Engineering, 2010, 2, 378-386
doi:10.4236/eng.2010.25049 Published Online May 2010 (http://www.SciRP.org/journal/eng)
Comparison Studies on Dynamic Packaging Properties of
Corrugated Paperboard Pads
Yanfeng Guo1, Wencai Xu2, Yungang Fu1, Wei Zhang1
1Department of Packaging Engineering, Xi’an University of Technology, Xi’an, China
2Department of Packaging Engineering, Beijing Institute of Graphic Communication, Beijing, China
Received December 17, 2009; revised February 23, 2010; accepted February 26, 2010
Abstract
Corrugated paperboard is a kind of inexpensive and environmental-friendly packaging material, and may be
made into pads of package cushioning to protect products from shock and vibration damage by isolation
during distribution. This article deals with the characterization of dynamic packaging properties of corru-
gated paperboard pads, such as dynamic cushioning curves, vibration transmissibility and frequency curves.
The main feature of article is the evaluation on the dynamic shock cushioning property and vibration trans-
missibility of corrugated paperboard pads by a series of experimental studies on the drop shock tester and
vibration tester, the establishment of experimental formulas of dynamic cushioning curves, and the analysis
of resonance frequencies and vibration transmissibility. By using the fitting polynomial of curve and method
of the least mean square, the experimental formulas with third order polynomial function of dynamic cush-
ioning curves for corrugated paperboard pads are obtained. By using linear vibration theory with single de-
gree of freedom, the resonance frequencies, vibration transmissibility and damping ratios of corrugated pa-
perboard pads at different static loads are acquired. All results show the dynamic properties relevant to de-
sign applications of corrugated paperboard pads for protective packaging.
Keywords: Corrugated Paperboard Pads, Dynamic Shock Cushioning Property, Dynamic Cushioning Curve,
Vibration Transmissibility, Resonance Frequency
1. Introduction
Corrugated paperboard is a kind of inexpensive and en-
vironmental-friendly packaging material with corrugated
sandwich structure, holds lightweight, high strength-to-
weight and stiffness-to-weight ratios, and has economic
and environmental advantages over plastic foams [1,2]. It
also has excellent machining technology of packaging,
and may be made into pads of package cushioning to
protect products from shock and vibration damage by
isolation during distribution. The usual technology is to
interpose the corrugated paperboard pad between the
product and the container to provide the necessary isola-
tion [3-5]. So, there is an increasing interest in utilizing
corrugated paperboard pads for protective packaging of
products (e.g. precise equipment and instrument, house-
hold appliance and fragile goods etc).
For corrugated paperboard, the compressive strength,
crush strength, bending defection and flexural stiffness,
creep property and recoverability were investigated by
Hahn, Lee, Urbanik, Guo et al. [6-9]. By using some
finite element models and commercial finite element
code ABAQUS or ANSYS, the mechanical behaviors of
corrugated paperboard such as buckling, transverse shear,
elasticity, stability, collapse and ultimate failure were
studied by Gilchrist, Nordstrand, Aboura, Rami, Talbi
et al. [10-14]. Within the finite element models (e.g. thin
shell element, simplified homogenization model), both
geometric nonlinearity (large deformation) and material
nonlinearity (anisotropy or orthotropy) effects were con-
sidered. The cushioning property and its predictive
model, the vibration transmissibility and frequency re-
sponse of single-wall corrugated paperboard were ana-
lyzed by Sek et al. [15,16]. But for the corrugated pa-
perboard pads (e.g. single layer pad, two layers pad,
three layers pad), the lack of dynamic packaging proper-
ties such as dynamic cushioning curves and vibration
transmissibility hampers its application for protective
packaging of products [4-5]. Therefore the aims of this
research work are as follows: Firstly, evaluate the dy-

