Affiliations: College of Civil Engineering, Nanjing University of
Technology, Nanjing 210009, P.R. China | School of Mechanical, Aerospace and Civil Engineering,
The University of Manchester, Manchester, UK
Abstract: 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.
