BUCKLING LOAD ENHANCEMENT OF GLASS/EPOXY COMPOSITE
COLUMNS WITH PIEZOELECTRIC ACTUATORS
R. Minia, C. Lakshmana Raob and S. M. Sivakumarb
Research Scholar, Department of Civil Engineering, Indian Institute of Technology Madras, India.
b
Professor, Department of Applied Mechanics, Indian Institute of Technology Madras, India.
[email protected], [email protected], [email protected]
a
ABSTRACT
This paper describes an experimental investigation into the effect of piezoelectric force on active control of buckling in
glass/epoxy composite columns. The tests were conducted on two column specimens. After fabrication of columns,
piezoceramic actuator was surface bonded at their mid-heights. Sensing was carried out using a pair of strain gauges which
were connected in half bridge circuit to a strain gauge amplifier. Experiments were initially conducted for a continuous
application of 100V and the load strain plot was obtained for this case. A 16.88% increase in the load carrying capacity of
column was achieved compared to those without the application of a 100V. The experiments were also conducted with active
control on composite columns. A simple proportional control strategy was adopted for the closed loop control. The test
procedure is outlined and load strain plots, obtained with and without control are presented. The columns with active control
demonstrated a 24.05% increase in the load carrying capacity of the column compared to those without induced actuation. It
shows that the buckling of the column can be postponed to a higher load by means of feedback using piezoelectric actuators
and strain gauge sensors.
Introduction
The buckling of compressively-loaded members is one of the most important factors limiting the overall strength and stability of
a structure. In many cases, especially in aerospace applications, it may be more beneficial and sometimes absolutely
necessary to resort to active methods to enhance the buckling load of slender structures. Active control can increase the load
carrying capacity of a structure and piezoelectric materials are good actuators to provide this active control. In literature,
Bailey and Hubbard [1] have reported that distributed piezoelectric polymers bonded on the surface of the structure can be
used to control the vibration of a cantilever beam. Mini et.al [2] have demonstated a 11% increase in the load carrying
capacity of aluminium column strips by the application of 100V to the piezoceramic actuator. An exact theoretical analysis of
their experiments was carried out introducing an equivalent imperfection to the column and it gave the predictions that
matched well with experiments [3]. Rao and Singh [4] have proposed an enhancement of buckling load of a column by
introducing a follower force paradigm and have shown that there is theoretically a possibility of increasing the buckling load by
a factor of up to 3.5 in the case of a uniform cantilever column. Most literature on buckling control of columns using PZT
materials deals mainly with theoretical and numerical calculations. Limited experimental studies are reported in literature.
Composite materials offer a number of potential advantages in the aerospace, marine and automotive applications due to their
high specific strength, low density, excellent durability, design flexibility and high stiffness to weight ratio. Thomson and
Loughlan [5] have carried out experiments on composite column strips fabricated from commercially available carbon-epoxy
pre-impregnated sheets and have demonstrated that an increase in load carrying capacity of the order of about 20% to 37% is
possible in slender columns. In this paper experiments were carried out on glass/epoxy composite columns. Glass fibres
have reasonably good mechanical properties and are less expensive compared to many other fibres. Hence glass fibre
reinforced composites are used extensively for primary and secondary load bearing applications.
Methodology
The objective of the current experimental study is to control the first mode of a pinned end slender glass/epoxy composite
column using a piezoelectric strip that is surface bonded at the centre of the column on one side. The piezoelectric strip acts
as an actuator. Sensing is carried out using strain gauges pasted on both sides of the column. A half bridge circuit with two
strain gauges is employed to measure bending strains in the column subjected to a slowly varying load. The load was
increased very slowly at the rate of 7g/s to avoid any inertial effects on the buckling of columns. The half bridge circuit in turn
is connected to a strain gauge amplifier. The analogue voltage output from the strain gauge amplifier is fed to the ADC
(Analogue to Digital Converter) card interfaced with the computer. The ADC card converts the analogue voltage signal to
digital values and stores it in a data file. The digital values of the analogue voltage signal from the sensors are then transmitted
to a controller. The controller computes the error and determines the amount of command voltage that is required to
counteract the bending deformations due to axial load. This command voltage is sent to a voltage amplifier to provide the
necessary voltage that drives the piezoelectric actuator surface-bonded to the column. The controller responds to the column
motion in real time. The voltage is applied across the electrode of the actuator so that the net effect is to impart a localized
moment to the column. The strains induced by these moments compensate the bending strains that were originally monitored
by the strain gauges.
