The variability of the natural frequencies and mode shapes of uncertain structures
Abstract
For analysis purposes, structures are usually assumed to have well-defined properties. Recently, structures with continuous random variation of structural properties are receiving considerable interest. The variability of the response due to the variability of the structural properties is of concern. Engineers and researchers have turned to probabilistic analysis for statistical properties of the response. This study deals with the statistical properties of natural frequencies and mode shapes in structures. The dynamic characteristics vary within a certain confidence interval because of the variability of the material properties of a structure. This confidence interval is applicable to the design for dynamic excitations. Monte Carlo Simulation (MCS) is a reliable method to compute the response statistics. However, it is computationally demanding since a large number of samples must be generated for good results. Alternatively, the perturbation method can be used efficiently for the same purpose if the coefficient of variation of the material properties is small. An efficient formulation is proposed here to evaluate the mean and variance of the eigensolutions of a system with spatially-varying stiffness properties. The formulation is applied to the finite element models of frame and plate structures in which the modulus of elasticity is simulated by a random process rather than by a set of independent random variables. Results calculated by the perturbation method are verified by MCS. The frequency polygons based on MCS solutions are compared with assumed Gaussian probability density functions in which the mean and variance are calculated by the perturbation method. A modified vector iteration method is used in MCS to improve the efficiency. Simple eigenvalue problems and the repeated eigenvalue problems are solved by different formulations. For close eigenvalue problems, choosing the appropriate formulation is critical. The process of choosing the correct formulation is also studied.
Degree
Ph.D.
Advisors
Jeong, Purdue University.
Subject Area
Civil engineering|Mechanics
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