Received 11 April 2007 Published 29 June 2007
Online at
stacks.iop.org/SMS/16/1179 AbstractThis paper describes a method to vary the flexural bending stiffness of a multi-layered beam. The multi-layered beam comprises a base layer with polymer layers on the upper and lower surfaces, and stiff cover layers.
Flexural stiffness variation is based on the concept that when the polymer layer is stiff, the cover layers are strongly coupled to the base beam and the entire multi-layered beam bends as an integral unit. In effect, we have a
‘thick’ beam with contributions from all layers to the flexural bending stiffness. On the other hand, if the shear modulus of the polymer layers is reduced, the polymer layers shear as the base beam undergoes flexural bending, the cover layers are largely decoupled from the base, and the overall flexural bending stiffness correspondingly reduces. The shear modulus of the polymer layer is reduced by increasing its temperature through the glass transition. This is accomplished by using embedded ultra-thin electric heating blankets. From experiments conducted using two different polymer materials, polymer layer thicknesses and beam lengths, the flexural stiffness of the multi-layered beam at low temperature was observed to be between two and four times greater than that at high temperature.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
There has been considerable interest in recent years in the use of variable-stiffness elements for semi-active structural control.
In the early 1990s seminal work was conducted in Japan using variable-stiffness devices for seismic response control [1, 2].
These were hydraulic devices with regulator valves which effectively activated or deactivated the chevron bracing in the different stories of the building to minimize the seismic response. In [3], a semi-active variable-stiffness device was proposed comprising four spring and telescoping tube elements arranged in a rhombus configuration. The device stiffness changes by reconfiguring the aspect ratio of the rhombus using a control rod powered by a DC servomotor. Reference [4]
reports on variable-stiffness telescoping axial truss members.
When a piezoelectric actuator installed on the inside contracts, the clamp between the two telescoping elements is released and the axial stiffness goes to zero. Extension of the piezoelectric actuator clamps the elements to each other and restores the
3 Author to whom any correspondence should be addressed.
axial stiffness. The smart spring concept in [5] comprises a primary spring in the load path and a secondary active spring in parallel, connected to a piezoelectric stack actuator. On application of a voltage the piezoelectric actuator generates a normal force against a structural sleeve and engages the secondary spring. One of the disadvantages of such a system is that it is dependent on friction.
Stiffness variation can also be implemented through the use of smart materials. For example, researchers have demonstrated stiffness change through capacitive shunting [6]
and state-switching of piezoelectric materials [7, 8]. Shape memory alloys (SMAs) undergo austenite–martensite phase transformations with change in temperature, and the Young’s modulus in the austenite phase can be 2–3 times greater than that in the martensite phase [9, 10]. More recently, there has been a great deal of interest in shape memory polymers (SMPs), which display large reductions in modulus and high strain capability at high temperature but can store the strains and stiffen by orders of magnitude when cooled below the glass transition temperature [11–13]. The stored strain can be recovered on heating the polymer.
Figure 1. Schematic representation of a multi-layered beam, and deformation modes corresponding to high and low polymer shear moduli.
References [14] and [15] examine the use of SMPs for morphing aircraft wings. Variable-stiffness elements are particularly interesting for application to morphing aircraft structures because load-bearing aircraft structures are required to be stiff under normal operation, but such structures would require very high morphing actuation force and power.
The possibility of reducing the stiffness during morphing, accomplishing shape or form change at low actuation cost, and reverting to a high-stiffness load-bearing structure for normal operation, is certainly an intriguing idea. Another interesting recent example of variable stiffness in morphing aerospace applications proposes the use of rotating spars in adaptive aeroelastic wings [16]. In [17], the authors report on laminar morphing materials using SMPs for variable connectivity between stiff elements.
Depending on the specific application, the stiffness variations required may either be per cycle or quasi- static. Semi-active systems with quasi-static stiffness/damping changes are also described as adaptive–passive systems. A capacitively shunted piezoelectric material can undergo a rapid change in stiffness, but the magnitude of the stiffness change is relatively modest. In contrast, a shape memory polymer can undergo very large changes in stiffness but since the stiffness change is temperature driven, the bandwidth is expected to be quite low. Such systems, however, would be very well suited for applications where quasi-static, or relatively slow, variation in stiffness is required.
