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

Abstract

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.

On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper System

“…Numerous authors have studied the free and/or forced response of beams carrying in-span mass or spring-mass systems. In most investigations on the free vibration, different authors have used analytical methods to determine the exact solutions for the natural frequencies and mode shapes (e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13] and references mentioned therein).…”

Natural characteristics for transverse vibration of Euler Bernoulli beams with variable end constraints

“…For the last decades. many scholars have extended the scope of this type of research for considering specific cases, cantilever beam [19], clamped-free beam [20], buckled beam [21] varying cross-section beams [22] and uniform multi-span beam [23] have been discovered. This system is mainly regarded as the solution to obtain the effect of the new substructure on the dynamic characteristics of the beam system.…”