This report summarizes a shock test experiment on a cantilevered aluminum beam. A rotating hammer struck the beam at various angles, and a string gauge measured the resulting deformation. The maximum impact strain of 1876 μ-strain occurred at 20 degrees. Calculations determined the maximum stress on the beam was 18760.69 psi, which is 40.43% of the yield stress for aluminum. The energy loss in the system was approximately 28.5%, and the natural frequency of the beam was 76.92 Hz. The experiment verified relationships between impact energy, beam deformation, and impact angle.

1. University of New Haven
Department of Mechanical Engineering
ME 315
March 24, 2005
Shock Test
Analysis
Report
Author: Franco Pezza
Partners: Mudar Al-Bayat, Tareq Al-Saflan, Derek Shoemaker
1

2. Table of Content
Abstract 3
Introduction 3
Theory and Analysis 4
Equipment 5
Procedure 7
Results and Discussions 7
Conclusions 11
Recommendations 11
Reference 11
2

3. Abstract
Correlating dynamic testing with simple beam deflection and strain
measurements was accomplished by using a rotating hammer that produced a measurable
deformation in a cantilevered rectangular aluminum beam. The deformation was then
used to find the potential and kinetic energies of the falling hammer.
The maximum impact strain was 1876 µ-strain that occurred at 20o
from
vertical. At that angle, the maximum calculated impact strain was 2291 µ-strain. The time
of impact was determined to be 0.023 s, while the natural frequency of oscillation was
found to be 76.92 Hz. The energy loss of the system had a constant value of 7.89%. The
maximum stress due to the shock test that acted on the beam was 18760.69 Psi, which is
40.43% of the yield stress for Aluminum.
Introduction
Shock tests are used to make sure that a design can manage transient vibrations
that may occur during its operational use. The shock test determines how much stress,
strain and deflection actually develops in the test specimen which may then be used to
modify the design. An example of a design that would undergo a shock test would be an
automobile’s bumper. The manufacturer would adjust the design of the bumper so that it
may withstand impacts up to a certain speed.
(Fig.1: Schematic of the shock test system)
In figure 1 is represented the apparatus used for the experiment in which a
rotating hammer hits a cantilevered rectangular beam of aluminum, creating deformation.
A string gage measures the deformation created and the data obtained is used for
calculations.
3

4. Theory & Analysis
Shock tests are designed to study direct impact loading at a short period of time.
The load is characterized as transient and should produce decaying motion due to the
damping characteristics of the specimen involved.
Shock testing produces damages which levels can be divided into low-energy and
high-energy, depending on the acceleration produced and the length of the time interval.
Figure 2 shows the categories of the mechanical shock. The low-energy shock test may
result in low velocities whereas the high-energy shock test results in high velocities.
(Figure 2: Characteristics of Mechanical Shock)
Using the conservation of energy and momentum theories, the velocity of the
specimen and the loading device can be calculated before and after contact.
Conservation of Energy:
ghV 21 =
Conservation of Momentum:
( ) 22111 VmmmV +=
where V1 is the initial velocity, V2 is the velocity after impact, m1 is the mass of the
hammer and m2 is the mass of the rubber stop.
Also, using the Principle of Work and Energy, the energy absorbed by the beam
can be found.
( ) 2
2212
2
1
Vmm
g
U
c
+=
where U2 is the energy of the system after impact.
The value of U2 can then be used to find the maximum force applied to the
specimen.
4

5. 3
2
max
32
2
6
6
L
EIU
F
EI
LF
U
=∴
=
where Fmax is the maximum force applied, E is the modules of elasticity, I is the moment
of inertia of the beam, and L is the length of the beam.
Having found the maximum force, the strain can be found using the Flexure
formula because the specimen is a cantilever beam. The maximum strain will then be
used to find the maximum stress using Hooke’s Law.
Flexure Formula:
EI
Mc
=ε
Hooke’s Law:
εσ E=
where M is the bending moment due to Fmax and c is the distance from the neutral axis to
the surface of the beam.
Using the data obtained from the testing, the period of free vibration is found by
simply reading the time between two consecutive peaks. The reciprocal of the period of
free vibration determines the natural frequency of the beam, fn
Equipment
The equipment used for the experiment was the following:
1. Custom built shock test setup (Figure 3).
(Figure 3: Shock Test System)
5

