<p>Auxetic meta-sandwich structures are well known for their excellent energy absorption, but they often fail due to core–face sheet debonding caused by vibration-induced fatigue. This study presents a novel auxetic sandwich panel with a bioinspired butterfly lattice core and dual functionally graded (FG) nanocomposite face sheets, for enhanced auxeticity and active damping. The lightweight metastructure integrates a piezoelectric sensor–actuator pair governed by a constant velocity feedback controller to suppress induced vibration in a closed-loop system. In contrast with computationally involved nonlocal homogenization approaches, an efficient multiscale framework is adopted that combines (1) RVE-based finite element (FE) homogenization to capture material anisotropy and negative Poisson’s ratio (NPR) of the auxetic core and (2) FSDT-based FE modeling with quadratic interpolation functions to solve dynamic motion equations, predicting transient response of the plate structure under active control. Parametric analysis reveals that cell wall thickness and total unit cell length of the architected core critically govern the core’s NPR (− 0.227 to − 0.097) and modal characteristics, while adding carbon nanotubes (CNTs) to the FG Al–ZrO₂ blend significantly elevates structural stiffness and inherent damping. Comparative studies show the butterfly auxetic sandwich structure (BASS) achieves superior auxeticity, whereas the re-entrant design (RASS) offers higher natural frequencies and improved vibration suppression at same material volume. Validated against benchmarks, the work establishes a paradigm for designing auxetic metastructures with tunable dynamic performance, emphasizing synergy between architectured cores, dual-FG CNT nanocomposites, and active control for fatigue-resistant applications.</p>