Spectral Representation of Uncertainty in Experimental Vibration Modal Data

Abstract

It is well known that structures exhibit uncertainty due to various sources, such as manufacturing tolerances and variations in physical properties of individual components. Modeling and accurate representation of these uncertainties are desirable in many practical applications. In this paper, spectral-based method is employed to represent uncertainty in the natural frequencies of fiber-reinforced composite plates. For that, experimental modal analysis using noncontact method employing Laser-Vibrometer is conducted on 100 samples of plates having identical nominal topology. The random frequencies then are represented employing generalized Polynomial Chaos (gPC) expansions having unknown deterministic coefficients. This provides us with major advantage to approximate the random experimental data using closed form functions combining deterministic coefficients and random orthogonal basis. Knowing the orthogonal basis, the statistical moments of the data are used to estimate the unknown coefficients.

Stochastic Non-Parametric Identification in Composite Structures Using Experimental Modal Data

“…The PDFs of the measured eigen frequencies and corresponding stochastic representations are shown in Figure 1. Third order gPC expansion, employing one dimensional Hermite polynomial H i , is used to construct the experimental eigen frequencies [18] as…”

“…The standard deviation of the elastic parameters are also calculated in Table 2 referring Eq. (18). The PDFs of the uncertain elastic parameters are constructed using gPC expansion and are presented in Figure 3.…”