The paper presents the dynamic response of annular three-layered plate subjected to loads variable in time. The plate is loaded in the plane of outer layers. The plate core has the electrorheological properties expressed by the Bingham body model. The dynamic stability loss of plate with elastic core is determined by the critical state parameters, particularly by the critical stresses. Numerous numerical observations show the influence of the values of viscosity constant and critical shear stresses, being the Bingham body parameters, on the supercritical viscous fluid plate behaviour. The problem has been solved analytically and numerically using the orthogonalization method and finite difference method. The solution includes both axisymmetric and asymmetric plate dynamic modes.
 Chen Y.R. Chen L.W. Vibration and stability of rotating polar orthotropic sandwich annular plates with a viscoelastic core layer Composite Structures 2007 78 45–57.
 Chen Y.R. Chen L.W. Wang C.C. Axisymmetric dynamic instability of rotating polar orthotropic sandwich annular plates with a constrained damping layer Composite Structures 2006 73(2) 290–302.
 Pawlus D. Dynamic stability of three-layered annular plates with viscoelastic core Scientific Bulletin of the Technical University of Łódź Łódź 2010 1075 (in Polish).
 Pawlus D. Dynamic stability of three-layered annular plates with wavy forms of buckling Acta Mech. 2011 216 123–138.
 Pawlus D. Solution to the problem of axisymmetric and asymmetric dynamic instability of three-layered annular plates Thin-Walled Structures 2011 49 660–668.
 Pawlus D. Critical loads calculations of annular three-layered plates with soft elastic or viscoelastic core Archives of Civil and Mechanical Engineering 2011 XI 4 993–1009.
 Pawlus D. Solution to the Dynamic Stability Problem of Three-Layered Annular Plate with Viscoelastic Core Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium BEYOND THE LIMITS OF MAN 23–27 September 2013 Wrocław University of Technology Poland J.B. Obrębski and R. Tarczewski (Eds.).
 Jordan T.C. Shaw M.T. Electrorheology Transactions on Electrical Insulation 1989 Vol. 24 No. 5 849–878.
 Yalcintas M. Dai H. Magnetorheological and electrorheological materials in adaptive structures and their performance comparison Smart. Mater. Struc. 1999 8 560–573.
 Yeh J.Y. Vibration control of a sandwich annular plate with an electrorheological fluid core layer Smart. Mater. Struc. 2007 16 837–842.
 Yeh J.Y. Active dynamic instability control analysis of polar orthotropic sandwich annular plate with electrorheological fluid damping treatment Journal of Engineering Technology and Education 2012 Vol. 9 No. 3 290–299.
 Volmir C. Nonlinear dynamic of plates and shells Science Moskwa 1972 (in Russian).
 Volmir C. Stability of deformed system Science Moscow 1967 (in Russian).
 Trombski M. Wojciech S. The cylindrically orthotropic annular plate subjected to time-dependent pressure acting in its plane The Archive of Mechanical Engineering 1981 Vol. XXVIII 2 161–181 (in Polish).
 Pawlus D. Dynamic response control of three-layered annular plate due to various parameters of electrorheological core Archive of Mechanical Engineering 2016 Vol. LXIII 1 73–91.