6. 2. Computer with DAQ and LabVIEW 7 (Figure 4).
(Figure 4: LabVIEW Scheme)
3. Vishay strain gage conditioner (Figure 5).
(Figure 5: Vishay Strain Gage Conditioner)
4. NI ELVIS Interface (Figure 6).
(Figure 6: NI ELVIS Interface)
5. Micrometer caliper and digital weight scale
6

7. Procedure
The conditioner was first calibrated following steps 4.9 thru 4.13 of the lab
manual. Next, the NI ELVIS interface was wired by connecting the BNC plug from the
strain gage conditioner to one of the connectors on the NI ELVIS.
The breadboard was wired to connect the BNC to one of the six available analog
in/out channels. Excessive noise was eliminated by using the differential voltage
measurements. The dimensions of the beam as well as the masses of the plastic disk and
hammer were taken.
The procedure for the shock test itself was as follows:
1. The shock test machine was setup and the leveling screws were adjusted
2. A LabVIEW program was created to collect the data and store it to an
Excel file
3. Three samples were taken for angles of 5, 8, 10, 12, 15, 18, and 20
degrees.
Results
Using the Flexure equation, the maximum value for stress was found to be
18760.69 +/- 40.9 psi at an angle of 20o
+/- 0.5o
. This value is 40.43% of the yield stress
for Al 6061. The values for strain ranged from 506 +/- 38.38 µ-strain at 5o
+/- 0.5o
to
1876 +/- 4.09 µ-strain at 20o
+/- 0.5o
.
The energy loss in the system was determined about 28.5%. The natural
frequency of the beam was found to be 76.92 Hz and the period of the free beam was
read as 0.013 s. The time of contact between the hammer and the beam was determined to
be 0.023 s.
Angle
Trial #
1
Trial #
2
Trial #
3 Average
Strain
Measured
degrees Volts Volts Volts Volts µ-strain
5 1.00 1.04 1.11 1.05 506
8 1.55 1.60 1.65 1.60 774
10 2.01 2.00 2.05 2.02 975
12 2.48 2.39 2.41 2.43 1173
15 2.98 3.00 2.99 2.99 1445
18 3.49 3.42 3.51 3.47 1678
20 3.89 3.88 3.89 3.88 1876
(Table 1:Recorded Data)
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8. Max Stress = 18760.69 psi
σy = 46.4 Kpsi
% Yield = 40.43 %
T = 0.013 s
f = 76.92 Hz
k = 149.9 lbf/in
tc = 0.0231 s
Angle H V1 V2 U2 Fmax M2
Strain
Calculated Strain Based
degrees inches in/s in/s in.lbf lbf in.lbf µ-strain Angle (deg)
5 0.05 6.00 5.53 0.08 5.02 16.95 575 4.40
8 0.12 9.59 8.84 0.22 8.03 27.11 920 6.73
10 0.19 11.99 11.04 0.34 10.04 33.87 1150 8.48
12 0.27 14.38 13.24 0.48 12.04 40.62 1379 10.21
15 0.42 17.95 16.53 0.75 15.03 50.73 1722 12.59
18 0.60 21.51 19.82 1.08 18.01 60.80 2064 14.63
20 0.74 23.88 22.00 1.33 20.00 67.49 2291 16.38
(Table 2: Calculated Results)
Angle
Strain
Measured
Strain
Calculated
Strain
Difference Uε Uθ
Degrees µ-strain µ-strain % µ-strain Degrees
5 506 575 12.04 +/- 38.38 +/- 0.5
8 774 920 15.93 +/- 35.38 +/- 0.5
10 975 1150 15.21 +/- 18.16 +/- 0.5
12 1173 1379 14.93 +/- 33.44 +/- 0.5
15 1445 1722 16.08 +/- 8.90 +/- 0.5
18 1678 2064 18.70 +/- 32.11 +/- 0.5
20 1876 2291 18.11 +/- 4.09 +/- 0.5
Average
Difference = 15.86%
(Table 3: Uncertainty)
Angle Fmax U1 U2 Energy Loss
degrees lbf in.lbf in.lbf in.lbf
5 1.50 0.09 0.07 0.017
8 2.29 0.23 0.17 0.059
10 2.88 0.36 0.28 0.088
12 3.46 0.52 0.40 0.124
15 4.27 0.82 0.61 0.210
18 4.96 1.18 0.82 0.356
20 5.54 1.45 1.02 0.424
(Table 4: Energy Loss)
8

