifolds (SSM) for model reduction of nonlinear mechanical systems subject to parametric excitations. Specifically, we develop expressions for higher-order nonautonomous terms in the parameterization…
Dynamical systems are often subject to algebraic constraints in conjunction to their governing ordinary differential equations. In particular, multibody systems are commonly subject to configuration constraints that define kinematic…
Time-delay dynamical systems inherently embody infinite-dimensional dynamics, thereby amplifying their complexity. This aspect is especially notable in nonlinear dynamical systems, which frequently defy analytical solutions and necessitate…
Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…
We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate a low-dimensional, attracting slow SSM and compute a…
Spectral subspaces of a linear dynamical system identify a large class of invariant structures that highlight/isolate the dynamics associated to select subsets of the spectrum. The corresponding notion for nonlinear systems is that of…
Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element methods. The complexity of these systems present…
The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear mechanical systems. A direct computation of SSMs requires…
Large amplitude vibrations can cause hazards and failure to engineering structures. Active control has been an effective strategy to suppress vibrations, but it faces great challenges in the real-time control of nonlinear flexible…
Spectral submanifolds (SSMs) have emerged as accurate and predictive model reduction tools for dynamical systems defined either by equations or data sets. While finite-elements (FE) models belong to the equation-based class of problems,…
Rotating structures are widely observed in engineering applications such as turbomachinary and wind turbine. These rotating structures, particularly for blades made by lightweight materials, can undergo large deformation in operations and…
The dynamics in a primary Spectral Submanifold (SSM) constructed over the slowest modes of a dynamical system provide an ideal reduced-order model for nearby trajectories. Modeling the dynamics of trajectories further away from the primary…