Sandwich　plate　structures　are　extensively　utilized　in　engineering　due　to　their　favorable　stiffness-to-weight　ratio.　Nonetheless,　these　lightweight　thin-walled　structures　frequently　encounter　challenges　related　to　inadequate　lowfrequency　vibration　performance,　which　significantly　restricts　their　applications,　particularly　in　the　realm　of　precision　instruments　which　is　sensitive　to　vibration.　This　study　introduces　an　innovative　design　of　an　active　nonlinear　metamaterial,　to　achieve　tunable　broadband　low-frequency　bandgaps　for　sandwich　plates.　The　nonlinear　oscillator　incorporates　an　inertia　amplification　mechanism　(IAM),　Euler-buckled　beams,　mass　elements,　and　magneto-rheological　elastomers　(MREs),　which　are　modulated　via　external　magnetic　fields　to　adjust　the　material＇s　stiffness　dynamically.　Employing　Hamilton＇s　principles　and　the　plate　wave　expansion　method　(PWE),　the　dispersion　relations　for　the　metamaterial　plate　are　derived,　elucidating　the　dispersion　surfaces　and　the　band　structures　within　its　sandwich-like　plates.　The　dynamical　equations　of　the　metamaterial　plate　are　formulated　and　validated　through　numerical　simulations　using　the　Galerkin　method,　confirming　the　theoretical　predictions.　The　results　demonstrate　effective　control　over　low-frequency　and　broadband　bandgaps　under　low　mass　ratio　conditions　through　strategic　manipulation　of　the　inertia　amplification　factor　and　magnetic　flux.　The　study　extensively　explores　the　nonlinear　dynamic　responses　of　the　metamaterial,　highlighting　the　significant　impact　of　excitation　amplitudes　on　the　amplitudedependent　bandgaps.