Dynamics of shell with destructive heat-protective coating under running load

Abstract

The problem of dynamic deformation of a plate with a two-layer composite shell with a heat-shattering coating collapsing in time under the action of a running load is solved approximately. The problem is solved in a dynamic formulation, considering that the deformed state of the shell depends both on the spatial coordinates and on time. The problem is reduced to solving two differential equations of the shell in partial derivatives with respect to deflections and the stress function. These equations contain discontinuous ratios for unknowns, which are associated with the dynamic destruction of the heat-shielding coating. According to the Bubnov method, the problem is also reduced to a system of differential equations, but already in ordinary derivatives. The solution of these equations is obtained in closed form. In addition, the natural vibration frequencies of the structure and the critical velocities of the load are found depending on the degree of damage to the protective layer. Formulas for oscillation frequencies and critical speeds are obtained in closed form.