The current paper describes a method for introducing change in flexural stiffness of a multi-layered beam. A complete description of the underlying physical mechanisms is presented in section2. This is followed by a description of the experiment and a discussion of the experimental results in sections3and4.
2. Description of concept for beam flexural stiffness variation
Figure 1(a) shows a schematic representation of a multi- layered beam with stiff (metal or composite) layers and an intermediate polymer layer. For the purpose of discussion here, the bottom layer is referred to as the base beam, and the top layer is also referred to as the cover layer. When subjected to
Figure 2. Typical variation in the polymer shear modulus with increase in temperature.
flexural bending, the deformation mode of this multi-layered beam depends strongly on the shear modulus of the polymer layer, vis-`a-vis the properties of the base beam and cover layer.
If the shear modulus of the polymer layer is very high, the deformation is as shown in the schematic in figure1(b). The stiff top layer is coupled to the base beam, and all three layers contribute to the flexural bending stiffness. Thus, when the polymer layer is stiff, the multi-layer beam behaves like an integral structure with a large cross-section thickness and a correspondingly high flexural bending stiffness. On the other hand, if the shear modulus of the polymer layer is low, the multi-layered beam deforms as depicted in the schematic in figure1(c). In this case, the cover layer acts as a constraining layer, thereby inducing shear in the compliant polymer layer, as the base beam undergoes flexural bending. Passive and active constrained layer damping treatments work on this very principle (see, for example, [18–21]). Flexural vibration of the base structure induces cyclic shear in the viscoelastic layer that is covered by a stiff constraining layer. This results in energy dissipation and damping augmentation. For the purposes of this work, it should be noted that shear deformation in a compliant polymer layer essentially decouples the stiff cover layer from the base beam, and the overall flexural stiffness then is determined largely by the contribution of the base beam, with little contribution from the cover layer. On the other hand, when the base beam and cover layer are coupled by a stiff shear layer, the multi-layered beam behaves more like an integral beam structure with high thickness, and all sections contribute to the overall flexural stiffness. It is clear, then, that the overall flexural stiffness could be controlled if the shear modulus of the intermediate polymer layer could be varied.
The shear modulus of a typical polymer reduces significantly with increase in temperature. Figure 2 (with data from [22]) shows this characteristic for a couple of commercially available polymers. At low temperatures, the polymer is in the glassy state and has high shear modulus.
As the temperature increases, the polymer goes through glass transition and its shear modulus rapidly decreases. At high temperatures, the polymer is in the rubbery state and its shear modulus can be several orders of magnitude lower than the glassy modulus. By varying the temperature of the polymer layer, and correspondingly varying its shear modulus, the cover
Figure 4. Schematic representation of the experimental set-up.
layer could be decoupled, to varying degrees, from the base beam (at high temperatures) or strongly coupled to the base beam (at low temperatures). Correspondingly, the overall flexural stiffness of the multi-layered beam could be varied.
In the present work, a thin electric heat pad is used control the temperature of the intermediate polymer layers.
3. Experimental set-up
This section describes the tests conducted to demonstrate the concept described in the previous section. Figure3shows a photograph of a section of a multi-layered beam comprising a central aluminum base beam, polymer layers attached to the top and bottom surfaces of the base beam, and aluminum cover sheets. The multi-layer beam is symmetric about the mid- plane. Each polymer layer itself comprises two sublayers, with an ultra-thin Kapton electric heat blanket embedded between. The heating blankets have adhesive backs and can thus be easily attached to the polymer sublayers. The polymer sublayers are glued to the aluminum layers using Permabond 922 allyl cyanoacrylate high-temperature adhesive.
By applying a current to the heating pad the temperature of the polymer can be raised.
Figure4provides a schematic representation of the entire experimental set-up and figure 5 provides a photograph of the same. The multi-layered beam is clamped at one end (only the base beam) and is free at the other, as shown.
A Barber–Colman Model 7SF temperature controller was used to maintain a constant temperature of the heating pads
Figure 5. Photograph of the experimental set-up.
based on the feedback from a thermocouple. A Barber–
Colman Type J strand construction thermocouple, model P111- 00100-048-7-03, was used, and was glued between the top aluminum layer and the adjacent polymer sublayer. A set- point was input manually into the temperature controller, which then provided power to the heating pads until this set- point was reached. The controller was able to maintain this temperature while increments in upward vertical force were applied to the free end of the beam, and the corresponding tip displacements were measured using a dial gage. From the force versus tip displacement curve generated in this manner, an effective flexural stiffness at that specified temperature could be calculated. The temperature set-point is then varied, and the process repeated to obtain the changed flexural stiffness.
