Comment on "The Eigenvalue Problem for Structural Systems with Statistical Properties"

Abstract

we have that Finally, substituting Eq. (12) into (11) and dividing by co 2 we obtain the standard equation (l/co 2 ) Xl = (13) Assuming that kn" 1 is available, the only matrix inversion required in Eq. (13) is for the product (Ti2 r miiTi 2 ) which, for three-dimensional structures, is of the order (6 X 6). This compares with two inversions in Eq. (9), one for (Ti 2 r mi 2 + m 22 ) of order (6 X 6) in R and another for (I -T 12 R) of order (n X ri), where n is the number of degrees of freedom in Xi. It follows therefore that, in general, if the introduction of a few massless node points in the structure is an acceptable idealization so that m 22 = 0 and mi 2 = 0 (zero inertia in the direction of x 2 ) then it would be preferable to compute the nonzero frequencies of a free-free system from Eq. (13).

A Normalized Modal Eigenvalue Approach for Resolving Modal Interaction

“…1968) shows that the changes In natural frequencies and modes are small if the variation is small. The statistical behavior of the frequencies and modes of systems with well separated natural frequencies have been extensively studied, for example, by Collins and Thomson (1969) and Kiefling (1970). However, it is not unusual for a two-or three-dimensional structure to have closely spaced natural frequencies.…”