Some questions of the dynamic stability of a plate from a material obeying the hereditary law of viscoelasticity
E.L. Kosheleva, Cand. tech. Sciences, Assoc .;
V.P. Nosyrin, Master
Moscow State University of Civil Engineering
(National Research University)
Abstract. The problem of dynamic stability of a rectangular plate is considered, the material of which obeys the hereditary BoltzmannVolterra deformation law. A weakly singular creep core is used that has three parameters, which makes it possible to describe the behavior of many polymer materials that obey the hereditary deformation law. The solution of the integrodifferential equation of plate oscillations loaded with a constant and variable loads in the plate plane is considered as a series with separated variables satisfying the plate fastening conditions. For the time function by the BubnovGalerkin method, integrodifferential equations are obtained. To construct regions of dynamic instability, the critical frequency equations for odd and even stability regions were obtained. The main regions of dynamic instability are constructed for different values of the nuclear parameters entering into the equation. The effect of nuclear parameters on the position of the main region of dynamic instability is investigated.
Key words: dynamic stability, rectangular plate, viscoelastic material.