Passive Damping of Solar Array Vibrations Using Hyperelastic Shape Memory Alloy with Multilayered Viscous Lamina

Abstract

A novel passive vibration-damping device is proposed and investigated for a large deployable solar array. One strategy for achieving high damping in a solar panel is using a yoke structure comprising a hyperelastic shape memory alloy and multiple viscous adhesive layers of acrylic tape. The effectiveness of the proposed system in achieving a high damping performance was demonstrated by conducting free vibration and low-level sine sweep tests using a solar array, and a 0.75-m-long flexible dummy structure was simulated. We also investigated the dependence of the damping performance of the proposed structure on the number of viscous lamina layers. Finally, the damping characteristics of the proposed system were assessed under predictable on-orbit temperature conditions.

1. Introduction

The global demand for the development of satellites aligned with New Space trends is steadily growing [1]. Economic satellite development is one of the philosophies underlying the New Space concept, for which small satellites are suitable because they can be developed in the short term at a low cost. Owing to the massive production of small satellites, large constellation systems can be realized, and such systems have been increasingly used [2]. However, the number of system requirements required to satisfy the power budget has increased because satellite missions are becoming much more complicated and advanced. To satisfy these requirements, deployable solar panels are primarily used. With technological advancements, the size of such solar panels is also increasing. Satellite attitude maneuvers and thermal shock induce elastic vibration modes in large solar panels, which degrade the mission performance of satellites when strict pointing accuracies are required [3]. Moreover, one main source that degrades the performance of observation satellites is the vibration induced in their solar panels due to frequency coupling between flexible vibration modes of solar panels and jitter disturbance sources (e.g., reaction wheels, control moment gyroscopes, and cryogenic coolers). However, except for some deep space probes, most satellites are not equipped to obtain solar energy without using a large deployable solar panel. Unlike the trend of decreasing satellite size, external payloads tend to increase. Therefore, the need to monitor and manage the vibrations of large deployable appendages has increased. Thus, a new technical solution must be developed to suppress the vibrations of large deployable solar panels to realize future advanced missions, such as inter-satellite laser communication, ultra-silent high observation platforms, and rendezvous docking missions.

The two approaches for suppressing vibrations are active and passive control methods. Active vibration control is based on a sensor that analyzes the vibration signal transmitted to a mechanical system and an actuator that generates an antiphase vibration signal [4,5,6]. Active control systems exhibit a high vibration-reduction performance because the torque or force produced by an additional actuator directly suppresses the vibrations in the structure. Several types of active vibration control strategies for reducing solar-array vibrations have been proposed in previous studies. For example, Li et al. [7] proposed an autonomous decentralized intelligent vibration control for large split-blanket solar arrays. Numerical simulations were also performed to validate the proposed control strategy, which verified that the elastic vibration of the solar panel could be reduced by decreasing the speed fluctuation in the deployment phase. For smart grid structures, Kwak et al. [4] proposed an active vibration control based on multi-input and multi-output positive position feedback controllers to manage the stability and spillover effect of the systems.

Passive systems have the advantage of system simplicity, although their performance is lower than that of active systems. Additionally, the so-called spillover phenomenon, which is a major limitation in active systems, does not occur in passive systems. The usage of passive systems due to their high reliability is an attractive strategy for space applications. Several passive systems have been proposed for this purpose. Kong et al. [8] proposed a passive damper to suppress the vibrations of a deployable solar panel. This damper system was placed at the root hinge of the solar panel, and it effectively improved the damping performance of a satellite equipped with a solar array driving mechanism. Anandakrishnan et al. [9] proposed a passive system comprising titanium flexural and viscoelastic damping materials to suppress the vibration of an SA-3 Hubble Space Telescope solar array. The proposed damper was attached to the lower part of the solar panel mast to reduce the structural vibrations induced in the control system and to improve the damping performance of the overall structure.

