The use of He's variational iteration method for obtaining the free vibration of an Euler-Bernoulli beam

DOI10.1016/j.mcm.2009.09.005zbMath1185.74031OpenAlexW2070165579MaRDI QIDQ970064

Chandra S. Gurram, Yu-Cheng Liu

Publication date: 8 May 2010

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2009.09.005

zbMATH Keywords

mode shapeEuler-Bernoulli beamnatural frequencyfree vibrationHe's variational iteration method

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items

Sextic B-spline collocation method for solving Euler-Bernoulli beam models ⋮ Modeling and analysis of forced vibrations in transversely isotropic thermoelastic thin beams ⋮ Compatibility of interval fuzzy preference relations with the COWA operator and its application to group decision making ⋮ Numerical investigation of dynamic Euler-Bernoulli equation via 3-Scale Haar wavelet collocation method ⋮ Vibration analysis of conveying fluid pipe via He's variational iteration method ⋮ Application of variational iteration method to free vibration analysis of a tapered beam mounted on two-degree of freedom subsystems ⋮ Free vibration and stability analysis of a multi-span pipe conveying fluid using exact and variational iteration methods combined with transfer matrix method

Uses Software

• Matlab

Cites Work

• Application of He's variational iteration method to nonlinear heat transfer equations
• Vibration and stability of an Euler--Bernoulli beam with up to three-step changes in cross-section and in axial force
• Solution of problems in calculus of variations via He's variational iteration method
• The application of He's variational iteration method to nonlinear equations arising in heat transfer
• Variational iteration method for solving integro-differential equations
• He's variational iteration method for solving a semi-linear inverse parabolic equation
• Variational iteration method -- a kind of non-linear analytical technique: Some examples
• Applying He's variational iteration method for solving differential-difference equation
• Variational iteration method -- some recent results and new interpretations
• Application of He's variational iteration method to nonlinear Jaulent-Miodek equations and comparing it with ADM
• An approximation solution of a nonlinear equation with Riemann-Liouville's fractional derivatives by He's variational iteration method
• A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials
• Variational iteration method for delay differential equations
• Vibration of an Euler--Bernoulli beam on elastic end supports and with up to three step changes in cross-section.
• Applications of dual MRM for determining the natural frequencies and natural modes of an Euler-Bernoulli beam using the singular value decomposition method
• An innovative eigenvalue problem solver for free vibration of Euler-Bernoulli beam by using the adomian decomposition method
• Application of He's variational iteration method for solving the Cauchy reaction-diffusion problem
• Transverse vibration of an uniform Euler–Bernoulli beam under linearly varying axial force
• A fully Sinc-Galerkin method for Euler-Bernoulli beam models
• The use of He's variational iteration method for solving a Fokker–Planck equation
• Variational iteration method for autonomous ordinary differential systems