Introduction Axisymmetrical deformations of geometrically nonlinear cylindrically orthotropic circular plates under a multiparametric system of loading where thermal stresses are also taken into account are investigated. In theses cases there may be nonuniqueness of equilibrium states, i.e., for the same parameter of loading or temperature, there can exist a number of equilibrium states for the plate. This effect may lead to a loss of stability by snapping of different kinds. Therefore, there is a necessity to study the stability of all the possible equilibrium states. The numerical method used for investigating the stability of the equilibrium states is the well-known dynamical method (method of small vibrations). To the best of our knowledge, this method was used for the first time for nonlinear shells in [1] and systematically for isotropic geometrically nonlinear plates and shells in Since eigenfrequencies (eigenvalues) are the basis for this method (when the eigenfrequencies are real the examined equilibrium states are stable in the corresponding sense, and when they are imaginary these states are unstable) it is necessary to find them for plates under different conditions. As opposed to the linear case the eignfrequencies in question are dependent on the values and character of the external cross forces and temperature
