Analytical analysis of free vibration of non-uniform and non-homogenous beams: Asymptotic perturbation approach
Applied Mathematical Modelling(2019)
Abstract
•Perturbation method is proposed to solve differential equation with variable coefficients.•Analytical formula is derived for frequencies of non-uniform and non-homogeneity beams.•Laminated beam and axially functional graded beam are analyzed.•Different boundary conditions are considered.•Solution is validated by the FEM and the published references.
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Key words
Asymptotic perturbation approach,Free vibration,Non-uniform and non-homogenous beams,Natural frequencies
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