Tip force increments were applied by rotating a 1/4 inch, 28 cap screw located under the free end of the beam, with the cap screw acting like a small mechanical jack when rotated gently by hand. The force exerted was measured by an Omega 25 pound capacity ‘S-beam’ load cell (model LCCA-25). The load cell has a 1/4 inch 28-thread pattern tapped into both ends that allowed for connection to the cap screw above, and provided a mounting point to secure the load cell to a platform below. This load cell was connected to an Omega model LCCA-25 strain gage panel meter. The meter provided a 10 V excitation voltage, and conditioned the returning signal such that the resulting output was displayed in engineering units. The output of the load cell was previously calibrated by applying known static loads. A mechanical dial gage was mounted above the tip of the test specimen to register the deflection as the load was being applied.
Eight different specimens were fabricated and tested, using two different polymer types, two different beam lengths, and two different polymer thickness values. The two polymer materials used were a cast acrylic material (polymer 1) and PVC type I material (polymer 2), purchased from McMaster Carr. The polymer sublayer thickness values used in the tests were 0.0625 and 0.125 inch. The width of all sections—the base beam, polymer-layers, and the cover layers—was 1 inch.
Each of the Kapton heat blankets was 1 inch in width and 5 inch in length. The specimens tested had a beam length,L, in figure4, of either 4.5 inch (using a single heat blanket between two polymer sublayers) or 9 inch (using two heat blankets along the length between polymer sublayers). The aluminum
Figure 6. Measured tip displacement versus applied tip load, corresponding to different polymer layer temperatures.
Figure 7. Compilation of variation in beam flexural stiffness versus temperature results for polymer 1.
central base layer and the top and bottom cover layers were each 0.1875 inch thick×1 inch wide. The Kapton heat blankets were rated at 10 W of power per linear inch, so the total power consumption was under 100 W for the 4.5 inch specimens tested and under 200 W for the longer 10 inch specimens.
4. Experimental results and discussion
For increments in applied load, figure 6(a) shows the corresponding measured tip displacements for 0.061 25 inch thick polymer 1 (cast acrylic) sublayers. Figure 6(b) shows similar results for 0.125 inch thick polymer 1 sublayers. The beam length for the results in both figures is 4.5 inch and data are presented for several different temperatures ranging from
80 to 300◦F. Since the force versus tip displacement behavior at any temperature appears linear, the slope of the line, dF/dx, is used as a measure of the effective flexural stiffness at that temperature.
Figures7and8present a compilation of variation in beam flexural stiffness versus temperature results for polymers 1 and 2, respectively. For polymer 1 a clear reduction in beam flexural stiffness is observed between 125 and 250◦F for the 0.06125 inch sublayer thickness cases (figures7(a) and (b)).
For larger sublayer thickness of 0.125 inch (figures 7(c) and (d)), the stiffness reduction appears to begin at lower tem- peratures. The shorter beams (figures7(a) and (c)) have a larger flexural stiffness than the longer beams (figures 9(b) and (d)), as expected, and appear to show smaller changes in flex-
Figure 8. Compilation of variation in beam flexural stiffness versus temperature results for polymer 2.
ural bending stiffness (low-temperature to high-temperature stiffness ratios of 2.03 to 2.6) than the longer beams (low- temperature to high-temperature stiffness ratios of 2.83 to 3.2).
For polymer 2 reductions in beam flexural stiffness are again observed mostly between 125 and 250◦F (figure 8), corresponding to the transition of the polymer from the glassy to the rubbery state. As with polymer 1, the longer beams undergo a larger changes in flexural bending stiffness (low- temperature to high-temperature stiffness ratios of 2.83 to 4, figures8(b) and (d)) than the shorter beams (low-temperature to high-temperature stiffness ratios of 2.1 to 2.25, figures8(a) and (c)).
It should be noted that the magnitude of the flexural bending stiffness change that can be achieved is strongly dependent on the system parameters. The key parameters are the thickness and the modulus of the cover layer, relative to the base beam; and the thickness, the shear modulus, and the variation in the shear modulus through glass transition, of the polymer layer relative to the base beam. For thicker, stiffer cover layers, and polymers that undergo very large reduction in shear modulus through the glass transition, the reductions in flexural bending stiffness of the multi-layered beam can be substantially larger than those seen in the experiments reported in this paper. An attractive feature of the proposed method for flexural stiffness variation is that only the polymer layers, and not the entire structure, need to be heated. Thus the energy requirements are very modest.
