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The “Spectrum Dip”: Dynamic Interaction of System Components

[+] Author and Article Information
Rudolph J. Scavuzzo

Professor of Mechanical Engineering Emeritus
The University of Akron,
Akron, OH 44325-3904

George D. (Jerry) Hill, Peter Saxe

Alion Science and Technology,
4300 King Street,
Arlington, VA 22302

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received February 12, 2014; final manuscript received September 29, 2014; published online February 20, 2015. Assoc. Editor: Spyros A. Karamanos. The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

J. Pressure Vessel Technol 137(4), 044701 (Aug 01, 2015) (7 pages) Paper No: PVT-14-1023; doi: 10.1115/1.4028748 History: Received February 12, 2014; Revised September 29, 2014; Online February 20, 2015

In the early 1960s, many full sized surface combatants, submarines and structural models were tested with underwater explosions in order to evaluate the shock load to the ship and internal equipment 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 were re-analyzed 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 re-analysis led to shock spectra design curves for navy ships. This paper presents a review of an experimental study and analytical demonstration 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 and some of the results of that study are included.

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References

Figures

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Fig. 1

Isometric drawing of test apparatus mounted on the MWSM [1,2]

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Fig. 2

Test apparatus mounted on the MWSM showing the foundation input point, D [1,2]

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Fig. 3

Shock spectrum curves calculated from motion measured at location D in Figs. 1 or 2. Dips occur at the fixed-base frequencies. The frequencies are as follows: f11 is the first mode frequency of the first configuration, f31 is the third mode frequency of the first configuration, f12 is the first mode frequency of the second configuration, and f32 is the third mode frequency of the second configuration [1,2].

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Fig. 4

An envelope of the maximum and minimum spectrum curves of the 12 configurations. Spectrum values at the two fixed-base frequencies are plotted as points; the first mode, which has over 90% of the vibration energy, establishes the minimum below 200 Hz [1,2].

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Fig. 5

Analytical model used by Cunniff and O’Hara [6] to demonstrate the spectrum dip

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Fig. 6

Calculated shock spectrum curves for damping values, α, from 1% to 5%. The three arrows show the three fixed-base frequencies of the dynamic system consisting of masses M2, M3, and M4. The dip in the second mode can be observed [6].

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Fig. 7

Top view of the deck used in the study [9]

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Fig. 8

Bottom view of the deck used in the study showing main transverse beams and longitudinal reinforcement [9]

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Fig. 9

As seen above, edge reinforcements were added to the deck to represent longitudinal bulkheads and connections to the driving mass at node 700. Nodes 701–704 are locations of concentrated mass connected to the deck by vertical springs. Motions of these masses at these four nodes are constrained except in the vertical direction [9].

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Fig. 10

Deck modes 1–4 with frequencies from 16.2 Hz to 23.7 Hz [9]

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Fig. 11

Deck modes 5–8 with frequencies from 26.9 Hz to 33.6 Hz [9]

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Fig. 12

Deck modes 9–10 with frequencies of 39.4 Hz and 40.1 Hz [9]

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Fig. 13

Model showing the vertical springs and masses. Frequencies weights and grid points are listed in Table 2 [9].

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Fig. 14

Calculated accelerations of the free deck at the nodes where masses are to be attached [9]

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Fig. 15

Calculated accelerations of the deck at the nodes with masses to be attached except for node 121. A 1,500 lb weight is attached at node 121 with a fixed-base frequency of 22 Hz. Note the reduction in the peak from 7800 Gs to 6000 Gs by comparing results with Fig. 14 [9].

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Fig. 16

Shock spectrum curves at specified nodes of the free deck [9]

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Fig. 17

Shock spectrum curve at node 121 with a 1,500 lb weight with a fixed-base frequency of 22 Hz compared to the free deck spectrum curve at the same node. The spectrum dip is obvious [9].

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Fig. 18

Shock spectrum curve at node 595 with a 7,000 lb weight with a fixed-base frequency of 30Hz compared to the free deck spectrum curve at the same node. The spectrum dip is obvious [9].

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Fig. 19

Shock spectrum curve at node 242 with a 200 lb weight with a fixed-base frequency of 23 Hz compared to the free deck spectrum curve at the same node. In addition, the arrow from “All Masses” in the graph indicates the spectrum at node 242 with all dynamic masses attached to the deck. There is a further suppression of the spectrum by the other masses on the deck [9].

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