Interval natural frequency and mode shape analysis for truss structures with interval parameters

Abstract

A new method called the interval factor method (IFM) for the natural frequency and mode shape analysis of truss structures with interval parameters is presented in this paper. Using the IFM, the structural physical parameters and geometric dimensions can be considered as interval variables. The structural stiffness and mass matrices can then be, respectively, divided into the product of two parts corresponding to the interval factors and the deterministic matrix. The computational expressions for the lower and upper bound and interval change ratio of the natural frequency and mode shape are derived from Rayleigh quotient by means of the interval operations. The influences of the change of the structural parameters on the natural frequency and mode shape are demonstrated by using truss structures.