In this study, the vibration of the solar panel was damped using a passive control method, which is advantageous for system simplification, and avoids the need for a separate damper and increased stiffness by applying a strut structure. To suppress solar-panel vibrations using a passive control method, we focused on two technical aspects: the hyperelastic effect of a shape memory alloy (SMA) and a multilayered structure containing viscoelastic tapes. Hyperelasticity is a unique characteristic of SMA materials. It occurs when the materials undergo a phase transformation from austenite to martensite at a temperature above the finish temperature of austenite. It allows the materials to deform significantly without facing plastic deformation and thus to return to their original shape when the load is removed. This effect is related to the large hysteresis damping caused by phase transformation [10]. Due to hyperelasticity, SMA materials exhibit excellent damping performance in a vibration environment. Many studies have been conducted on the space applications of hyperelastic SMAs. Kwon et al. [11] proposed a thin blade-type hyperelastic SMA gear wheel to improve the performance of a two-axis gimbal-type X-band antenna by isolating micro-jitter vibrations without causing plastic deformation of the blades under excessive load conditions. Kwon et al. [12] proposed a blade-type cooler isolator designed using a hyperelastic SMA material. A vibration test was conducted to demonstrate the effectiveness of the blade, and its performance was compared to that of an isolator made of common titanium.

However, a hyperelastic SMA shows effective damping performance only when the critical stress point exceeds a threshold at which phase change occurs. This implies that, if structural deformation is not sufficiently large, the SMA may exhibit relatively poor damping performance. To address this, a multilayered structure containing viscoelastic tapes was used to improve the damping performance of an SMA material even under relatively small structural deformations of the material. The damping performance of a hyperelastic SMA material, along with multilayered viscoelastic tapes, has been validated in previous studies. Park et al. [13] proposed a whole-spacecraft vibration isolator (WSVI) to attenuate the dynamic launch loads transmitted to small satellites. The isolator used hyperelastic SMA blades comprising multilayered thin plates laminated with a viscous tape to achieve excellent damping using the WSVI. Several tests were performed to validate the effectiveness of the design. The results showed that the proposed WSVI exhibited satisfactory launch-vibration isolation performance.

A multilayered viscous damping strategy that maximizes the damping capability of a system has been implemented in many applications, such as printed circuit board (PCB) and CubeSat solar panels. A high-damping PCB with multilayered viscoelastic tapes was proposed for wedge-lock applications to validate the effectiveness of the proposed strategy in a launch random vibration environment [14,15]. The test results indicated that the proposed PCB effectively enhanced the fatigue life of the solder without causing any mechanical failures of the solder joints or delamination and fracture of the interlaminated layers. Additionally, the use of 3U and 6U solar panels incorporating multilayered viscoelastic tapes to ensure the structural safety of brittle solar cells under severe launch vibration environments has been validated for CubeSat applications [16,17].

In this study, we focus on the effective mechanism of vibration energy dissipation attained by the use of a hyperelastic SMA and multilayered viscous lamina to suppress the vibrations of a large flexible deployable solar array. One strategy for achieving high damping in a solar panel is to use a yoke comprising hyperelastic SMA plates bounded with multilayered viscous adhesive layers of acrylic tape. Based on this, we propose a hyperelastic SMA-based multilayered high-damping yoke that can contribute to system simplification by effectively damping solar panel vibration via a passive vibration control method that ensures high damping performance to the yoke—the interface between the solar panel and satellite. Significantly, one of the advantages of the proposed technology, which involves providing damping performance to the yoke part, is its ease of application to various systems, including SADA, without the need for additional structures and constraints. The method and technology for reducing solar panel vibration, as presented here, is a novel approach that has not been previously proposed.

To validate the effectiveness of the design in terms of reduction of the elastic vibrations of the solar panel, free vibration tests and low-level sine sweep (LLSS) tests were performed using a 0.75-m-long dummy solar panel at a 1st eigenfrequency of 1.2 Hz. Additionally, the dependence on temperature of the damping performance of the proposed system was investigated. The test results demonstrate that the proposed approaches are effective in achieving the design goals of this research.

