The relatively efficient and accurate Adomian modified decomposition method (AMDM) is used in this paper to investigate the free vibrations of Euler-Bernoulli beams, with a single section discontinuity present, and resting on a two-parameter elastic foundation. The discontinuity can stem from a geometric change in the beam cross-section, a sudden material change within the beam or a sudden change in foundation material properties. The proposed AMDM is used to analyze the vibration of beams using a recursive approach. The solution is obtained by solving a set of algebraic equations with only three unknown parameters, and the method can easily be extended to obtain approximate solutions to vibration problems for any type of non-uniform beam. This work develops a fast and accurate method of calculation, with the ability to change boundary conditions easily. Analytical calculations are presented for natural frequencies and associated mode shapes, which are compared with experimental and calculated results found by experimental and other calculation methods reported in the literature.
Associate Professor, Rose-Hulman Institute of Technology
Professional interests include undergraduate engineering education, finite element modeling, ground-borne vibrations, vibrations of musical instruments, and dynamics of toys.
