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Periodic and chiral orientation of microstructures, here we call phononic crystals, have extraordinary capabilities to facilitate the innovative design of new generation metamaterials. Periodic arrangements of phononic crystals are capable of opening portals of non-passing, non-dispersive mechanical waves. Defying conventional design of regular periodicity, in this paper spirally periodic but chiral orientation of resonators are envisioned. Dynamics of the spirally connected resonators and the acoustic wave propagation through the spirally connected multiple local resonators are studied using fundamental physics. In present study the spiral systems with local resonators are assumed to be discrete media immersed in fluid. In this paper it is assumed that acoustic or ultrasonic waves in fluid are propagated along the plane of the spiral resonators and thus only the longitudinal wave mode exists due to nonexistence of shear stress in the fluid. Lagrangian formulation of the spiral systems were employed to obtain the governing Euler-Lagrange equation of the system. Discrete element method was employed to verify the equation assuming nearest neighboring effect.