Y. F. GUO ET AL.379
namic shock cushioning property of corrugated paper-
board pads by drop shock tests, and establish the experi-
mental formulas of dynamic cushioning curves. Secondly,
study the vibration transmissibility of corrugated paper-
board pads at different static loads by vibration tests, and
analyze the resonance frequencies, vibration transmissi-
bility and damping ratios.
2. Structure of Corrugated Paperboard Pads
The structure of corrugated paperboard pads usually
covers single layer corrugated paperboard pad in Fig-
ure 1(a), two layers corrugated paperboard pad in Fig-
ure 1(b), and three layers corrugated paperboard pad in
Figure 1(c). The difference of these pads is the layer
quantity (or thickness of pad). The thicknesses of single
layer pad, two layers pad, three layers pad are 7.81 mm,
15.62 mm and 23.43 mm, respectively. The top surface
of all test specimens is square, and the dimension is
15 cm × 15 cm. They would be respectively called sin-
gle layer pad, two layers pad, three layers pad for short.
These corrugated paperboard pads are also made of
double-wall corrugated paperboard with A and B flutes
by machining technology of cutting, folding and pasting.
The single layer pad is directly made of the double-wall
corrugated paperboard, the structure of two layers pad
comprises two layers of the double-wall corrugated pa-
perboard, and the structure of three layers pad consists of
three layers of the double-wall corrugated paperboard.
The thickness of double-wall corrugated paperboard
with A and B flutes is 7.81 mm, the corrugated cores
and inner sheet are corrugated paper with grammage
of 150 g/m2, and the face sheets are kraft linerboard
with grammage of 250 g/m2. Before each of tests, all test
(a) (b) (c)
Figure 1. Photograph of corrugated paperboard pads.
specimens of corrugated paperboard pads should be pre-
conditioned to equilibrium in air uniformly maintained
for at least 24 hours at ambient temperature 23℃ and
relative humidity 60%.
3. Description of Dynamic Packaging
Properties
3.1. Description of Dynamic Shock Cushioning
Property
The dynamic shock cushioning property describes the
capability of absorbing drop shock energy of corrugated
paperboard pads, and reflects the relationship between
peak acceleration and static stress during drop shock.
The peak acceleration is a non-dimension ratio of peak
acceleration of the packaged item to gravity acceleration.
It is usually presented as a family of dynamic cushioning
curves (or peak acceleration and static stress curve),
which shows peak acceleration during drop shock for a
range of static loads and is constructed for several drop
heights [3]. The test system for dynamic shock cushi-
oning property (Figure 2) shall consist of a drop shock
tester, a signal acquisition & processing device, a set of
Data Acquisition & Signal Processing Engineering Tech-
nology (DASP-ET) software. The drop shock tester has a
drop block and weight (to represent the packaged item)
and impact base for dynamic loading of a test specimen
to simulate drop shock in handling. The weight is
mounted on the drop block. The mass of weight and drop
height of the drop block are adjustable. An acceleration
sensor is mounted on the drop block, and the signal out-
put from the acceleration sensor is firstly fed into the
signal acquisition & processing device, then the drop
shock acceleration and time curve may be read and dis-
played by DASP-ET.
While the drop block with the weight impacts the test
specimen of corrugated paperboard pad from a predeter-
mined drop height by means of area contact, according to
the law of conservation of energy, the potential energy of
weight and drop block shall be transferred as the kinetic
energy of weight and drop block and the deformation
energy of test specimen [3]. The relationship may be
described as the following expression
2
0
1()( )
2mVATdmg hT


  
 (1)
where m stands for mass of drop block and weight, V is
impact velocity of weight and drop block, A is contact
area between test specimen and drop block, T is thick-
ness of test specimen, σ and ε are compression stress and
strain of test specimen, and h is a predetermined drop
height. When the impact velocity of weight and drop
block becomes zero (V = 0), the maximum deformation

Y. F. GUO ET AL. 380
Figure 2. Test system of dynamic shock cushioning prop-
erty: 1.Weight; 2.Drop block; 3.Guide column; 4.Test speci-
men 5. Acceleration sensor.
m

of test specimen is reached, and the maximum stress
m

of test specimen and peak acceleration would
be occurred, and Equation (1) may be rewritten as
m
G
0()() ()
m
ms m
mg hh
d
A
TT


  
 (2)
where
s

is static stress exerted on test specimen. In
addition, according to the Newton’s law of motion, the
maximum force exerted on weight and drop block equals
to its inertial force plus its own weight [3], and the rela-
tionship may be written as
(1)
mm
Gs

