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Beam-type structures with non-uniform cross sections are widely used in mechanical, architectural, and civil engineering fields. This paper deals with dynamic characteristics and vibration problems. Governing equations are first derived by using local coordinates. Their solutions are then assumed by using Galerkin's mode summation method. Bisection method is also applied in solving the determinant of the matrix which can provide natural frequencies. Whereas finite element methods adopt admissible functions satisfying only geometric boundary condition, in this study we apply Galerkin's mode summation method which uses eigen-functions satisfying both governing equations and boundary conditions. Modal analysis and experimental tests are finally performed using simply-supported beams with four different non-uniform cross-sections. Our analytical results then show good agreement with experimental ones.

Modal Analysis and Experiment of a Simply-supported Beam with Non-uniform Cross Sections