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UDC 531.76+534.134+534.141.2
DOI: 10.18698/0236-3941-2021-1-103-113
EVALUATION OF THE COMPOSITE BARRIER NATURAL OSCILLATIONS INFLUENCE ON THE GENERATED SHOCK LOADING
A.S. Borozenets A.V. Proskurin A.V. Shlishevskiy
niik@vniitf.ru
Federal State Unitary Enterprise "Russian Federal Nuclear Center — Zababakhin All-Russia Research Institute of Technical Physics", Snezhinsk, Chelyabinsk Region, Russian Federation
Abstract
The problem of studying behavior of various structures under the influence of intense impulsive (shock) loads arising during operation of many modern facilities, machines and devices remains relevant for many years. Shock loading in laboratory conditions is generated due to interaction between the test object and the braking device (barrier). In this case, braking device or barrier could be a one-piece or a prefabricated structure. If the braking device (barrier) dimensions commensurate with the test object, the braking device natural oscillation frequencies excited during interaction between the test object and the braking device (barrier) could be found in the range of the test object natural oscillation frequencies. Frequency determination within the signal spectrum registered on the test object and caused by oscillations of the braking device (barrier) or test equipment, would assist in better assessing the test object shock loading and its compliance with real operating conditions
Keywords
Reinforced concrete barrier, shock loading, longitudinal oscillations, piezo accelerome-ter, digital filtering, spectral density
Received 22.08.2020 Accepted 29.09.2020 © Author(s), 2021
Introduction. Shock loading [1-3] in laboratory testing could be set in the form of collision conditions (drop height, approach speed) [4-6], or in the form of impact impulse parameters (amplitude and duration of impact acceleration) [7, 8]. In the first case of setting the shock loading in the form of implementing the collision conditions, test equipment as it is misses, and a test object (TO) stays in conditions as close as possible to the real ones. However, the real (semi-infinite) barrier in this case is replaced by a composite barrier, i.e., a barrier possessing its natural oscillation frequencies. In the second
case, loading conditions are set in the form of impact impulse parameters. With this approach, intermediate elements in the form of test equipment are positioned between the TO and the braking device, and they have their individual set of natural vibration frequencies. In addition, the braking device has its own set of natural frequencies. Obviously, when analyzing results of a TO shock loading, it is necessary to evaluate natural oscillation frequencies of composite obstacles, test equipment or braking devices in order to assess these elements oscillation influence on the TO shock loading.
Works [7, 8] present studies of shock loading set in the form of its parameters. The main drawback of these works is that influence of the test equipment natural oscillation frequencies on the generated shock loading is not being assessed, which in some cases could provoke a significant error in estimation of the TO reaction during the impact testing. This article is devoted to assessing the influence of composite barrier oscillations on accelerations of the TO interacting with it.
Impact testing. TO 4 m long was exposed to shock loading. The load was generated due to interaction between the TO and the barrier, which appeared to be a structure made of reinforced concrete blocks with internal reinforcement (Fig. 1).
Table 1 presents physical and mechanical characteristics of the barrier element materials [9-12], as well as longitudinal dimensions (thickness and length) for blocks of types 1, 2 and 3.
Block of type 3
0.6 m'
Fig. 1. Barrier external appearance
Table 1
Physical and mechanical characteristics of the barrier element materials
Element Material E, MPa P, kg/m3 H- a, m/s2 h (l), m
Block of type 1 M400 concrete 3.25 • 104 2170 0.18 4487* (4750)* 0.6
Block of type 2 М300 concrete 3 • 104 2183 0.18 4200* 0,6
Block of type 3 М300 concrete 3 • 104 2183 0.18 4200* 3
TO * Speed of sour block of type 1 is ] Steel id determinec provided in br; 2 • 105 experiment; ickets). 7850 illy (spe 0.3 ed of sou 5200 nd value i 4 n second
To register accelerations near the TO end face opposite to the impact zone, four piezo accelerometers (PMT — primary measurement transducer) were installed with symbols 1X, 2X, 3X and 4X of the AP11 type (conversion coefficient 11 ± 4 pC/g, registered acceleration amplitude up to 5000 g, operating frequency range 2-15 000 Hz) for VGO-1 adhesive sealant. Signal registration from piezo accelerometers was carried out using the PARUS 01.01.000 autonomous registration device designed and developed by the FTI UB RAS, Izhevsk (shock resistance up to 100 000 m/s2; number of channels is 4; registration time is 4, 8, 16 and 32 s, upper cutoff frequency is 55 000 Hz, sampling frequency is 120, 60, 30 and 15 Hz).
Signals registered by piezo accelerometers are shown in Fig. 2. The A peak acceleration values and the x acceleration pulse duration for each piezo accel-erometer signal (see Fig. 2) are presented in Table 2. Besides, average values of these Aav and Xav parameters are provided there. Signal spectral densities [13] shown in Fig. 2 are provided in Fig. 3.