  (3)
where is peak acceleration divided by gravity ac-
celeration g. Then substituting Equation (3) into Equa-
tion (2), the following expression may be derived
m
G
0
()
()
m
m
mm
h
GT
d


 

1 (4)
where
0()
m
m
d




 is the ratio of maximum stress to unit
volume stored energy. It is obvious that peak acceleration
may directly indicate the capability of absorbing drop
shock energy of corrugated paperboard pad, and may ex-
press the dynamic shock cushioning property of corru-
gated paperboard pad. So the dynamic cushioning curve
has proved to be the most practical basis for describing the
dynamic shock cushioning property, the lower the dy-
namic cushioning curve swings, and the better protection
the package cushioning provides [4,5].
3.2. Description of Vibration Transmissibility
The vibration transmissibility is usually described as the
relationship between vibration transmissibility and reso-
nance frequency of corrugated paperboard pads at different
static loads. Vibration transmissibility is a non-dimension
ratio of response acceleration amplitude of the packaged
item in steady-state forced vibration to excitation accel-
eration amplitude [3]. The test system for vibration
transmissibility (Figure 3) shall consist of a dynamo-
electric vibration tester, a signal acquisition & processing
device, a set of DASP-ET software. Two test specimens
combination under investigation are placed in the test
fixture, and the mass block is placed on the bottom test
specimen. The two test specimens, mass block (to repre-
sent the packaged item) and fixture are mounted on the
vibration tester. The weight of mass block is changeable,
and the static load exerted on the bottom test specimen
may be adjusted by changing the weight of mass block.
One acceleration sensor is attached to the platform of
vibration table to monitor the excitation acceleration, and
the other is located in the mass block to measure the re-
sponse acceleration. The signal outputs from the sensor
located in the mass block and on the platform of vibra-
tion table are simultaneously fed into the signal acquisi-
tion & processing device, then the experimental data
shall be analyzed and presented in the form of vibration
transmissibility and frequency curve by DASP-ET.
Although most package cushioning materials exhibit
nonlinear property, a brief discussion of linear system
with single degree of freedom will aid in understanding
some of the fundamental aspects of vibration as related
to packaging considerations [4,5]. For the vibration test
system in Figure 3, the mass block cushioned on the test
specimen may be idealized as the linear single degree of
freedom system with viscous damping, and the vibration
transmissibility of package cushioning system with
corrugated paperboard pads would be described as
r
T
2
22 2
1(2 )
(1)( 2)
r
T




 (5)
where λ stands for frequency ratio (
r
f
f
 ), f is excita-
tion frequency of vibration table, fr is resonance fre-
quency of the package cushioning system, and ζ repre-
sents damping ratio. It is evident that vibration transmis-
sibility has a close relationship with frequency ratio and
damping ratio. When the resonance takes place (λ = 1),
the damping ratio ζ may be derived from Equation (5)
and written as
Figure 3. Test system of vibration transmissibility: 1)
Clamp device; 2) Test specimens; 3) Mass block; 4) Accel-
eration sensors.

