In the event of seismic occurrences, structures and their components often resonate. Resonance occurs when the structure’s natural frequency coincides with the seismic activity’s frequency. For structures to be designed to withstand such occurrences, engineers perform an equivalent static analysis with forces proportional to the structure’s weight. Researchers eventually determined that the equivalent static analysis was only adequate for certain structures—mainly shorter structures with natural frequencies that have large separation margins from the seismic occurrence. Taller structures, such as long vertical service water pumps, have natural frequencies that coincide with frequencies present during seismic occurrences. Therefore, dynamic properties of the structure or system (mode shapes and natural frequencies) must be considered with the response spectrum of the structure, which then can be used to determine the resulting response in the event of a seismic occurrence. Reponses can include displacement, velocity, acceleration, force and moment.
Careful planning can save equipment from damage caused by unexpected events.
04/09/2015
Figure 1. Acceleration vs. frequency (Graphics courtesy of Sulzer)
Figure 2 (left). Mode 1: 0.93014 Hertz (Hz). Figure 3 (center). Mode 2: 7.12033 Hz. Figure 4 (right). Mode 3: 10.348 Hz
Table 1. Results from modal analysis
First, a modal analysis must be performed to obtain the first three mode shapes, participation factors, effective masses and relative displacements at the suction bell (see Table 1).
Now the mode coefficients can be calculated. The spectrum input provided was acceleration, therefore the mode coefficient can be calculated by Equation 1.
Table 2. Results from modal analysis including mode coefficients
Finally, the displacement response for the mode shapes can be determined by multiplying the mode coefficient with the relative displacement.
Table 3. Results from modal analysis including mode coefficients and displacement response
Now that the responses have been determined, an appropriate combination method must be chosen for combining the responses. The first three mode shapes account for approximately 75 percent of the total mass, which means more modes need to be analyzed to capture a more accurate response.