To detail the graphs of spectral densities, let us exclude from consideration the range from 0 to 77 Hz, which characterizes shock loading with the 13 ms pulse duration (fimp.load = 1/Tav = 1000/13 = 77 Hz). Detailed graphs of the signal spectral density registered by 1X, 2X, 3X and 4X piezo accelerometers in the 77-2000 Hz range are shown in Fig. 4.
Values of the spectral density peak frequencies pertaining to the 1X, 2X, 3X and 4X piezo accelerometer signals in the 77-2000 Hz frequency range are given in Table 3. Only those peaks were considered, which amplitudes corresponded to the A > 0.1Amax condition, where Amax is the maximum peak amplitude.
A g 1700
1450
1200
950
700
450
200
-50
-300
-550
-800
Primary measurement transducer А, g Äav, g X, ms Tav, ms
1Х 1348 1500 13 13
2Х 1750 12.5
3Х 1414 13
4X 1486 12.5
Sp(f), g^/Hz
80000 70000 60000 50000 40000 30000 20000 10000
0 200 400 600 800 f, Hz
Fig. 3. Graphs of the registered impact accelerations spectral density
Computational study. Let us consider the barrier blocks and the TO as a set of rods with different lengths.
As is known from work [14], longitudinal oscillation frequencies of a rod with free ends are determined by the following formula:
0.005 0.010 0.015 0.020 0.025 0.030 t, s Fig. 2. Graphs of registered impact accelerations
Table 2
Impact acceleration signal parameters
ai
fi = —, i = 1, 2, 3,... is an integer,
(1)
where l is the rod length; a is the wave speed in the rod. Let us restrict ourselves to considering only the first oscillation modes, i.e., by the i = 1 case.
Sp(f), g2/Hz
500
276 456 J 604
524 630
Fig. 4. Spectral density of signals registered by piezo accelerometers
Table 3
Piezo accelerometer signal spectral density peak frequencies
Primary measurement transducer Frequency value, Hz
1X 114 272 364 431 657
2X 114 273 363 440 634
3X 113 272 363 431 658
4X 114 273 363 431 634
Average frequency value 113.8 272.5 363.3 433.3 645.8
When a composite barrier is excited, the shock wave propagates and entrains elements of the barrier into the oscillatory process. The wave divides at the barrier element boundary into reflected and passing waves. Reflected wave moves in the opposite direction to the original motion direction. The passing wave continues to move in the original direction until the next boundary. Thus, the distance to the boundary of any barrier element determines the l length of a conventional rod, which is used to identify the longitudinal oscillation frequency according to (1). The first boundary in the collision scheme shown in Fig. 1 lies
between the TO and the face side of the first block of type 1. Thus, the highest frequency of longitudinal oscillations would be determined by the TO dimensions. The distance to the number 1 boundary is determined by the TO length. Boundary number 2 stays between the back side of the first block of type
1 and the front side of the second block of type 1. Distance to boundary number
2 is determined by the total of the TO length and the thickness of block of type 1. Distances to other boundaries are determined in the same way. Table 4 provides the numbers of boundaries that determine the barrier oscillation natural frequencies, barrier composite elements, which dimensions indicate the distance to these boundaries, and the l parameter value for these boundaries.
Table 4
Barrier boundary numbers and elements, which dimensions determine the distance to the boundary
Boundary number Composition l, m Frequency, Hz
1 TO 4 630
2 TO + Block of type 1 4.6 604
3 TO + two Blocks of type 1 5.2 524
4 TO + two Blocks of type 1 + Block of type 2 5.8 456
5 TO + two Blocks of type 1 + Block of type 2 + Block of type 3 8.8 276
Oscillation frequency determined by boundary number 1 depends on the wave motion speed along the TO. Then, let us consider TO as a steel rod, apply formula (1) to the boundary number 1, and find the highest frequency of longitudinal oscillations:
J(2 •1011)/7850 =630 Hz,
2l1 2l1 2 • 4
where a1 is the wave speed in TO; l1 is the TO length.
Let us consider the following boundaries. Common to the boundaries numbers 2-5 is the fact that wave motion to these boundaries occurs along the barrier constituent elements with different speeds determined by these constituent element properties. It follows from (1) that the longitudinal oscillation frequency is determined by the time of wave passing along the rod [14]. Thus, longitudinal oscillation frequencies determined by boundaries numbers 2-5 could be found by the following formula:
= 1_ 1 ( )
f = T ' (2)
k = 1 ak
where T is the oscillation period; ak is the wave speed in the k-th barrier component; lk is the length of the k-th barrier component; N is the boundary number.
