Explicit stability conditions for viscoelastic structural members

For a linear viscoelastic system, the authors derive sufficient stability conditions formulated explicitly in terms of the system coefficients. These conditions are determined by two parameters of relaxation kernels. The first is the standard norm of the kernel. The other characteristic (maximum of the norm for the Laplace transform of the relaxation kernel) is newly developed. To demonstrate efficiency of these conditions, the authors apply them to two problems of practical interest. The first example is concerned with a system of two bars (elastic and viscoelastic) linked by a thin adhesive layer. The viscoelastic bar is compressed, and the elastic bar is stretched. Explicit restrictions on the compressive load are developed that ensure the system stability. Dependence of the critical compressive force on the tensile load and on the material parameters is analyzed numerically.The other problem is concerned with flutter of a viscoelastic compressed panel in a supersonic gas flow. Explicit restrictions on the compressive load and on the gas speed are derived for an arbitrary relaxation kernel of the panel material. Dependence of the critical flow speed on the material viscosity is studied numerically.