Modal analysis of structures with uncertain-but-bounded parameters via interval analysis

Abstract

In this paper, the modal interval analysis method to estimate modal parameters, frequency response function (FRF), and mode shapes of structures with uncertain-but-bounded is presented. Although the system parameters or properties are uncertain in many engineering problems, but their probable range of values i.e. upper and lower bounds, can be provided from practical experience and engineering knowledge. Moreover, to avoid the resonance of a structure and to consider the dynamic response of an uncertain one, and also for reliability and stability analysis, we often need the bounds of the ranges of structural characteristic parameters such as natural frequency and normal mode. By using modal analysis and interval calculus, we investigate the method of computing upper and lower bounds of paramenters such as, natural frequencies, modal shapes, and FRFs. Theoretically, it is possible to analyze the uncertain-but-bounded of a structure by using modal analysis and interval calculus. They can be estimated by modal interval analysis. On the basis of the estimated intervals, the engineering structure parameters can be applied into engineering design. A numerical example is presented for a tower structure, and the results illustrate that the proposed method is effective. A comparison of the modal interval method with the results of Monte Carlo simulation serves to validate the solutions and to identify the bounded ranges of parameters.