The remainder of this paper is organized as follows. Section 2 describes the design of the proposed high-damping yoke structure, as well as the test specimens and the experimental setup. Section 3 presents the results obtained, technical assessments of the proposed high-damping yoke, and its vibration suppression performance. Finally, Section 4 presents the concluding remarks.

2. Materials and Methods

2.1. Design Description of the High Damping Yoke

Figure 1 shows the design of the high-damping yoke structure proposed for the passive suppression of vibrations in a solar array assembly. The yoke structure is positioned at the root of the solar array, as shown in Figure 1a, which significantly helps in dissipating the vibration energy of the solar array. A passive-based strategy for improving the capability of the yoke in damping the vibrations is illustrated in Figure 1b. As shown in the figure, the yoke is mainly composed of hyperelastic SMA, viscoelastic, and thin plates. Hyperelastic SMA plates are used as the yoke base to provide mechanical stability for the solar array when it is in orbit. Additionally, the base is used as a mechanical interface for stacking multilayered viscous lamina on both sides of the SMA plate. The double-sided viscoelastic adhesive tapes (3M™ 966, 3M Company, Saint Paul, MN, USA) provide sufficient bonding strength for each layer constrained by FR4 thin plates. FR4 is used to implement a mechanical constraint on each adhesive layer. This is because it is an electrically nonconductive material and can thus prevent unexpected electrostatic discharge in an orbit environment. The thicknesses of the various layers in the high-damping SMA yoke structure are shown in Figure 1b.

The hyperelastic SMA material used in the yoke has the advantage of being hyperelastic; moreover, it exhibits high damping capability compared to ordinary metal materials [10]. Hyperelasticity is known to allow an SMA a complete reversion to its original size for strains up to 8–15% while preventing the material from undergoing plastic deformation, which is an unusual feature for metallic materials [3]. Additionally, it exhibits hysteresis characteristics so that mechanical energy is dissipated during the phase change from austenite and martensite depending on the presence or absence of an external load [10]. As per the aforementioned characteristics, the phase-change-enhanced damping capability of the SMA material is expected to contribute to the effective suppression of the vibrations of the solar panel while preventing the material from undergoing plastic deformation when the displacement of the solar panel is large.

Table 1. Material properties of the hyperelastic SMA. Data from [12].

Characteristic		Value
Martensite Finish Temperature (Mf, °C)		−21
Martensite Start Temperature (Ms, °C)		−12
Austenite Start Temperature (As, °C)		−5
Austenite Finish Temperature (Af, °C)		15
Young’s Modulus (GPa)	Martensite	75
	Austenite	80
Tensile Strength (MPa)		1300
Elongation at Break (%)		45
Density (g/cm3)		6.45
Poisson’s Ratio (ρ)		0.33

summarizes the material properties of the hyperelastic SMA used in this study [12].

However, the usage of hyperelastic SMA materials for suppressing the vibrations of solar panels has some limitations when the amplitude of vibration is relatively small because the phase transformation between austenite and martensite may not induce increased damping in this case. To maximize the damping performance of the passive system, regardless of the amplitude of the vibrations of the solar panel, we used a multilayered viscous lamina comprising double-sided viscoelastic adhesive tapes and a thin-plate constraint layer. The adhesive bonding technique is an attractive method that easily reduces stress and weight and is cost-effective [18]. Additionally, it offers ecological benefits, such as reduced corrosion and improved fatigue behavior [19]. The effectiveness of this strategy has been validated in several previous studies, including those conducted on vibration damping for PCB and CubeSat solar panels [14,15,16,17]. The mechanism of vibration energy dissipation in the proposed design is as follows: each boundary layer between the adhesive tapes and constrained thin plates experiences slip in the shear direction when the yoke is deformed, resulting in frictional energy dissipation. The viscoelastic tape used in this study has a history of actual space missions, and its specifications are listed in

Table 2. Specifications of the viscoelastic adhesive tape (3M966). Data from [20].

