A real-time Lie-group differential algebraic equations method to solve the inverse nonlinear vibration problems

DOI10.1080/17415977.2015.1130043zbMath1348.65134OpenAlexW2502308433WikidataQ115295098 ScholiaQ115295098MaRDI QIDQ2831871

Chih-Wen Chang, Chein-Shan Liu

Publication date: 3 November 2016

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2015.1130043

zbMATH Keywords

Duffing nonlinear oscillatornonlinear inverse vibration problemDuffing-van der Pol nonlinear oscillatorLie-group differential algebraic equations (LGDAE) methodreal-time recovery of external force

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Inverse problems for PDEs (35R30) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical methods for differential-algebraic equations (65L80) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)

Related Items (4)

The recovery of external force in nonlinear system by using a weak-form integral method ⋮ Closed-form higher-order numerical differentiators for differentiating noisy signals ⋮ A high-order Lie groups scheme for solving the recovery of external force in nonlinear system ⋮ A fictitious time Lie-group integrator for the Brinkman-Forchheimer momentum equation modeling flow of fully developed forced convection

Cites Work

• An iterative \(GL(n,\mathbb{R})\) method for solving non-linear inverse vibration problems
• Cone of non-linear dynamical system and group preserving schemes
• Inverse eigenvalue problems for damped vibrating systems
• A generalized inverse force vibration problem for simultaneously estimating the time-dependent external forces
• A non-linear inverse vibration problem of estimating the time-dependent stiffness coefficients by conjugate gradient method
• Solution of the Duffing–van der Pol oscillator equation by a differential transform method
• A Symmetric Inverse Vibration Problem for Nonproportional Underdamped Systems
• Adaptive weighting inverse method for the estimation of input loads
• Comment on ‘Solution of the Duffing–van der Pol oscillator equation by a differential transform method’
• Iteration method for equation of viscoelastic motion with fractional differential operator of damping

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