Investigation of shock interaction of a solid body and viscoelastic isotropic plate by means of nonlinearly elastic buffer
"Математика. Компьютер. Образование". Cб. трудов XII международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2005. Vol. 2, 466pp. Pp. 711-720.
The present paper is devoted to mathematical modeling of the impact of a solid body upon a buffer having physical nonlinearity and positioned on a thin plate. The dynamic behaviour of a thin plate is described by the equations taking the rotary inertia and shear deformations into account. As this takes place, viscoelastic properties of the material are considered only for shear deformations. During the interaction of the body with the plate, a quasilongitudinal and quasitransverse waves representing the surfaces of strong discontinuity begin to propagate. Behind the wave fronts, the solution is constructed in terms of ray series representing power series, whose coefficients are the different order discontinuities in the time-derivatives of the required functions, and the variable is the time passed from the moment of arrival of a wave to the given points of the plate.