Natural Frequencies of Beams with Step Change in Cross-Section

J. Ocean Eng. Technol. 2004;18(2):46-51.

Kim Yong-Cheul,Nam Alexander-V.

School of Mechanical Engineering Yeungnam University,School of Mechanical Engineering Yeungnam University

Keywords: Natural Frequencies, Asymptotic Closed Form Solution, WKB method, Variable Properties, Step Change in Cross-Section

Abstract

Natural frequencies of the transverse vibration of beams with step change in cross-section are obtained by using the asymptotic closed form solution. This closed form solution is found by using WKB method under the assumption of slowly varying properties, such as mass, cross-section, tension etc., along the beam length. However, this solution is found to be still very accurate even in the case of large variation in cross-section and tension. Therefore, this result can be easily applied to many engineering problems.