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Shock and Vibration
Volume 14 (2007), Issue 4, Pages 271-282

Estimation of Dynamic Characteristics of a Spring-Mass-Beam System

Ding Zhou1,2 and Tianjian Ji2

1College of Civil Engineering, Nanjing University of Technology, Nanjing 210009, China
2School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester, UK

Received 22 June 2007; Revised 22 June 2007

Copyright © 2007 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents an approximate solution for the analysis of the dynamic characteristics of a spring-mass-beam system. The spring-mass can be distributed or concentrated on a beam, which can represent a crowd or an individual on a beam. The analysis is based on the fact that a spring-mass-beam system can be modeled approximately as a series of two degree-of-freedom (TDOF) systems and the frequency coupling occurs mainly at the first TDOF system. The Galerkin method is used to derive the frequency equation of the TDOF system. Static beam functions of a beam with distributed and concentrated spring-masses are developed for the solutions, in which the effect of the magnitude and position of the mass of the spring-mass on the beam is considered. Using a set of simple formulae, the first pair of coupled frequencies and the corresponding mode can be obtained. The mass and stiffness factors in the TDOF system are tabled for engineering applications. For verification and use of the proposed method, a case of human-structure interaction is analysed using the proposed method and FE method. Parametric studies show that using the proposed functions, not only the first pair of natural frequencies but also the mode and internal forces of the coupled system can be obtained with high accuracy.