The “Spectrum Dip”: Dynamic Interaction of System Components

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In the early 1960s, many full sized surface combatants, submarines and structural models were tested with underwater explosive in order to evaluate the shock load to the ship and internal equipment and structures. Initially, shock spectra were calculated from base motion measurements of internal equipment and components. Attempts were made to envelop these spectra to develop shock design spectra inputs. At that time, earthquake engineers were using this enveloping method to develop design procedures from ground motion measurements to protect structures from earthquakes. However, for the measurements on ships, this procedure resulted in calculated loads that would have caused catastrophic failure of the equipment; yet the equipment had not failed on the ship tests. As a result, the data was reanalyzed over a period of over a year. It was concluded that the dynamic interaction of each component or structure reduced the measured spectral motion at the fixed-base frequencies of the structure by about an order of magnitude. In many cases, there was a dip in the shock spectra at the fixed-base frequencies: the “spectrum dip” phenomenon. This reanalysis led to shock spectra design curves for navy ships. This paper will present a review of an experimental study and an analytical model to explain the effect of dynamic interaction on the shock or response spectrum. In addition, a practical example of interaction of four single mass dynamic systems mounted on a realistic deck and subjected to a high impact shock input was studied by the authors.