Dynamic Analysis of Light Equipment in Structures: Modal Properties of the Combined System

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Abstract
Perturbation methods are employed to determine the dynamic properties of a combined system composed of a multi‐degree‐of‐freedom structure to which is attached a light, less single‐degree‐of‐freedom equipment item. Closed‐form expressions are derived for the natural frequencies, mode shapes, modal dampings, and other modal properties of the combined system in terms of the dynamic properties of the structure alone, and the equipment alone. The effect of tuning and equipment‐structure interaction are included in this analysis. The derived properties can be used in conjunction with a mode‐super‐position procedure to determine the response of the equipment to any excitation of the combined system. For an example structure, the natural frequencies and mode shapes based on the method developed agree well with exact results.

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