Parameter-splitting perturbation method for the improved solutions to strongly nonlinear systems

DOI10.1007/s11071-019-04887-wzbMath1437.70033OpenAlexW2923231185MaRDI QIDQ783614

Vai Pan Iu, Hai-En Du, Guo-Kang Er

Publication date: 4 August 2020

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-019-04887-w

zbMATH Keywords

nonlinear oscillatorstrong nonlinearitymultiple-scales methodoptimum solutionparameter splitting

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Multiple scale methods for ordinary differential equations (34E13)

Related Items

Constrained Parameter-Splitting Multiple-Scales Method for the Primary/Sub-Harmonic Resonance of a Cantilever-Type Vibration Energy Harvester

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A study on the convergence of homotopy analysis method
• Notes on the homotopy analysis method: some definitions and theorems
• Newton-harmonic balancing approach for accurate solutions to nonlinear cubic-quintic duffing oscillators
• A new perturbation procedure for limit cycle analysis in three-dimensional nonlinear autonomous dynamical systems
• Analytical approximation to large-amplitude oscillation of a non-linear conservative system
• A new perturbation algorithm with better convergence properties: multiple scales Lindstedt Poincaré method
• On the multi-scale analysis of strongly nonlinear forced oscillators
• A review of the decomposition method in applied mathematics
• Investigating a hybrid perturbation-Galerkin technique using computer algebra
• A modified Lindstedt-Poincaré method for certain strongly non-linear oscillators
• The decomposition method for forward and backward time-dependent problems
• A new analytical approach to the Duffing-harmonic oscillator
• Analysis of internal resonance in a two-degree-of-freedom nonlinear dynamical system
• A new analytic solution for buckling of doubly clamped nano-actuators with integro differential governing equation using Duan-Rach Adomian decomposition method
• Application of modified Adomian decomposition method to pull-in instability of nano-switches using nonlocal Timoshenko beam theory
• Nonlinear coupling of transverse modes of a fixed-fixed microbeam under direct and parametric excitation
• Nonlinear vibrations of FGM rectangular plates in thermal environments
• Methods of nonlinear analysis. Vol. 1
• Numerical continuation methods for dynamical systems. Path following and boundary value problems.
• Nonlinear Ordinary Differential Equations
• Comparison of two Lindstedt–Poincaré-type perturbation methods
• Linear and Nonlinear Structural Mechanics
• A Perturbation Method for Treating Nonlinear Oscillation Problems
• A Hybrid Perturbation-Galerkin Technique That Combines Multiple Expansions