Dynamic Stability of the Plate at the Second Resonance with Creep Taken into Account

The problem of determining the side regions of dynamic stability of a rectangular plate, the material of which obeys the linear creep law, is considered. The solution of the differential equation of vibrations of a plate loaded with constant and variable periodic loads in the plane of the plate is presented as a series with separated variables, which satisfies the conditions for fixing the plate. As a result of using the Bubnov-Galerkin method, differential equations of the third order with variable periodic coefficients are obtained for finding functions that depend on time. To construct even domains of dynamic instability, a solution in the form of a trigonometric series was used. As a result, a system of equations was compiled for the coefficients of the series. To calculate the even regions of instability of the plate, an equation of critical frequencies was obtained in the form of a system determinant. This equation allows us to construct the boundaries of the regions of instability. The study of the influence of the relaxation time and the ratio of long-term and instantaneous moduli of elasticity on the position of the second region of dynamic instability has been carried out.