Abstract
The authors relate the proper orthogonal modes, as applied in discrete vibration systems, to normal modes of vibration in systems with a known mass matrix. In the case of undamped free vibration, the proper orthogonal modes converge to the linear normal modes as the amount of data increases. This interpretation is also practical for lightly modally damped systems. Forced resonances lead to proper orthogonal modes which approximate vibration modes. A particular case of non-linear normal modes are looked at in which the motion of a single mode follows a curve in the co-ordinate space. In this case, the proper orthogonal modes represent the principal axes of inertia formed by the distribution of data on the modal co-ordinate curve. More generally, the proper orthogonal modes represent the principal axes of inertia of the data.
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