Tracking amplitude extrema of nonlinear frequency responses using the harmonic balance method

DOI10.1002/nme.7376OpenAlexW4387703479MaRDI QIDQ6148523

Ghislain Raze, Unnamed Author, Gaëtan Kerschen

Publication date: 7 February 2024

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nme.7376

zbMATH Keywords

companion matrixharmonic balancebordered systemalternating frequency-timeamplitude resonanceextremum tracking

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Numerical differentiation (65D25)

Cites Work

• Unnamed Item
• Computing the zeros, maxima and inflection points of Chebyshev, Legendre and Fourier series: solving transcendental equations by spectral interpolation and polynomial rootfinding
• A fast algorithm to compute the \(H_{\infty}\)-norm of a transfer function matrix
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• RWPKV: A software package for continuation and bifurcation problems in two-point boundary value problems
• Vibration prediction of bladed disks coupled by friction joints
• The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems
• Practical bifurcation and stability analysis
• Structural optimization for nonlinear dynamic response
• Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming
• Efficient MATLAB Computations with Sparse and Factored Tensors
• A Collocation Solver for Mixed Order Systems of Boundary Value Problems
• An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS
• A fully passive nonlinear piezoelectric vibration absorber
• Numerical Methods for Bifurcations of Dynamical Equilibria
• How do conservative backbone curves perturb into forced responses? A Melnikov function analysis
• Harmonic Balance for Nonlinear Vibration Problems
• MATCONT