Accuracy improvement of the method of multiple scales for nonlinear vibration analyses of continuous systems with quadratic and cubic nonlinearities

DOI10.1155/2010/890813zbMath1285.74015OpenAlexW1998853591WikidataQ58653397 ScholiaQ58653397MaRDI QIDQ624735

Akira Abe

Publication date: 9 February 2011

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2010/890813

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Finite difference methods applied to problems in solid mechanics (74S20)

Cites Work

• Unnamed Item
• Unnamed Item
• On methods for continuous systems with quadratic, cubic and quartic nonlinearities
• Resonant non-linear normal modes. I: Analytical treatment for structural one-dimensional systems
• Validity and accuracy of solutions for nonlinear vibration analyses of suspended cables with one-to-one internal resonance
• On non-linear vibration analyses of continuous systems with quadratic and cubic non-linearities
• Two-to-one internal resonance in microscanners
• Reduced-order models of weakly nonlinear spatially continuous systems
• On mode interactions for a weakly nonlinear beam equation
• Experimental validation of reduction methods for nonlinear vibrations of distributed-parameter systems: Analysis of a buckled beam
• A comparison of two perturbation methods for vibrations of systems with quadratic and cubic nonlinearities
• On the discretization of distributed-parameter systems with quadratic and cubic nonlinearities
• Two-mode response of simply supported, rectangular laminated plates
• Multiple resonances in suspended cables: direct versus reduced-order models
• On a Galerkin-averaging method for weakly non-linear wave equations
• The Galerkin-averaging method for nonlinear, undamped continuous systems
• An Asymptotic Theory for a Class of Initial-Boundary Value Problems for Weakly Nonlinear Wave Equations with an Application to a Model of the Galloping Oscillations of Overhead Transmission Lines
• Asymptotics for a class of semilinear hyperbolic equations with an application to a problem with a quadratic nonlinearity
• Asymptotic solutions of nonlinear wave equations using the methods of averaging and two-timing
• Bifurcation and Chaos in Externally Excited Circular Cylindrical Shells
• Comparison of direct-perturbation methods with discretization-perturbation methods for non-linear vibrations
• Multimode Interactions in Suspended Cables
• An Asymptotic Theory for a Weakly Nonlinear Beam Equation with a Quadratic Perturbation
• Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis
• DIRECT TREATMENT AND DISCRETIZATIONS OF NON-LINEAR SPATIALLY CONTINUOUS SYSTEMS
• Asymptotic Solutions of Initial Value Problems for Nonlinear Partial Differential Equations
• Asymptotic Solutions of Inhomogeneous Initial Boundary Value Problems for Weakly Nonlinear Partial Differential Equations
• A Perturbation Method for Hyperbolic Equations with Small Nonlinearities

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