• Home
  • About
  • Featured Articles
  • Editorial Team
  • Announcements
  • Home
  • About
  • Featured Articles
  • Editorial Team
  • Announcements
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
  • Home
  • About
  • Featured Articles
  • Editorial Team
  • Announcements

Featured Articles

    Archives

    September 2023
    July 2023
    May 2023
    March 2023
    February 2023
    September 2022
    August 2022
    April 2022
    March 2022
    December 2021
    October 2021
    September 2021

    Categories

    All
    Actuators
    Approximation
    Artificial Neural Networks
    Bifurcation
    Boundary Conditions
    Boundary-value Problems
    Cables
    Contact
    Continuation Methods
    Control
    Co-simulation
    Co-simulation Interface
    Damping
    Delays
    Density
    Displacement
    Dynamic Models
    Dynamics
    Dynamic Systems
    Eigenvalues
    Error Estimator
    Errors
    Exact Mode Shapes
    Exoskeleton Devices
    Friction
    Fuzzy Logic
    Galerkin Method
    Geometry
    Heat
    Heat Transfer
    Homoclinic Orbits
    Kinematics
    Limit Cycles
    Loaded Beam
    Machine Learning
    Manifolds
    Manipulators
    Midplane Stretching
    Multibody Dynamics
    Multibody Systems
    Multiphysics
    Multirate
    Noise
    Nonlinear Dynamical Systems
    Nonlinear Frequency
    Nonlinear Vibration
    Nonlinear Vibration Absorber
    NVA
    Origami
    Parallelization
    Parametrization
    Perturbation Methods
    Probability
    Prostheses
    Railroad Dynamics
    Real-time Dynamics Simulation
    Reinforcement Learning
    Resonance
    Robots
    Ships
    Simulation
    Solver Coupling
    Space
    Stability
    Time Delay Systems
    Topology
    Variable Macro-step Size
    Vehicular Dynamics
    Vibration
    Waves

    RSS Feed

Back to Blog

Floquet Theory for Linear Time-Periodic Delay Differential Equations Using Orthonormal History Functions

7/25/2023

 
Junaidvali Shaik, Sankalp Tiwari, and C. P. Vyasarayani
J. Comput. Nonlinear Dynam. Sep 2023, 18(9): 091005, https://doi.org/10.1115/1.4062633​
Delayed systems are those in which the present dynamics is governed by what happened in the past. They are encountered in manufacturing, biology, population dynamics, control systems, etc. Determining linear stability of such systems is an important and difficult problem. In this work, we propose a new method to determine stability of time-periodic delay differential equations (DDEs). In the usual approaches, the DDE is converted into an approximate system of time-periodic ordinary differential equations (ODEs). Later, standard ODE techniques are employed. In this paper, we develop a method that is more direct and general. Our approach is analogous to the well-known Floquet theory for ODEs: we consider one polynomial basis function at a time as the input function and stack the coefficients of the corresponding DDE solutions to construct a matrix whose largest magnitude eigenvalue determines linear stability. We demonstrate the correctness, efficacy and convergence of our method by studying several candidate DDEs with time-periodic parameters and/or delays, and comparing the results with those obtained from other standard methods. Our approach has the following additional advantages: (a) it is parallelizable, (b) it converges quickly, and (c) it requires knowledge of only elementary linear algebra and numerical computation of DDE solutions. ​
Picture
Full article
0 Comments
Read More
Picture
JOURNAL OF COMPUTATIONAL and
​NONLINEAR DYNAMICS
COMPANION

QUICK LINKS

Submit Paper
Author Resources
Digital Collection
Indexing Information
Order Journal
Announcements and Call for Papers
Copyright © 2021 Journal of Computational and Nonlinear Dynamics