## 2 Application to Flexible Structures
### Other Structural Applications
[PERSON] proposed an adaptive absorber using an SMA actuator for vibration control of the spring-mass system in a wide range of frequencies where passive control method associated with the phase transformation was implemented [70]. [PERSON] et al. devised a linear actuator using synergistically configured SMA wires to achieve variable stiffness actuation in which both the stiffness feedback controller and force feedback controller were implemented [71]. [PERSON] et al. utilized advantages of the Bowden tube, which can provide faster actuation speed by devising Bowden tube SMA actuators consisting of a rotary platform and a micro controller in which a sliding mode controller was realized to take account for uncertain parameters [72]. [PERSON] et al. proposed an adaptive multi-modal tuned mass damper using SMA wires to change the eigenvalues of the structure and hence recover shifts of the natural frequencies in which one SMA wire was used to change of the axial load and the other wire to change the geometry of the device [73]. [PERSON] et al. used SMA wires to achieve passive control of mechanical vibrations of rotating machines where the amplitude of the lateral vibrations of a rotating shaft was reduced by thermally activating SMA wires [74]. Vibro-acoustic radiation of a laminated composite structure, which has SMA orthogonal asymmetry, was proposed by [PERSON] et al. [75]. The governing equations were derived by using the constitutive equation, Hamilton principle, and energy methods. It was demonstrated that the composite laminates embedded with SMA wires have good performance to adjust the mode frequency and can change sound radiation characteristics. Several studies have been presented for the use of SMA actuators in systems to prepare for earthquakes in civil engineering. [PERSON] et al. developed a passive SMA damper for structural seismic protection where the SMA damper has been installed on the building structure as an energy dissipative device associated with the hysteretic behavior [76]. [PERSON] used a fuzzy logic controller to control unwanted vibrations of civil structures using an SMA actuator in which the maximum roof displacement of a five-story building structure was evaluated [77]. [PERSON] and [PERSON] proposed a long-stroke SMA restrainer consisting of an SMA bar, a steel tube, and a filler material to achieve both energy dissipation and restrainer under cyclic tension and compression loadings in which bucking and post-bucking response of the SMA bar were characterized via finite element analysis [78]. [PERSON] et al. devised a passive control device for vibration using an SMA tuned mass damper inerter. Here, the SMA element and the mass amplification effect of the inerter was used to dissipate the energy of the primary oscillator through hysteretic phase conversion and utilized to reduce the oscillation displacement of the secondary oscillator, respectively. [79]. [PERSON] et al. devised the deformation mechanism of super-elastic SMA U-shaped dampers for vibration control of civil structures subjected to seismic excitation in which the stable energy dissipation under the different direction of the loadings was analyzed via the finite element method [80]. The applications and control methods for various structures are summarized in Table 2. It is clearly seen that the passive controller is used in many applications. Examples of the application of the radius of curvature control and vibration control of civil structures using SMA actuators are shown in Figure 3a,b, respectively. \begin{table}
\begin{tabular}{c c c c} \hline
**Reference** & **Control Type** & **Controller** & **Application** \\ \hline
[72] & Robust Control & sliding mode controller & fast control of a rotary platform \\ \hline
[67] & Adaptive Control & direct adaptive controller & position control \\ \hline \end{tabular}
\end{table} 
Table 2: Control methods for various structural systems.