Item	Specification
Type	Double-Sided Tape
Material	Acrylic
Thickness (mm)	0.06
Allowable Temperature (°C, for long period)	−40 to 149
Adhesion Strength (N/100 mm)	58 (20 min Dwell)
	85 (72 h Dwell)
	159 (Ultimate Bond)
Outgassing (%, TML/CVCM)	0.93/0.01

[20,21].

The notable features of the proposed multilayered SMA yoke are its simplicity and system stability: high damping can be easily achieved using the multilayered viscous lamina, and the system is highly stable because it dissipates energy via a passive mechanism. It can also be used for solar array driving mechanism applications because it can be directly connected to a solar array driving assembly without degrading the stiffness of the solar array.

2.2. Vibration Suppression Test of the Solar Array

To verify the effectiveness of the proposed high-damping SMA yoke structure, we performed free vibration and LLSS tests for the passive suppression of the vibrations of a solar array for various laminated layers in the yoke structure. Additionally, we obtained and investigated the damping characteristics of the multi-laminated adhesive layers under various temperature conditions through a free vibration test.

Figure 2a shows the overall test setup configuration used for the passive suppression of the vibrations of a solar array assembly. A 0.75-m-long dummy solar array of mass 3 kg, supported by the proposed yoke, was used in the test, and the tip of the dummy structure was hung by an elastic cable for 1 g compensation. The 1st and 2nd eigenfrequencies of the solar panel were 1.2 Hz and 5.2 Hz, respectively. These correspond to the bending modes observed in the in-plane directional dynamic behavior of the solar panel under the 1 g compensation constraint.

To demonstrate the technical feasibility of the proposed design, the displacement at the center of the solar panel was measured by a laser displacement sensor (optoNCDT 2300LL, Micro-Epsilon, Ortenburg, Germany), capable of measuring data 100 times per second [22] (Figure 2b). In the free-vibration test, a certain value for the initial displacement was intentionally imposed on the middle of the solar panel. The initial displacement was then released, and the damping performance under the subsequent free-vibration response was evaluated using the calculated damping ratio. The damping ratio ($\zeta$) is calculated using the logarithmic decrement method as follows [23]:

$$\delta =ln\frac{u\left(t\right)}{u\left(t+T\right)},$$

(1)

$$\zeta =\frac{\delta }{\sqrt{4{\pi }^2+{\delta }^2}},$$

(2)

where $u\left(t\right)$ is the behavioral displacement of the middle of the solar panel, which is the final value of the amplitude—that is, the overshoot at time $t$; and $T$ is the period of the solar panel vibrations. The forced response of the solar panel assembly, including the 1st and 2nd eigenfrequencies of the solar panel, was measured through an LLSS test. In the test, the solar array was excited using an eddy-current-type noncontact vibration shaker. The shaker comprises a permanent magnet and a solenoid coil, as shown in Figure 2c. The magnitude of the vibration force produced by the shaker can be adjusted using an amplifier and an input frequency signal generated from a function generator. Additionally, the frequency was increased from 0.1 Hz to 15 Hz for 500 s by a function generator, considering the natural frequencies of the first and second modes of the solar panel yoke. This corresponds to an increase of 0.0298 Hz per second, which is considered sufficient to measure the solar panel response for each mode.

Figure 3 shows the different test specimens used as the yoke. The specimens comprising aluminum (Case 1), hyperelastic SMA (Case 2), and SMA with multi-laminated adhesive layers (Case 3) are shown in Figure 3a–c, respectively. Detailed specifications are listed in

Table 3. Specifications of the yoke specimens.

Item	Specifications
Case	1	2		3
Material	Aluminum	Hyperelastic SMA		Hyperelastic SMA, Viscoelastic Tape, FR4
Dimension (mm)	350 × 90
No. of Constraint Layers	0	0	2	4	6
Thickness (mm)	1.1	1.5	2.1	2.7	3.3
Mass (g)	66	158	182	206	230

. We tested Case 3 specimens comprising three different numbers of viscous layers: two, four, and six. This was carried out to investigate the influence of the number of viscous lamina on the damping performance of the system.