Let us present several comments on the speed of wave propagation in reinforced concrete barriers. The best option is to use the wave speed values in reinforced concrete block obtained experimentally, since the type of internal reinforcement would affect the wave propagation speed. In the absence of experimental data, it is preferable to use the speed of elastic wave propagation in the continuous medium [15]:
a =
E(1 - |Д) 3.25 • 1010(1 - 0.18)
(1 + ^)(1 "2|Ф ^ (1 + 0.18)(1 -2 • 0.18) • 2170
= 4033 m/s,
where E is the material elasticity modulus; ^ is Poisson's ratio; p is the material density rather than the speed of elastic wave propagation in the rods:
a =
E 3.25 • 1010
= 3870 m/s.
p V 2170
Using expression (2), let us determine the first natural frequency of longitudinal oscillations for boundary number 2:
f2 =arifc =-rr-1-T06 = 604Hz.
-+- . +-
a1 a2 ^(2 • 1011)/7850 4487
Oscillation frequencies for boundaries numbers 3-5 are determined in the same way. Calculation results are provided in Table 4. Values of the calculated frequencies obtained are plotted in Fig. 4 as vertical lines.
Let us compare calculated values of the composite barrier longitudinal oscillation frequencies and average values of frequency peaks in the piezo accelerometer signal spectral density. Comparison results are shown in Table 5 and demonstrate sufficient agreement between the obtained values. Compared values have a relative deviation of 5.3 %.
This makes it possible to conclude that piezo accelerometers installed on the TO register natural longitudinal oscillations of the composite barrier. It could be assumed that the longitudinal oscillation calculated frequencies
of 524 and 604 Hz are not highlighted in the acceleration signal spectral density graphs in the form of peaks for two reasons.
1. Insufficiently high sampling rate equal to 120 Hz, when registering the acceleration signal.
2. Mutual adhesion of blocks is improved at the boundaries numbers 2 and 3 due to the screed of blocks of types 1 and 2 using beams and studs, which reduces the reflected wave amplitude at these boundaries.
Table 5
Results of comparing the frequency longitudinal oscillation values
Boundary number Frequency calculated value, Hz Peak frequency average value on the piezo accelerometer signal spectral density, Hz Relative deviation, %
5 276 272.5 1.3
4 456 433.3 5.3
3 524 - -
2 604 - -
1 630 645.8 2.3
Obviously, no peaks at 276 and 456 Hz frequencies should be registered in collisions with a semi-infinite barrier at the test object. In order to forecast the form of a piezo accelerometer signal on the TO upon collision with a semi-infinite barrier, let us filter the signals shown in Fig. 2 by the 10-th order Butterworth blocking filters with frequency bands of 276 ± 27.6 Hz and 456 ± 45.6 Hz.
Received signals are shown in Fig. 5.
A g
0 0.005 0.010 0.015 0.020 0.025 0.030 0.035 t, s Fig. 5. Results of acceleration signal digital filtering
The Ai peak accelerations and the n acceleration pulse duration for each piezo accelerometer signal shown in Fig. 5 are presented in Table 6. Average values of these Alav and ziav parameters are also provided there.
Impact acceleration signal parameters shown in Fig. 5 are presented in Table 6.
Table 6
Impact acceleration signal parameters after filtering
Primary measurement transducer Ab g Auv, g Tu ms T1ov, ms
1Х 1329 1431 14.5 14.3
2Х 1580 14.4
3Х 1402 13.9
4Х 1414 14.5
Comparing the average values of amplitude and duration provided in Tables 2 and 6, it could be seen that acceleration amplitude after filtering decreased by 4.6 %, and duration increased by 10 %.
Conclusion. Comparison of calculated and experimental data demonstrated that the load registered on the TO interacting with a composite braking device (barrier) contains a component determined by the braking device (barrier) oscillations at natural frequencies. This should be taken into account when studying the TO reaction to shock loading, and when simulating collisions with real (semi-infinite) barriers in laboratory conditions, selecting the braking device (barrier) size and design in such a way as to minimize this component.
Translated by K. Zykova
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Borozenets A.S. — Head of the Department, Federal State Unitary Enterprise "Russian Federal Nuclear Center — Zababakhin All-Russia Research Institute of Technical Physics" (Vasileva ul. 13, Snezhinsk, Chelyabinsk Region, 456770 Russian Federation).
Proskurin A.V. — Dr. Sc. (Eng.), Deputy Chief Design Officer, Federal State Unitary Enterprise "Russian Federal Nuclear Center — Zababakhin All-Russia Research Institute of Technical Physics" (Vasileva ul. 13, Snezhinsk, Chelyabinsk Region, 456770 Russian Federation).
Shlishevskiy A.V. — Head of the Group, Federal State Unitary Enterprise "Russian Federal Nuclear Center — Zababakhin All-Russia Research Institute of Technical Physics" (Vasileva ul. 13, Snezhinsk, Chelyabinsk Region, 456770 Russian Federation).
Please cite this article as:
Borozenets A.S., Proskurin A.V., Shlishevskiy A.V. Evaluation of the composite barrier natural oscillations influence on the generated shock loading. Herald of the Bau-man Moscow State Technical University. Series Mechanical Engineering, 2021, no. 1 (136), pp. 103-113. DOI: https://doi.org/10.18698/0236-3941-2021-1-103-113
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