Floor Spectra with Equipment‐Structure‐Equipment Interaction Effects

Abstract

In the current practice of seismic design of secondary systems, the interaction between the supporting structure and the secondary systems is often ignored, the interaction between any two secondary systems through their supporting structure is rarely considered. This paper examines the latter type of interaction between simple pieces of equipment. This is done by evaluating the effect on the floor response spectra, representing the response of an oscillator with varying frequency due to an addition of a second oscillator. To include the interaction effect, the modal properties of a composite system consisting of the primary structure and two oscillators are obtained and used in calculating the floor spectra. The frequencies are calculated by solving a characteristic equation, the expression of which is defined in terms of the parameters of the oscillators and the eigenproperties of the supporting structure. A method is presented to solve this characteristic equation by a simple Newton‐Raphson scheme. The mode shape for a calculated frequency is defined by a closed‐form expression. A parametric study is conducted to ascertain the interaction effect. This interaction between the two pieces of equipment can be significant if the second piece of equipment is tuned to a dominant mode of the supporting structure. The effect also depends upon the mass of the second piece of equipment as well as its location with respect to the first piece of equipment.