3. Results

3.1. Free Vibration Test

The basic characteristics of the yoke specimens described in Section 3 were obtained by conducting free-vibration tests at room temperature (25 °C). The free vibration response of the solar panel assembly for the various yoke specimens was obtained after releasing an initial displacement of 10–40 mm from the middle of the solar panel, where a laser displacement sensor was attached. Initial displacement was increased to verify whether the proposed strategy was effective in suppressing both large- and small-amplitude vibrations of the solar panel.

Figure 4 shows a representative example of the free vibration test results obtained for each specimen under an initial displacement of 40 mm. The test results indicate that the SMA yoke with laminated layers (Case 3) exhibits a higher damping performance than the Case 2 specimen. These results indicate that the damping performance of the hyperelastic SMA yoke can be greatly improved by increasing the number of laminated layers, although there might be a relationship between the number of layers and the convergence of the performance. The damping enhancement owing to an increase in the number of layers is explained as follows. The shear deformation of the laminated layers is caused by the deformation of the yoke, which increases the friction and resistance force at the contact surface. Consequently, the energy dissipation of stacked viscoelastic adhesive tape layers improves.

Figure 5 shows the calculated damping ratio $\zeta$ (Equation (2)) with respect to initial displacement for each specimen. As can be observed from the figure, the hyperelastic SMA yoke (Case 2) exhibits better damping performance than does the aluminum yoke (Case 1), owing to the inherent damping characteristics of the SMA material. Moreover, the damping performance of the hyperelastic SMA yoke improves as the initial displacement increases. This is because the phase change induced by the deformation of the SMA leads to increased reversibility owing to hyperelasticity, which is an inherent characteristic of the SMA. Additionally, the hyperelastic SMA yoke did not undergo any plastic deformation when the test was repeated under large solar-panel deformation, in contrast to the aluminum yoke. This is also one of the significant advantages of the application of hyperelastic SMA materials for passive vibration suppression in solar array assembly. However, to enhance the damping performance of the passive vibration suppression system using the hyperelastic SMA, the system should be equipped to further dampen even low-amplitude vibrations of the solar panel, wherein the large hysteresis damping induced by the phase transformation of the SMA cannot be expected. The test results obtained from the multilayered SMA yoke structure demonstrate the effectiveness of the design proposed in this study. The results indicate that the damping performance is significantly enhanced by increasing the number of laminated layers. Even under a small displacement of 10 mm, the laminated yoke with 24 layers (Case 3) produces a damping ratio of approximately 0.01, which is three times higher than that exhibited by Case 2 (which does not have any laminated layers). Additionally, even at an initial displacement of 40 mm, where the damping ratio exhibited by Case 2 is the highest, the damping ratio produced by Case 3 is approximately 2.2 times higher than that produced by Case 2. This is because the large deformation of the multilayered yoke structure increases the slip on the boundary layers, which increases the amount of frictional energy dissipated. The effective dissipation of vibration energy is caused by the strong molecular attraction forces between the constraint layers and viscoelastic adhesive tapes [24]. Additionally, a resistance force generated by the adhesion of the tape to each constrained layer is observed. These phenomena cause energy dissipation within the material to achieve damping of the multilayered structure. However, the difference in the damping ratio between 16 and 24 layers is not as high as that observed between the other systems. This indicates that, as the number of layers increases, the damping performance may be saturated owing to the increment in the bending stiffness.

