The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

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.