9. Discussion
From a typical graph obtained from the data recorded for each of the trials, we
were able to make few considerations and observations:
• The maximum impact strain was observed to be proportional to the impact energy
(see graph 1).
Strain Vs. Angle
0
500
1000
1500
2000
2500
0 5 10 15 20 25
Angle (Degrees)
Strain(µ-strain)
Strain Measured µ-strain
Strain Calculated µ-strain
(Graph 1: Strain vs. Initial Angle)
• The impact energy of the hammer was also proportional to the deformation of the
beam itself (see table 2).
• The contact time of the hammer was proportional to the initial angle and was
measured being 0.013 seconds.
• The energy loss between the potential initial energy to the energy after impact
was proportional to the initial angle (see table 4), and the percent energy loss
respect the initial potential energy U1= mgh was almost 28.5% (see Graph 2).
9

10. Final Energy Vs. Initial Energy
y = 0.7149x
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60
Initial Energy (in.lbf)
FinalEnergy(in.lbf)
(Graph 2. Energy Loss Graph)
• The natural frequency of oscillation of the beam was observed to be 76.92 Hz.
• The damping effect of the beam vibration was observed by the smaller amplitude
over time (excluding the first impact peak) with a damping constant Lambda
value of about 2.49 (see graph 3).
Damping Curve
y = 1.1588e
-2.4947x
-2
-1
0
1
2
3
4
5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Time (seconds)
Amplitude(scalar)
(Graph 3: Typical response curve obtained from the experiment)
10

11. The value of the strain obtained from the experimental data is out of the
acceptable range calculated with uncertainties. Few considerations may be made on the
fact that we did not take into consideration several factors such as:
• The energy loss due to the impact caused by not perfectly elastic materials. In
fact, some energy is absorbed by the bodies as plastic and thermal energy.
• The friction due to the bearing of the hammer’s attachment, air resistance and the
parallax error in leveling the unit and reading the initial angle.
• The error due to materials specification data utilized for the calculations and the
approximation in the significant figures utilized.
Conclusion
In this experiment, we were able to verify the relationship of a dynamic impact of
a body and the relative deformation in the beam which absorb the kinetic energy. We
were able to measure the strain of the beam, and the time of contact. The relationship
between the initial angle and the energy absorbed by the beam was also verified.
• The maximum value for stress was found to be 18760.69 +/- 40.9 psi at an angle
of 20o
+/- 0.5o
. This value is 40.43% of the yield stress for Al 6061. The values for
strain ranged from 506 +/- 38.38 µ-strain at 5o
+/- 0.5o
to 1876 +/- 4.09 µ-strain at
20o
+/- 0.5o
.
• The energy loss in the system was determined about 28.5%.
• The natural frequency of the beam was found to be 76.92 Hz and the period of the
free beam was read as 0.013 s.
• The time of contact between the hammer and the beam was determined to be
0.023 s.
Recommendations
In this experiment we were able to obtain and record data which was analyzed and
discussed above. In addition, it will be interesting also to analyze the behavior of
different beam materials and the relationship of them with the impact hammer. Another
recommendation is the opportunity to observe and analyze the damping effect of the
beam.
References
Mechanical measurements 5th
edition, Bechwith-Marangoni- Lienard. –Addison-
Wesley Publishing Company, 1995
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