Fabrication and specimen preparation
The glass fibre used was E-glass WRM (Woven Roving Mat, bidiirectional, plain weave) of aerial density 610gsm. The
composites consisting of 4 plies were prepared by hand lay-up technique. LY556 Araldite was used as the epoxy matrix and
HY951 as the corresponding hardener. The glass fibre woven cloth of dimensions 1m × 1.5m was laid over an aluminium
sheet of dimensions 1.2m × 1.7m and thickness 3mm. For preparation of epoxy resin matrix 10% hardener was used. The
prepared matrix was poured over the the woven cloth using a brush. A hand roller was used to distibute the resin uniformly,
and to remove air pockets. The sequence was repeated for the rest of the four layers. All the four layers were oriented at an
o
angle of 0 . The layered structure was allowed to cure at room temperature for one day. After curing, the laminate was
detached from the aluminium sheet. A weight fraction of 50% was maintained (approximately 30% volume fraction) for the
laminate. The composite laminate was cut to a size of 50cm × 2.6cm by a hacksaw and the edges were filed. Sample
specimens for static tests were also cut from the same laminate.
Uniaxial Tension Tests on Laminates
Uniaxial tension tests were performed on the samples that were cut from the fabricated composite laminate. Ultimate Tensile
Strength and Tensile Modulus of Elasticity were determined using a Universal Testing Machine. The length and width of the
test coupon was 35cm and 2.6cm respectively. The average thickness of the coupons was 2.77mm. The tab length was
7.5cm and was bonded to the coupon using Anabond 202. The tabs were also cut from the same fabricated composite panel.
The drawing of the tabbed specimen is shown in Figure 1. The tension test was carried out on five specimens. The stress
strain plot of one of the specimens (coupon 4) is shown in Figure 2. The average E (Modulus of Elasticity) obtained was
12.5GPa with a standard deviation of 2.01GPa. The average Ultimate Tensile Strength of the composite was 120MPa.
coupon
tabs
2.77mm
7.5cm
7.5cm
35cm
Figure 1. Tension test specimen drawing
Experimental Setup
Composite rectangular column specimens were taken and a piezoelectric strip was surface bonded at their centre. The
dimensions and properties of composite columns used are listed in Table 1. The PZT strip which is used as actuator was
7
pasted on the column using Anabond 202 . The piezoceramic patch is rectangular in shape and had an electroded surface
facilitating easy connection to the voltage source. The dimensions and properties of the piezoceramic strip used are listed in
Table 2. The loading apparatus consisted of two polished vertical supports on which the loading platform slides. The loading
frame is shown in Figure 4. The column was fixed in between the platforms such that it simulates hinged supports. The
sliding platform simulates a roller joint. The self-weight of the sliding platform was balanced by using a simple pulley system
and suspending a counter weight which was equal to the self weight of the sliding platform. The load applied was increased
continuously and smoothly. This was accomplished by allowing water to flow through a small tube, into a container which was
placed on the loading platform. The control voltage in the open loop experiments was supplied by a high voltage DC supply.
For closed loop experiments, a high voltage DC amplifier was fabricated to supply the voltage. Details of experimental
procedure for both open loop and closed loop control are given in subsequent sections.
Stress Vs Strain
50
stress (N/mm2)
40
30
Δσ
20
Δε
10
0
0
0.001
0.002
0.003
0.004
-10
strain (in microns)
Figure 2. Stress strain curve of coupon 4
Total length
Effective length
Breadth
Thickness
Flexural Modulus (E)
Specimen – 1
500.0mm
456.5mm
26.81mm
2.756mm
12.5GPa
Specimen - 2
505.5mm
455.5mm
26.28mm
2.678mm
12.5GPa
Table 1. Dimensions and properties of glass/epoxy composite column
Length (mm)
Thickness (mm)
Piezoelectric Charge Constants
d33 ( x 10-12 C/N)
d31 ( x 10-12 C/N)
Piezoelectric Voltage Constants
g33 ( x 10-3 Vm/N)
g31 ( x 10-3 Vm/N)
Relative Dielectric Constant, KT3 (low
signal)
Density, ρ (kg/m3)
Dimensions of PZT
76.2
Breadth (mm)
1
Material properties of PZT
Elastic Constants, short circuit
550
- 265
19
-9
3100
7500
sE11 (x 10 –12 m2/N)
sE33 (x 10 –12 m2/N)
Frequency Constants (Hz-m)
Np (planar mode disk)
Nt (thickness mode disk)
Mechanical Quality Factor, Qm
o
Curie temperature, Tc ( C)
Table 2. Dimensions and properties of PZT
25.4
21
15
1950
2000
65
190
Experimental Procedure
Open-loop experiments were carried out first followed by closed loop experiments. Open loop experiments are those in which
there is no feedback (i.e the loop is open). In open loop experiments a constant voltage of 100V was applied to the PZT and
the effect of this voltage on the load carrying capacity of the column is studied. This was followed by closed loop experiments.
