## 1 Introduction  
The interest in SMA sheets primarily comes from their inherent damping performance, potentially making them a viable structural material intended for vibration damping in lightweight systems. Compared to other materials in which some damping is intrinsically present to a higher or lower degree, shape memory alloys display two additional energy dissipation mechanisms that make them stand out [1]. The first mechanism is related to the twinned martensitic phase which as a consequence of load application goes through de-twinning [1,2]. During load application, the hysteretic movement of martensitic variant interfaces within the alloy causes an increase in internal friction, thus increasing energy dissipation [3, 4, 5]. The second mechanism of energy dissipation is related to the increased internal friction during temperature-induced direct (cooling) and reverse (heating) martensitic phase transformations of the shape memory alloy, which result in a damping peak [6, 7, 8]. To date, NiTi remains the most researched and most widely adopted shape memory alloy in the industry. However, despite its reliability and high performance, the high costs of raw materials and fabrication have been motivating researchers to look for alternative solutions for decades. One such alternative is the Cu-based shape memory alloys, which despite cost advantages have yet to see wider application due to issues such as high brittleness, low workability, martensitic stabilization, and more modest shape memory performance in comparison to NiTi [9]. Nonetheless, significant advances in the understanding of Cu-Al-Mn alloys have been made by scholars. These efforts resulted in significantly improved material workability, higher levels of damping performance, better shape recovery, etc. The reduction in aluminum content within the alloy to below 17% at. allowed for workability higher than 60%, where workability was defined as the percentage of thickness reduction before cracking, which is caused by a low degree of order in the parent phase [10]. Improvements in both shape recovery properties and passive damping performance in the martensitic phase were achieved by increasing the relative grain size,which is a consequence of a reduction in the dimensionality of constraints between individual martensitic grains within the alloy [11; 12; 13]. Specifically, a loss factor of tan\(\delta\approx 0.07\) can be achieved by increasing the relative grain size inside the alloy to d/D \(\approx 1\), where d and D are the grain diameter and the diameter of a Cu-Al-Mn wire, respectively [6]. Here, the loss factor tan\(\delta\) is used to express the damping performance, which is defined as the ratio of the loss modulus E\({}^{\prime\prime}\) and the storage modulus E\({}^{\prime}\), and it is measured by dynamic mechanical analysis. Furthermore, at a relative grain size of d/t \(\approx 15.4\), it was possible to reach values of shape recovery up to 7%, where d and t are the mean grain size and Cu-Al-Mn sheet thickness, respectively [13]. Through the addition of alloying elements, it is possible to increase or decrease the martensitic start temperature Ms, as well as improve the shape memory properties of the Cu-Al-Mn alloy, but at the expense of reducing the cold workability [14]. The achieved improvements in the fabrication and performance of Cu-Al-Mn SMAs, which are making them a more competitive potential alternative to NiTi at lower costs, are being followed by diverse proposals for their application. Energy dissipation improvements via grain size and texture control have led to suggestions for Cu-Al-Mn applications as seismic dampers and isolators for buildings constructed in zones prone to natural disasters such as earthquakes and tsunamis.