## 1 Introduction
[PERSON] and [PERSON] [29] investigated the effect of physical as well as geometrical properties of periodic foundation on the stop band. They concluded that a lower band gap can be achieved by considering a higher mass density for the core. [PERSON] et al. [24] compared the seismic behaviour of a seven-story building mounted on a periodic foundation with the traditional foundation and base isolation system. They observed that the periodic foundation has a better performance compared to base isolation systems in attenuating the seismic responses when the predominant frequency of the wave incident lies in the stop band. [PERSON] et al. [30] proposed metaconcrete in which spherical metal cores coated with soft material are used instead of standard concrete. The coated metal core behaved as a resonator, activating when a dynamic blast load is applied with the frequency at or near the resonator frequency. Hence, the overall system exhibits negative effective mass, leading to the reduction of the amplitude of the applied blast wave. [PERSON] et al. [31] used mass-in-mass barriers being placed periodically to investigate the effect of locally resonant metamaterials. They connected internal mass to the outer mass by tendons and found that the input energy is filtered if the frequency falls in the stop band. [PERSON] and [PERSON] [32] conducted numerical analyses to evaluate the effect of MetaSoil on the amplification of in-plane waves due to topography irregularities. More recently, [PERSON] et al. [33] employed the concept of LRMs to alleviate the demand in liquid tanks due to seismic actions. The foundation was made of steel columns, and the concrete-type resonators were connected to these columns. They conducted an optimization procedure to obtain the optimized damping and frequency corresponding to the resonators. The obtained results demonstrated that the proposed system could decrease the base shear in a slender tank up to 30%. [PERSON] et al. [34] investigated the propagation of flexural waves in a thin reticulated plate augmented with two classes of metastructures for wave mitigation. Despite all the research on metamaterials, no study has been conducted on the performance of MetaFoundation, composed of concrete matrix and steel core, in liquid storage tanks. Moreover, it is vital to investigate the effect of various parameters influencing the performance of MF on the seismic behaviour of the superstructure. Particularly, due to the fact that the MF works in a range of frequencies, it is essential to investigate the effect of earthquake frequency on the seismic behaviour of MF. This paper aims to investigate the efficiency of a foundation made by concrete and locally resonant materials coated with a soft layer called MetaFoundation (MF) on the dynamic behaviour of cylindrical tanks made from steel materials. To that end, the theory and background of the MF based on [PERSON]'s theorem are studied, and a simplified mass-spring model is suggested for the dynamic analysis of the coupled MF-tank system. Then, the governing equations of motion of the system are derived and solved in the time domain. For the numerical study, two types of tanks, namely squat and slender, are subjected to a set of ground motions with far-field characteristics to compare the seismic responses of the tanks mounted on MF with corresponding responses in the fixed base condition. Besides, a parametric study is performed to investigate the influence of different parameters on seismic responses of considered tanks with MF. These parameters are the predominant frequency of ground motions, the number of layers of metamaterials, the thickness of the soft material, and the damping of the soft material.