In a closed–loop control system, the output of the process is constantly monitored by a sensor (i.e. strain gauges). Here the
output is the strain gauge voltage. Multiplying the stain gauge voltage with the calibration constant of the strain gauge amplifier
will give us the bending strain in the column. The sensor samples the system output and passes it to the controller. Here the
controller is the computer. Because the controller knows what the system is actually doing, it can make any adjustments that
are necessary to control the output. Since the controller knows the bending strain from the sensors, it can compute the
necessary voltage that must be applied to the actuator (PZT) to keep the bending strain as low as possible. The signal from
the controller to the actuator is the forward path, and the signal from the sensor to the controller is the feedback (which closes
the loop). Set point is the desired output. Here the desired output is zero bending strain (i.e. no lateral defection). By
subtracting the actual output (as reported by the sensor) from the desired output (set point), we get the system error. The
error signal represents the difference between “where you are” and “where you want to be”. The controller is always working
to minimize this error signal. Using a control strategy, which can be simple or complex, the controller minimizes this error.
Here a simple proportional control strategy was adopted for the closed loop control. The control procedure is schematically
represented in Figure 5.
Loading
Top cover plate
Roller
Sliding
Guide
Specimen column
Base
l
Figure 4. Fabricated experimental setup
Computer
with ADC Card
Wheatstone
bridge circuit and
amplifier
Load-strain
plots
High Voltage DC
Amplifier
Voltage(
Actuator
Sensors
Strain
Controlled Force
Structure (column)
Load
Figure 5. A block diagram showing the control procedure
Theoretical Analysis to find the critical buckling loads of the column specimen
The critical buckling load of the column specimens used for experiments is found theoretically assuming that the column is
ideal (i.e. without any imperfections) [2], [6]. Here the layered composite is modeled as a linear elastic and isotropic material.
The critical load as outlined in Reference [6], is obtained as a solution of the following equation.
k
(1)
tan(k1L1)tan(k 2L 2 ) = 1
k2
k1 =
P
and
(EI )1
k2 =
P
, where P is the axial load, (EI)1 is the flexural rigidity of the column alone and (EI)2 is the
(EI )2
flexural rigidity of the column including the surface bonded PZT. L1 is half the length of the PZT and L2 is ( L/2 − L1), where L is
the length of the column. Solving Equation 1 gives the critical buckling load of the stepped column. The critical buckling loads
of the column specimens with and without PZT are given in Table 3.
Pcritical
Specimen 1
With PZT
Without PZT
36.58N
27.81N
Specimen 2
With PZT
Without PZT
33.15N
25.12N
Table 3. Critical buckling load of column specimens
Open-loop experiments
In the open loop experiment, a 100V was applied continuously to the PZT and the effect of voltage on the buckling of column
was studied. The voltage was applied immediately after the loading commenced. The maximum DC operating field of the PZT
was 200V/mm. The PZT was axially polarized so that a voltage V, applied across its thickness resulted in strain along its
length. The voltage was applied to the PZT strip such that the strip contracts in the thickness direction and elongates in the
length direction. As a result the PZT strip induced a tensile force and a reactive moment at the column centre. This reduced
the bending strain in the test specimen and forced it to behave in a straighter manner. The results are shown in Figure 6.
Load Vs Strain
40
36.58N
35
32.19N
load (in N)
30
27.54N
25
with 100 V
without Voltage
P(critical)
20
15
10
5
0
0
50
100
150
200
250
strain (in microns)
Figure 6. Load strain plots with 100V
Specimen 1 was used in open loop experiments. Initially buckling analysis was performed without pasting the PZT. The
maximum load that the column could support was 18.16N. This is less than the theoretical buckling load calculated i.e.
27.81N, which is given in Table 3. This is postulated to be due to the initial imperfections, load eccentricity and flaws during
the fabrication of the composite. Then the buckling analysis was done after placing the PZT and without applying any voltage.
The maximum load the column could support was 27.54N. Then the PZT was actuated with 100V and the buckling analysis
was performed again. With a voltage of 100V, the bending strains were introduced into the column such that it counteracted
the bending strain due to loading, resulting in an increase in load carrying capacity of the column. The column buckled at a
load of 32.19N. The load carried by the column corresponding to a strain of 150 microns is used for comparison. Thus there
was an increase in the load carrying capacity of the column from 27.54N to 32.19N. This corresponds to 16.88% increase
compared to that of the uncontrolled behaviour. This indicates that the application of a control voltage can enhance the
buckling load of a column. In the open loop experiments, this enhancement is due to a predetermined external voltage. It is
possible to determine this required control voltage, actively, i.e., based on the difference between desired strain and the
observed bending strain. This is achieved in the closed loop experiments described in the next section. The theoretical
buckling load of specimen 1 (36.58N, Ref. Table 3) is also shown in Figure 6.
