Affiliations: College of Marine, Northwestern Polytechnical
University, Xi'an, Shaanxi, China | School of Naval Architecture and Ocean Engineering,
Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, China
Note: [] Corresponding author: Heye Xiao, College of Marine, Northwestern
Polytechnical University, Xi'an, Shaanxi, China. Tel.: +86 138 9284 7098; Fax:
+86 029 8847 4094; E-mail: raulwavell@163.com
Abstract: The flexible beams carrying attachments often appear in engineering
structures, modal analysis of those structures is important and necessary in
structural design. This manuscript develops a proposed analytical method as a
general tool for solving the free vibration of varying cross-section beams carrying various types of
attachments with different distributions and arbitrary boundary conditions. In
current practice, the natural frequencies of beam carrying lumped and uniform
sprung mass and resting on Pasternak soil are calculated and compared with
those in references to verify the methodology firstly. Then, the natural
frequencies of beam carrying non-uniform spring-mass systems and stepped beam
on Pasternak soil are calculated by the proposed method to study free vibration
of beam carrying attachments with non-uniform cross section or distribution.
Finally, some important conclusions are derived from results, which reveal that
distribution density of spring-mass system at peaks of the mode shape makes
dominate effects on the change of the natural frequencies at that mode and the
natural frequencies of the stepped beam resting on elastic foundation are more
sensitive to the increase of soil parameters.