Y. F. GUO ET AL.381
2
11
21
r
T
  (6)
So, after obtaining the vibration transmissibility and
frequency curves of corrugated paperboard pads by vi-
bration tests with slow sine sweep, resonance frequencies,
vibration transmissibility and damping ratios may be
analyzed, and the vibration transmissibility of corrugated
paperboard pads shall be comprehensively evaluated.
4. Experimental Methods of Dynamic
Packaging properties
The most comprehensive method for determining dy-
namic shock cushioning property is described in the
standard ASTM D 1596 “Standard test method for dy-
namic shock cushioning characteristics of packaging
materials”. The test procedure is as follows: Firstly, posi-
tion the test specimen on the impact base and prepare the
drop block to impact the test specimen. Secondly, impact
the test specimen at the predetermined drop block weight
(static load) and drop height, then repeat the same test
procedure with the other two test specimens. The drop
shock acceleration and time curve should be recorded for
each test. The average value of peak accelerations for
these three drop shock tests is taken as the peak accelera-
tion at the predetermined static load. Thirdly, repeat the
drop shock procedure with several more increments of
weight until sufficient data are derived to establish the
dynamic cushioning curve. Lastly, the same procedure
shall be employed for different drop heights. For a drop
height, a piece of dynamic cushioning curve may be
obtained by making drop shock tests for a range of
static loads. Then adjusting the drop height and making
similar drop shock tests, another piece of dynamic cush-
ioning curve may be also obtained. Therefore by making
a series of drop shock tests for different drop heights, a
family of dynamic cushioning curves should be obtained.
On the basis of the family of dynamic cushioning curves,
the dynamic shock cushioning property of corrugated
paperboard pads shall be thoroughly evaluated.
The most comprehensive method for determining vi-
bration transmissibility is described in the standard
ASTM D 4168 “Standard test method for vibration trans-
missibility of package cushioning material”. The test
procedure is as follows: Firstly, place two specimens
combination under investigation in the test fixture, one
below and the other above the mass block. The mass
block weighted for the desired static load is placed on the
bottom test specimen, and the top test specimen is placed
above the mass block, then the fixture is clamped in
place. Secondly, start the vibration test with slow sine
sweep, and present experimental data in the form of vi-
bration transmissibility and frequency curve. In order to
thoroughly evaluate the vibration transmissibility of cor-
rugated paperboard pads, the range of frequency sweep is
selected from 3 Hz to 600 Hz in order to wholly investi-
gate on the vibration propery of corrugated paperboard
pads. The frequency sweep rate is one octave per minute,
and sine excitation acceleration is held constant ampli-
tude at 0.5 g. Thirdly, the same procedure shall be used
for different static loads. These different static loads
would be selected from the family of dynamic cushion-
ing curves of corrugated paperboard pads. On the basis
of vibration transmissibility and frequency curves at dif-
ferent static loads, the vibration transmissibility of cor-
rugated paperboard pads would be investigated.
5. Results and Discussions
5.1. Dynamic Shock Cushioning Property of
Corrugated Paperboard Pads
According to the test method ASTM D 1596, the drop
shock tests of corrugated paperboard pads are made for
drop heights 30 cm, 60 cm and 90 cm respectively. The
waves of drop shock acceleration are similar to half-sine
pulses at different static loads for different drop height,
e.g. the wave in Figure 4 is that of single layer pad for
drop height (DH) 30 cm and static load 2.439 kPa, the
peak acceleration is 177.46 g (gravity acceleration). In
addition Figure 5 provides the wave of two layers pad
for drop height 60 cm and static load 2.613 kPa, the peak
acceleration is 203.61 g. Figure 6 is the wave of three
layers pad while drop height 90 cm and static load
3.049 kPa, the peak acceleration is 291.14 g. Due to the
limited space other drop shock acceleration and time
curves are omitted.
By comparison studies on the drop shock tests for cor-
rugated paperboard pads, seven pieces of dynamic cush-
ioning curve shall be obtained, which are shown in Fig-
ures 7 to 9. For single layer pad, while the drop height is
60 cm or 90 cm, the test specimens would be wholly
crushed and lose dynamic shock cushioning property, so it
has only one piece of dynamic cushioning curve for drop
height 30 cm (Figure 7). The curves in Figure 8 are for two
layers pad, and that of Figure 9 are for three layers pad.
These dynamic cushioning curves are the most practi-
cal basis for the package cushioning design procedure of
corrugated paperboard pads [4-5], so it is necessary to
develop experimental formulas of these curves. From the
characterization of dynamic cushioning curves summa-
rized above, these curves have a close relationship with
the drop height and static stress. When the drop height is
constant, the peak acceleration may be described as a
function of static stress, and the experimental formulas of
dynamic cushioning curves may be established by using
the fitting polynomial of curve [17-18]. By comparing

Y. F. GUO ET AL. 382
Figure 4. Drop shock acceleration and time curve of single
layer pad.
Figure 5. Drop shock acceleration and time curve of two
layers pad.
Figure 6. Drop shock acceleration and time curve of three
layers pad.
the test data of average peak acceleration with its theo-
retical data derived from the fitting polynomial of curve,
the third order polynomial function of static stress has
proved to be the best expression, and the experimental
formulas of dynamic cushioning curves of corrugated
paperboard pads is written as
2
ss 01 23 m
Gaa aa
3
s