Closed-loop experiments
In the closed loop experiments, the voltage applied to the actuator was proportional to the error. The control action of a
proportional controller is defined as [7]
Vin (t ) = K pe(t ) = K p (V (t ) − V0 (t ))
(4)
where, Vin(t) is the input voltage to the actuator (PZT), KP is the proportional gain constant and e(t) is the error signal = ( v(t) −
v0(t) ) in which v0(t) is the desired voltage and v(t) is the amplified strain gauge voltage (as reported by the sensor). The
proportional control applies a gain to the error signal and sends it as an input to the system so that the error signal decreases
in a few cycles.
Specimen 2 was used for closed loop experiments. From the experiments carried out without control, the maximum load the
column could support was 23.74N. This corresponds to 71.57% of the theoretical critical buckling load (33.15N, Ref Table. 3).
This could be due to manufacturing and geometric imperfections in the column specimen. Then active control was done with
KP = 1500. The column buckled at 29.45N. The load carried by the column corresponding to a strain of 200 microns is used
for comparison. Thus there was an increase in load carrying capacity of the column from 23.74N to 29.45N. This corresponds
to 24.05% increase compared to that of the uncontrolled behaviour. Figure. 7 shows the load-strain plots obtained for the
case of active control and the case without control. The theoretical buckling load of specimen 2 (33.15N, Ref. Table 3) is also
shown in Figure 7. The plots are smoothened by averaging to remove the noise in the data. The bend in the final part of the
plot without actuation is postulated to be due to kinking in the glass/epoxy composite specimen. The closed loop experiments
shows that the moments induced by the piezoelectric patches could force the column to behave in an ideal manner.
Figure 7. Load strain plots with active control
The results of both open loop experiments and closed loop experiments are shown in Table 4. A higher percentage of
increase in the load carrying capacity can be obtained using closed loop control. This increase in the load carrying capacity is
of the same order that was demonstrated by Thompson et.al[5]. But this increase in our experiments was achieved using a
single patch of PZT while Thompson et.al [5] used two patches of PZT. A better control over the bending strain can be
achieved by improving the control strategy. Thompson et.al[5] encapsulated the PZT actuators in E-glass/epoxy to provide
electrical insulation. In our experiments, the PZT was directly bonded to the specimen as glass/epoxy composite is a good
electrical insulator. If aluminium specimens are used, the specimens need to be anodised to avoid electrical contact between
the PZT strip and the column [2].
Without actuation
With actuation
% increase
Open loop
Experiment
27.54N
32.19N
16.88
Closed loop
Experiment
23.74N
29.45N
24.05
Table 4. Comparison of results
Summary and Conclusion
This paper investigates the use of PZT as actuator to control the buckling of composite column structures. Open loop
experiments and closed loop experiments were carried out on glass/epoxy composite column specimens. The open loop
experiments clearly indicated that the piezoelectric force could remove bending strain in an axially loaded column. From the
experience obtained from open loop experiments, closed loop experiments were done. The open loop experiments
demonstrated a 16.88% increase in the load carrying capacity of column compared to those without the application of voltage.
The closed loop experiments clearly demonstrated a 24.05% increase in the load carrying capacity of the column compared to
those without induced actuation.
Since the piezoelectric strip was placed only at the centre, the first mode alone could be controlled in the current experiments.
Applying reactive moments at the centre alone cannot force the column to carry a higher load than the theoretical critical
buckling load (Ref. Table 3). The load carrying capacity of the column can be increased above the theoretical critical buckling
load by forcing the column to buckle in the second mode (or any other higher mode). For this the number of actuators used
need to be increased, increasing the number of half waves into which the column is deformed. The placement and length of
these actuators need to be studied in detail to obtain optimum control. The future study will be focused on controlling the
higher modes of buckling of column structures and optimization of the location of sensors and actuators. The higher modes
can be controlled using a network of PZT actuators on the column.
Acknowledgements
This study has been carried out as part of an investigation of the project ‘Buckling control of nozzle shells using PZT’, a
sponsored project by IIT-ISRO cell. This support is kindly acknowledged. The authors would also like to thank the technical
assistance offered by Mr. Santhosh Kumar S and Mr. France K.
References
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Actuators”, Proceedings of the Fourth International Conference on Smart Materials, Structures and Systems, SA156 –
SA162(2005).
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(2006), presented.
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Actuators”, Composite Structures, 32, 59-67(1995).
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