This study introduces a numerical method for investigating the appropriate arrangement of visco-pseudo-elastic dampers applicable to shell and plate structures under large deformation. These passive dampers are considered as discrete shape memory alloy (SMA) wires and viscoelastic layers. The SMA constitutive model is adopted and developed based on carried out experimental tests (i.e., calorimetry and tensile tests) on Ni-rich Nitinol alloy samples. Pseudoelastic, pseudoplastic, strain recovery and de-twinning phenomena are perceived experimentally. The presented model characterizes pseudoelastic response of shape memory alloys. The current finite element formulation is based on an incremental updated Lagrangian (UL) approach along with the Newmark's integration technique. The used sandwich element is capable of accurate modeling of the viscoelastic core damping behavior, as a result of independent rotation of element's layers. Also, the creep functions regarding to the viscoelastic constitutive model are estimated using Dirichlet-Prony series. Employing the state variables, the viscoelastic deferred strain is presented in a proper incremental form. A nonlinear FE program is developed to assess the proposed procedure. Obtained results demonstrate that quick vibration mitigation may be possible using visco-pseudo-elastic dampers while overcoming their individual drawbacks.