   
(7)
where is average peak acceleration,
m
G
s

represents
static stress, 0, 1, 2, 3 are four characteristic fac-
tors. For example, Figure 10 gives the dynamic cush-
ioning curve of three layers pad at drop height 60 cm, and
the circle dots stand for test data of average peak accelera-
tion. The dynamic cushioning curve is obtained by using
the fitting polynomial with third order polynomial func-
tion of the curve. So, on the basis of test data of average
peak acceleration and static stress obtained from the drop
shock tests of corrugated paperboard pads for drop heights
30 cm, 60 cm and 90 cm respectively, using Equation (7)
and Method of the Least Mean Square, the characteristic
factors of dynamic cushioning curves are solved and
shown in Table 1.
aa a a
Figure 7. Dynamic cushioning curve of single layer pad.
Figure 8. Dynamic cushioning curves of two layers pad.
Figure 9. Dynamic cushioning curves of three layers pad.

Y. F. GUO ET AL.383
Figure 10. Dynamic cushioning curves of three layers pad
(DH = 60 cm).
By comparing and analyzing these dynamic cushion-
ing curves of corrugated paperboard pads, some conclu-
sions may be drawn as follows:
1) Each piece of dynamic cushioning curves of corru-
gated paperboard pads (Figures 7-9) is always concave
and upward, and has only one minimum value point.
This rule can be understood as follows [5]. If the mass of
weight and drop block is light, the drop shock would
result in very little compressive deformation, and the
corrugated paperboard pad absorbs and stores a little
mechanical energy per unit volume, so the acceleration
peak is relatively large. This represents the left hand side
of dynamic cushioning curve. In the middle area, the cor-
rugated paperboard pad is properly compressed and ab-
sorbs and stores much mechanical energy per unit vol-
ume, so the minimum peak acceleration shall be reached.
After passing through a certain point, the greater mass of
weight and drop block compresses the corrugated pa-
perboard pad too much, so the corrugated paperboad pad
shall be bottomed out, then the minimum peak acceler-
Table 1. Characteristic factors of dynamic cushioning curves.
Pad type Drop height
/cm a0, a1, a2, a3
Single layer pad 30 464, -2132.9, 3014.3, 3325
30 273.8, -632.6, -455.9, 2299.3
60 122.58, 4071.8, -37339,
86990
Two layers pad
90 600, -8067, 48250, -69897
30 344.2, -1796.3, 3717.5,
-2400.1
60 148.07, 1004.3, -7969.2,
13630
Three layers pad
90 190.4, -1103.5, 4217.2,
1792.7
ation increases. This is the right hand side of the curve.
So the middle area of the curve is the optimum perform-
ance range.
2) For the same corrugated paperboard pad, with the
increment of drop height, the concave point of dynamic
cushioning curves (Figures 8 and 9) has a trend to rise
along leftward and upward direction. Therefore the drop
height is an important factor to influence on the dynamic
shock cushioning property, and the selection of dynamic
cushioning curve should be coincided with the predeter-
mined drop height in package cushioning design of cor-
rugated paperboard pads.
3) For the same drop height, with the increment of
layer quantity of corrugated paperboard pads, the mini-
mum peak acceleration declines. The minimum peak
acceleration of three layers pad is least. So three layers
pad holds better dynamic shock cushioning property than
single layer pad and two layers pad.
5.2. Vibration Transmissibility of Corrugated
Paperboard Pads
On the basis of the family of dynamic cushioning curves
of corrugated paperboard pads (Figures 7 to 9), these
different static loads exerted on the bottom test specimen
are respectively selected as follows: 1) For single layer pad,
four kinds of different static loads, 2.178 kPa, 2.439 kPa,
3.049 kPa and 3.484 kPa; 2) For two layers pad, fourteen
kinds of different static loads, 0.871 kPa, 1.132 kPa,
1.307 kPa, 1.568 kPa, 1.742 kPa, 2.178 kPa, 2.439 kPa,
2.613 kPa, 3.049 kPa, 3.920 kPa, 4.617 kPa, 4.791 kPa,
5.227 kPa and 5.662 kPa; 3) For three layers pad, eleven
kinds of different static loads, 0.871 kPa, 1.307 kPa,
1.742 kPa, 2.178 kPa, 2.613 kPa, 3.049 kPa, 3.310 kPa,
3.484 kPa, 4.356 kPa, 4.791 kPa and 5.227 kPa. Accord-
ing to the test method ASTM D 4168, the vibration tests
with slow sine sweep for corrugated paperboard pads at
different static loads are made, and the vibration trans-
missibility and frequency curves are obtained. For exam-
ple, Figure 11 is the vibration transmissibility and fre-
quency curve of single layer pad at static load 2.439 kPa,
Figure 12 gives that of two layers pad at static load
4.617 kPa, and Figure 13 provides that of three layers
pad at static load 4.791 kPa. Due to the limited space,
other vibration transmissibility and frequency curves are
omitted.
On the basis of these vibration transmissibility and fre-
quency curves, resonance frequencies, vibration transmis-
sibility and damping ratios are analyzed by using linear
vibration theory with single degree of freedom, and the
damping ratios (smaller than one) are estimated by using
Equation (6). For example, Table 2 gives the experi-
mental results of single layer pad at static loads of 2.439 kPa
and 3.049 kPa. Table 3 provides that of two layers pad at
static loads of 1.568 kPa, 2.613 kPa, 3.920 kPa, 4.617 kPa,