However, the proposed multilayered high-damping yoke may exhibit nonlinear characteristics when the solar array assembly is free to vibrate [25] owing to effects such as the hyperelasticity and hysteresis dissipation of the hyperelastic SMA, as mentioned above. Therefore, to verify the nonlinear characteristics regarding frequency, we investigated the frequency as a function of displacement during free vibration of the solar array assembly. Consequently, the frequency of Case 3 (24 layers) is 1.282 Hz and 1.266 Hz in the case of large and small displacements, respectively, indicating a difference of approximately 1.3%. This is because the thickness of the applied viscoelastic tape is very thin at 0.05 mm. Therefore, the nonlinearity is relatively low. Additionally, the damping ratio shown in Figure 5 is based on the time-domain results shown in Figure 4. The damping ratio at the displacement (first and second peak points) was calculated using the logarithmic decrement method. However, as the nonlinear characteristics may also appear in the damping, the damping ratio was calculated using the logarithmic decrement method for all inflection points of the time-domain data shown in Figure 4. Consequently, the damping ratio tends to decrease as displacement decreases in Cases 2 and 3. This is because as the displacement of the solar array assembly decreases during free vibration, the deformation of the constrained layer becomes smaller, and the resistance force at the contact surface becomes weaker. Therefore, although the proposed multilayered high-damping yoke exhibits some nonlinearity with respect to damping depending on the solar panel motion displacement, owing to the hyperelasticity of the hyperelastic SMA and the damping mechanism of the multilayered structure, the proposed design strategy based on the passive damping method is considered effective in reducing solar panel vibration regardless of the motion displacement. Indeed, the method exhibits high damping performance with little frequency change as the number of layers increases in both the large and small displacements.

Figure 6 shows the natural frequency of the solar array assembly for various numbers of laminated layers. The frequency corresponding to Case 3 with 24 layers is only 1.03 times higher than that of Case 2. Therefore, increasing the number of layers also effectively increases the structural frequency of the solar array; thus, the number of layers is an important design parameter for determining the damping and frequency of the system.

The test results obtained from the free vibration test (Figure 4 and Figure 5) demonstrate that the proposed strategy of using a multilayered hyperelastic SMA yoke is effective in increasing the extent of damping for both small- and large-amplitude vibrations. As previously mentioned, the design is intended to implement a suppression system based on a passive energy dissipation mechanism.

3.2. Low Level Sine Sweep Test

To verify the dynamic response of the solar panel assembly integrated with the yoke specimens, an LLSS test was performed. In the test, the solar panel was excited using an eddy-current-type non-contact vibration shaker, as discussed in Section 3. Excitation of the 1st and 2nd modes, where the bending modes of the solar panel are the dominant mode shapes, was considered because they are the dominant disturbance sources that can affect the pointing performance of a satellite.

Figure 7 shows the time history of the solar array assembly, as obtained from the LLSS test results. The results indicate that the displacement of the solar array is highly damped as the number of laminated layers increases. The proposed design exhibits a high damping performance in a higher-frequency vibration range, which corresponds to the 2nd vibration mode. This phenomenon is observed in the frequency response of the solar array (Figure 8). Much higher damping performance is observed in the 2nd mode frequency range than that in the 1st mode.

Table 4. Modal damping value for each mode.

Type of Yoke	1st Mode	2nd Mode
Case 2	0.003	0.007
Case 3 with 8 Layers	0.008	0.035
Case 3 with 16 Layers	0.009	0.058
Case 3 with 24 Layers	0.011	0.079

summarizes the modal damping ratios calculated using the half-power bandwidth method [26]. The highest modal damping ratio is exhibited by Case 3 with 24 laminated layers at the 2nd eigenfrequency, which is 11 times higher than that exhibited by Case 2. The difference in the damping performance between the 1st and 2nd modes is related to the shapes of modes of the solar array assembly. The 2nd bending mode is significantly more effective in increasing the energy dissipation at the interlaminated layers in the shear direction than the 1st bending mode, where the translational behavior is dominant. These test results demonstrate that the proposed design strategy based on the passive approach is effective in exhibiting an excellent vibration suppression performance for multimode vibrations of the solar array assembly.

