An innovative eigenvalue problem solver for free vibration of Euler-Bernoulli beam by using the adomian decomposition method

DOI10.1016/j.camwa.2008.07.029zbMath1165.74352OpenAlexW1987515535MaRDI QIDQ2389441

Yanyan Li

Publication date: 16 July 2009

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2008.07.029

zbMATH Keywords

mode shapenatural frequencyfree vibrationuniform Euler-Bernoulli beamadomian decomposition method

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Vibrations in dynamical problems in solid mechanics (74H45) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (9)

Thermal vibration of nonhomogeneous Euler nanobeam resting on Winkler foundation ⋮ Free vibration analysis of stepped beams by using Adomian decomposition method ⋮ Modified decomposition method applied to laminated thick plates in nonlinear bending ⋮ Free vibration analysis of multiple-stepped beams by using Adomian decomposition method ⋮ The use of He's variational iteration method for obtaining the free vibration of an Euler-Bernoulli beam ⋮ Free vibration analysis of a type of tapered beams by using Adomian decomposition method ⋮ A general Fourier formulation for vibration analysis of functionally graded sandwich beams with arbitrary boundary condition and resting on elastic foundations ⋮ Simulation of tapered rotating beams with centrifugal stiffening using the Adomian decomposition method ⋮ Vibration analysis of a uniform pre-twisted rotating Euler–Bernoulli beam using the modified Adomian decomposition method

Cites Work

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• On the convergence of Adomian decomposition method
• A reliable modification of Adomian decomposition method
• Solving frontier problems of physics: the decomposition method
• A new algorithm for calculating Adomian polynomials for nonlinear operators
• The modified decomposition method and Padé approximants for solving the Thomas-Fermi equation
• A new modification of the Adomian decomposition method for linear and nonlinear operators
• Applications of dual MRM for determining the natural frequencies and natural modes of an Euler-Bernoulli beam using the singular value decomposition method
• Transverse vibration of an uniform Euler–Bernoulli beam under linearly varying axial force
• A Note on the Vibrations of Generally Restrained, End-Loaded Beams

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