Vibration Analysis of Exponential Cross-Section Beam Using Galerkin’s Method
Khosak Achawakorn, Thira Jearsiripongkul

Abstract
An approximation method is introduced to analyze the problem of uniform and non-uniform beam. Using the differential equation of motion based on the Euler-Bernoulli thin beam equation. The natural frequencies of the beams can be approximate by the Eigen-value of general form of normal mode characteristic function. The Analytical method gives the approximate solution, but need a lot of effort on calculation. The Finite Element Methods is also convenience and popular. This paper studies the vibration analysis in the uniform and exponential cross section beam using the Galerkin’s method. The natural frequencies of the beam are determined and, the analysis results are compared to the result from FEM.

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