Y. F. GUO ET AL. 384
Figure 11. Vibration transmissibility and frequency curve of single layer pad.
Figure 12. Vibration transmissibility and frequency curve of two layers pad.
Figure 13. Vibration transmissibility and frequency curve of three layers pad.
5.227 kPa and 5.662 kPa. Table 4 reflects that of three
layers pad at static loads of 0.871 kPa, 2.178 kPa, 3.049 kPa,
4.791 kPa and 5.227 kPa. Due to the limited space, other
experimental results are omitted.
By comparing and analyzing the experimental results
and curves of vibration transmissibility of corrugated
paperboard pads at different static loads, some conclu-
sions may be reached as follows:
1) The package cushioning system of corrugated pa-
perboard pads has different resonance frequencies, yet
only several resonance frequencies are primary and other
resonance frequencies have a little effect on the pack-
aged item during distribution. For instance, while static
load 4.617 kPa is exerted on two layers pad, the vibration

Y. F. GUO ET AL.385
Table 2. Vibration transmissibility of single layer corru-
gated paperboard pad.
Static load
/kPa
Resonance
Frequency /Hz
Vibration
transmissibility
Damping
ratio
12 0.995
73 1.364 0.539
97 1.814 0.330
132 8.031 0.062
191 2.445 0.224
2.439
339 0.475
12 0.985
73 1.453 0.474
97 1.966 0.295
123 9.928 0.050
189 2.206 0.254
3.049
338 0.429
Table 3. Vibration transmissibility of two layers corrugated
paperboard pad.
Static load
/kPa
Resonance
Frequency /Hz
Vibration
transmissibility
Damping
ratio
14 1.014
91 1.615 0.394
127 3.108 0.170
167 11.214 0.045
208 3.630 0.143
1.568
335 0.492
14 1.032
38 1.742 0.351
85 3.271 0.161
112 5.217 0.096
2.613
280 0.515
12 1.007
53 2.408 0.228
88 7.893 0.063
102 5.574 0.090
114 5.890 0.085
3.920
293 0.680
12 1.038
45 1.416 0.499
74 7.926 0.064
114 2.941 0.181
138 3.121 0.169
4.617
156 0.873
14 1.039
56 2.538 0.214
70 6.416 0.078
106 1.601 0.400
133 1.443 0.481
5.227
153 0.458
14 1.090
35 2.225 0.252
55 2.805 0.191
76 2.122 0.267
97 1.077
5.662
121 0.425
transmissibility and frequency curve (Table 3 and Fig-
ure 12) has six resonance frequencies such as 12 Hz, 45 Hz,
74 Hz, 114 Hz, 138 Hz and 156 Hz, their vibration
transmissibility are 1.038, 1.416, 7.926, 2.941, 3.121 and
0.873, respectively. The vibration transmissibility at 74 Hz
is about 9.08 times as much as that of 156 Hz, the vibra-
tion transmissibility at 138 Hz is about 3.58 times as
much as that of 156 Hz, so the resonance frequency 74 Hz
should be taken as the first principle mode of vibration,
resonance frequency 138 Hz as the second mode, etc.
The result indicates an important guidance that the pri-
mary resonance frequencies must be avoided in package
cushioning design of corrugated paperboard pads.
2) For the package cushioning system with corrugated
paperboard pad, there is critical frequency at which the
vibration transmissibility is high, and above the critical
frequency the vibration transmissibility drops and is
smaller than one. For example, the critical frequency of
single layer pad is 191 Hz (Table 2). When the excita-
tion frequency is higher than 191 Hz, the vibration
transmissibility is very low, and the corrugated paper-
board pad shall efficiently decrease vibration. In addition,
for two layers pad, the critical frequency is 208 Hz (Ta-
