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Statistical Analysis of the Modal Properties of Large Structural Systems
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English
Abstract
A theory is developed to predict eigenvalue and eigenvector uncertainty in large dynamic models. The uncertainty is based on physical property uncertainty and should not be confused with numerical roundoff, although the method can be extended to include the latter. The theory, when implemented on a computer, is used to analyze the uncertainties in frequencies and mode shapes based on uncertainties in mass, stiffness, modulus of elasticity, etc.
The method incorporates a linear statistical model which is quite adequate for handling property uncertainties of 10% or more. The model is not limited to small systems but uses certain statistical assumptions as well as selective matrix manipulations to keep the size of all matrix operations to within the number of degrees of freedom of the system.
Examples are given for two longitudinal vibration problems, and the results are supported by a Monte Carlo analysis.
Authors
Citation
Collins, J., Hart, G., and Kennedy, B., "Statistical Analysis of the Modal Properties of Large Structural Systems," SAE Technical Paper 710785, 1971, https://doi.org/10.4271/710785.Also In
References
- Collins J. D. Thomson W. T. “The Eigenvalue Problem for Structural Systems with Statistical Properties.” AIAA Journal 7 4 April 1969 642 648
- Hart G. C. Collins J. D. “The Treatment of Randomness in Finite Element Modeling.” SAE Transactions 79 1970 paper 700842
- Kiefling L. “Comment on ‘The Eigenvalue Problem for Structural Systems with Statistical Properties’.” AIAA Journal 7 July 1970