3.3. Thermal Test

To verify the feasibility of using a multilayered hyperelastic SMA yoke in an extreme on-orbit thermal environment, the thermal characteristics of the proposed design were obtained by conducting a free-vibration test under various temperature conditions. The basic characteristics of the hyperelastic SMA and viscoelastic tapes used in this study were temperature dependent. The hyperelasticity of an SMA is guaranteed when the environmental temperature is higher than the austenite finish temperature. The viscoelastic adhesive tape used in this research has a wide range of allowable temperatures from −40 °C to 149 °C. However, the viscoelastic adhesive tape used for the multilayered structure may affect the damping performance and frequency as it changes to a glassy or rubbery state, depending on the operating temperature conditions.

Figure 9 shows the thermal test results obtained for the solar array assembly with 8 and 24 laminated layers in the yoke. The natural frequency and damping performance of each specimen was assessed via a free-vibration test at an initial displacement of 40 mm. A temperature reference point was set to ensure the stabilization of the target temperature on the yoke and the temperature was varied from −25 °C to 55 °C by the implementation of a local shroud on the specimen. As can be observed, both specimens exhibit a similar phenomenon: the damping ratio decreases as the temperature increases beyond 5 °C; subsequently, the specimens exhibit the highest damping ratio over the tested temperature ranges. This phenomenon is similar to that exhibited by a multilayered CubeSat solar panel [16], except that the temperature at which the best performance is observed is 40 °C. The variation of the damping ratio with temperature seems to be mainly related to the characteristics of the multi-laminated adhesive tapes rather than that of the SMA, because the optimized temperature at which the highest performance is shown is less than 15° C, which is the austenite finish temperature for the SMA specimen used in this study. At low temperatures, the viscoelastic tape reaches the glassy region and behaves as an elastic material, which deteriorates the damping performance of the yoke specimen whose storage modulus is high [16]. As the temperature increases, the damping performance of the yoke specimens relatively improves because the shear deformation of the constraint layers containing the viscoelastic tape results in high vibration energy dissipation until the temperature reaches the glass transition temperature [16]. However, a further increase in temperature from 5 °C, wherein the highest damping performance is observed, decreases the damping ratio as the viscous molecules of the adhesive tape induces a rubbery state above the glass transition temperature. Additionally, if both the storage and dissipation coefficients of the viscoelastic material remain low, the periodic shear deformation of the viscoelastic tape results in minimal energy dissipation. On the basis of these test results, it is expected that the performance of the proposed system in an orbit can be maximized through a proper thermal design of the yoke that maintains the temperature of the yoke within 5 °C. Furthermore, although the frequency of the proposed system changes depending on the temperature conditions, the difference between the lowest temperature (−25 °C) and the highest temperature (55 °C) is very small, approximately 4%. Consequently, it is judged to have relatively little dependence on temperature as the thickness is very thin at 0.05 mm.

4. Conclusions

This paper proposed a multilayered hyperelastic SMA yoke, and its effectiveness in suppressing the elastic vibration of large solar panels was investigated. This is a novel passive vibration-suppression approach. The proposed design is based on the use of a hyperelastic SMA material in the yoke of a solar panel. Its performance can be maximized by incorporating a multilayered viscoelastic tape into the yoke; hence, excellent damping can be achieved. This is because the friction effects exerted on the laminated interfaces induce high energy dissipation according to the dynamic behavior of the yoke. To validate the effectiveness of the proposed design, three yoke specimens were fabricated. Their performances were investigated using a 0.75-m-long dummy solar panel integrated with the yoke specimens. The test results indicate that the proposed passive strategy is effective in suppressing both small- and large-amplitude vibrations. Additionally, the LLSS test results show that the strategy is also effective for suppressing multimode vibrations of the solar panel. In particular, the strategy exhibited significantly greater damping in the 2nd mode than in the 1st mode. The thermal aspect of the design was also verified to determine whether the proposed system could be used in an orbital thermal environment. In the thermal tests, the highest damping ratio was observed when the temperature was set to 5 °C. These facts indicate that the optimized damping of the proposed multilayered SMA yoke can be achieved via a proper on-orbit thermal design. This will be a future research topic to be explored in the next stage.