Simulation of oscillation of a dam-plate of variable thickness

The hereditary theory of viscoelasticity has provided ample opportunities for describing the dynamic processes of deformation of various materials. However, the implementation of these possibilities in many cases is difficult due to the lack of an adequate mathematical apparatus, especially in the study of dynamic processes in viscoelastic systems. There are fundamental reasons to believe that the apparatus of integral equations is very promising in this sense. The use of modern computer technology capabilities makes it possible to create effective mathematical modeling technologies for problems of great complexity, which include problems of dynamics and dynamic stability of viscoelastic elements of thin-walled structures with variable stiffness. Mathematical models of dynamic problems are constructed, efficient computational algorithms are developed, and forced vibrations of a dam-plate with variable stiffness are studied. The results of studies of problems on vibrations of a dam-plate of variable thickness are given, taking into account the viscoelastic properties of the material, the hydrodynamic pressure of water, soil and seismic load. Figs.:3, Refs.: 22 titles.