5. Summary and concluding remarks
This paper describes a method to control the flexural bending stiffness of a multi-layered beam. The multi-layered beam
comprises a base layer with polymer layers on the upper and lower surfaces, and cover layers. The base beam and the cover layers can be of metal or composite. The polymer layers each comprise two sublayers with an ultra-thin electric heating blanket between. The heating blankets, a thermocouple and a temperature controller are used to modulate the temperature of the polymer layers. A tip force was applied to the beam and the tip displacement was measured. The displacements were measured and stiffness calculated for variation in temperature of the polymer layer. Experiments were conducted for two different polymer materials, polymer thickness and beam lengths. The results showed that the flexural bending stiffness of the multi-layered beam reduced with increase in temperature, corresponding to the softening of the polymer as it transitions from the glassy to the rubbery state. For the experiments conducted, the flexural stiffness of the multi- layered beam at low temperature was observed to be between two and four times greater than that at high temperature.
References
[1] Kobori T, Takahashi M, Nasu T, Niwa N and
Ogasawara N 1993 Seismic response controlled structure with active variable stiffness system Earthq. Eng. Struct.
Dyn.22 925–41
[2] Takahashi M, Kobori T, Nasu T, Niwa N and Kurata N 1998 Active response control of buildings for large
earthquakes—seismic response control system with variable structural characteristics Smart Mater. Struct.7 522–9 [3] Nagarajaiah S and Sahasrabudhe S 2006 Seismic response
control of smart sliding isolated buildings using variable stiffness systems: an experimental and numerical study Earthq. Eng. Struct. Dyn.35 177–97
[7] Clark W W 2000 Vibration control with state-switching piezoelectric materials J. Intell. Mater. Syst. Struct. 11 263–71
[8] Corr L R and Clark W W 2002 Comparison of low-frequency piezoelectric switching shunt techniques for structural damping Smart Mater. Struct.11 370–6
[9] Otsuka K and Wayman C M 1998 Shape Memory Materials 1st edn (Cambridge: Cambridge University Press) pp 203–19
[10] Hodgson D E 1988 Using Shape Memory Alloys (Sunnyvale, CA: Shape Memory Applications)
[11] Wei Z G, Sandstrom R and Miyazaki S 1998 Review:
shape-memory materials and hybrid composites for smart systems J. Mater. Sci.33 3743–62
[12] Lendlein A and Kelch S 2002 Shape-memory polymers Angew.
Chem. Int. Edn41 2034–57
[13] Atli B, Gandhi F and Karst G 2007 Thermomechanical characterization of shape memory polymers Electroactive Polymers and Devices (EAPD); Proc. SPIE6524 65241S [14] Perkins D A, Reed J L Jr and Havens E 2004 Adaptive wing structures Smart Structures and Materials 2004: Industrial
May 2006) (Rhode Island: AIAA) AIAA 2006-2131 [17] McKnight G and Henry C 2005 Variable stiffness materials for
reconfigurable surface applications Smart Structures and Materials 2005: Active Materials: Behavior and Mechanics;
Proc. SPIE5761 119–26
[18] Gandhi F 2001 Influence of nonlinear viscoelastic material characterization on performance of constrained layer damping treatment AIAA J. 39 924–31
[19] Gandhi F and Munsky B 2002 Effectiveness of active
constrained layer damping treatments in attenuating resonant oscillations J. Vib. Control 8 747–75
[20] Gandhi F and Munsky B 2002 Comparison of damping augmentation mechanisms with position and velocity feedback in active constrained layer treatments J. Intell.
Mater. Syst. Struct.13 259–326
[21] Gandhi F, Remillat C, Tomlinson G and Austruy J 2007 Constrained layer damping with gradient viscoelastic polymers for effectiveness over broad temperature range Proc. Conf. on 13th AIAA/ ASME/AHS Adaptive Struct.
(Austin, TX, April 2005); AIAA J. 45 1885–93
[22] Nashif A D, Jones D I G and Henderson J P 1985 Vibration Damping (New York: Wiley)
