1. Random eigenvalue problems in structural dynamics: experimental investigations
- Author
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Adhikari, S. and Phani, A. Srikantha
- Subjects
Aerospace engineering -- Methods ,Monte Carlo method -- Usage ,Aerospace and defense industries ,Business - Abstract
This paper presents two experimental investigations of uncertainty in natural frequencies of linear structures estimated from measured frequency response function under dynamic loading. Experiments were conducted on 100 nominally identical realizations of two structures: a fixed--fixed beam and a thin plate with one edge fixed and the remaining three edges free. In the first set of experiments, on a fixed-fixed beam, 12 identical masses were placed at random spatial locations (generated by a computer) along the length of the beam. Each random arrangement of the masses constitutes one realization, and 100 such realizations were individually subjected to impulse loading to obtain frequency response functions. The total random mass is about 2% of the total mass of the beam. In the second set of experiments, 10 spring-mass oscillator units were attached to the cantilevered plate at random spatial locations determined from a computer-generated random matrix. Although the beam experiments represent parametric uncertainty in the mass matrix, the plate experiment pertain to unmodeled dynamics, which in turn results in randomness in both the mass and stiffness matrices. The results obtained from these experiments may be useful for the validation of many random eigenvalue analysis and prediction methods currently available to structural dynamicist. This paper is limited to comparisons with Monte Carlo simulation of deterministic finite elements models of the two structures. It is concluded that the method of estimation of natural frequencies from frequency response functions and the spatial location of the measurements has significant influence upon the first two moments (mean and standard deviation) of the natural frequency ensemble. Furthermore, although the Monte Carlo simulation estimates of the mean and standard deviation are in reasonable agreement with experiments at higher frequencies, the probability density function differ appreciably, within the limits of the sample size investigated in this study. DOI: 10.2514/1.44668
- Published
- 2010