ble 3), and for three layers pad, the critical frequency is
185 Hz (Table 4). So the package cushioning system of
corrugated paperboard pad may efficiently attenuate vi-
bration with higher excitation frequency during distribution.
3) The static load exerted on the corrugated paper-
board pad has an evident influence on vibration trans-
missibility. The influence relates to the mechanical be-
havior of corrugated paperboard, especially viscoelasticity.
The result suggests another important guidance that the
Table 4. Vibration transmissibility of three layers corru-
gated paperboard pad.
Static load
/kPa
Resonance
Frequency /Hz
Vibration
transmissibility
Damping
ratio
14 1.024
71 1.500 0.447
84 2.053 0.279
112 3.286 0.160
138 7.633 0.066
185 2.191 0.256
0.871
332 0.725
14 1.045
61 3.969 0.130
77 6.832 0.073
106 3.823 0.136
127 1.288 0.616
2.178
158 0.593
14 1.042
55 2.720 0.198
74 4.744 0.108
103 2.321 0.239
126 1.334 0.566
3.049
152 0.387
14 1.061
41 2.423 0.227
54 2.852 0.187
62 4.192 0.123
98 1.511 0.441
4.791
155 0.563
12 1.063
47 3.482 0.150
56 2.439 0.225
82 2.303 0.241
105 1.152 0.874
5.227
130 0.550

Y. F. GUO ET AL. 386
vibration transmissibility and frequency curve must be
selected according to the static load exerted on it in pack-
age cushioning design of corrugated paperboard pads.
6. Conclusions
This research work obtains dynamic cushioning curves,
vibration transmissibility and frequency curves of corru-
gated paperboard pads by a series of experimental stud-
ies, and evaluates its dynamic packaging properties rele-
vant to its application for protective packaging such as
dynamic shock cushioning property and vibration trans-
missibility. The waves of drop shock acceleration are
similar to half-sine pulses, the shapes of dynamic cush-
ioning curves are always concave and upward, and each
piece of dynamic cushioning curves has only one mini-
mum value point. The package cushioning system of
corrugated paperboard pads has different resonance fre-
quencies, and only several resonance frequencies are
primary. The results show that corrugated paperboard
pads possess dynamic shock cushioning property for
drop shock, and the three layers pad has better dynamic
shock cushioning property than single layer pad and two
layers pad. For the package cushioning system with cor-
rugated paperboard pads, there is critical frequency at
which the vibration transmissibility is high, and above
the critical frequency the vibration transmissibility drops
and is smaller than one. The critical frequency of single
layer pad is 191 Hz, that of two layers pad is 208 Hz, and
that of three layers pad is 185 Hz. The package cushion-
ing system of corrugated paperboard pad may efficiently
attenuate vibration with higher excitation frequency dur-
ing distribution.
7. Acknowledgements
This research work is supported by the Scientific Re-
search Foundation of Science and Technology Depart-
ment of Shaanxi Province under the Grant 2007K07 - 21
and the Scientific Research Foundation of Printing &
Packaging Material and Technology Beijing Area Major
Laboratory under the Grant KF200705. We would like to
thank Northwest Corrugated Paperboard Limited Com-
pany for providing test specimens of corrugated paper-
board pads.
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