## 1 Introduction  
Cylindrical liquid storage tanks made of steel or concrete materials are strategic structures, having been employed to store water for drinking or firefighting, oil and chemical products in urban areas, and industrial plants. Damages to these structures may have catastrophic consequences such as economic losses, fire due to flamable materials, environmental pollution, and disruption of human lives. The reported failure modes of these structures during past earthquakes indicate their inappropriate seismic performance [1; 2] and the need for a safeguard against seismic events. The seismic behaviour of liquid storage tanks has been studied extensively (e.g., [3; 4; 5; 6]). Generally, two approaches can be followed to improve the performance of liquid containers against seismic events. The first approach is the strengthening of tanks by increasing their wall thickness. However, increasing the thickness of the wall will increase the input seismic energy. The second approach, aiming to decrease and dissipate the input seismic energy, is exploiting the advantages of control devices, such as base isolation systems, dampers, or other innovative control devices [7]. For more than four decades, a wide variety of studies have been conducted to develop various base isolation devices and to study their effects on the improvement of the seismic performance of steel tanks [8; 9; 10; 11; 12; 13; 14]. However, several factors influence the seismic responses of structures [15; 16], and in the case of base-isolated liquid storage tanks, they may have adverse effects leading to an increase in seismic demands compared to the fixed base condition [17; 18; 19]. For example, [PERSON] and [PERSON] [17] showed that the base isolation may experience an excessive displacement when the system is subjected to near-fault excitations with severe pulses, resulting in a dramatic increase in the displacement of the impulsive mass and, consequently, base shear and overturning moment. The same results were observed through experimental tests conducted on the seismic response of scaled structures isolated by highly efficient, low-cost PVC-Rollers Sandwich seismic isolation [20; 21]. Besides, the traditional base isolation devices are less capable of improving the seismic performance of structures built on soft soil and cannot isolate structures from the vertical component of ground motions. Therefore, it would be beneficial to mitigate the seismic demands through other control systems without the shortages mentioned above. In recent years, the progress in the area of solid-state physics showed that the structures being placed periodically display distinctive properties called frequency stop band, which can be explained as a wave is blocked to propagate through a continuum model if its frequency falls in the stop band frequency and can propagate to the model for the frequencies other than the frequencies of stop band [22; 23; 24]. This fascinating feature attracted considerable attention, stimulating researchers to construct materials with periodic structures to block the propagation of waves. Locally resonant metamaterials (LRMs) and phononic crystals (PCs) have been known as two types of periodic structures which are employed to avoid the propagation of waves [25]. Compared to PCs, LRMs have a more suitable performance to diminish vibrations with low frequency because the local resonances have the ability to create the stop band. LRMs, made from heavy materials (metamaterials) coated with a soft layer in a stiff matrix [26] (usually concrete), have been employed as foundations and barriers to decrease the propagation of seismic waves into structures and to protect them against the harmful consequences of earthquakes. The benefits of such a foundation would be magnified in the case of different structures, such as liquid storage tanks as well as modular structures, in which their performance under seismic actions is still a big question [27; 28].