A method for determining the number of dominant modes in sinusoidal structural response

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Virginia Polytechnic Institute and State University


Modal analysis is a tool widely used to describe mathematically the vibratory behavior of structures. In modal analysis, the response of a structure at a given frequency of excitation is represented as the summation of the contributions of a 11 the modes of vibration. Although continuous structures have an infinite number of modes, only a few of them are present to a significant degree in the response at any frequency of excitation. These modes are the dominant modes at the given frequency.

A vector fit method was developed to determine the number of dominant modes. This method uses only the transfer function matrix (or some part of it) as input, and it approximates each column vector of the matrix as a linear sum, using as a basis a set of orthogonal unit vectors. The errors resulting from these approximations, defined in a least squares sense, are the plotted versus frequency. The relative magnitudes of the error curves indicate the number of dominant modes in the frequency band in question.

The method was tested numerically on three models with known modal parameters. These models were designed to have regions of high modal density.

It was found that interpretation of the error curves required a certain amount of qualitative judgement based upon criteria other than simply the relative error magnitudes. With these criteria. identified, it was concluded that the vector fit method reliably predicts the correct number of dominant modes provided only that a sufficiently large transfer function matrix is: employed. Specifically, both the number of rows and the number of columns must be greater than the number of dominant mopes.