Использование теоремы Эфроса для учета диссипативных свойств деформируемых элементов конструкций

Abstract

A new approach to the analysis of transient processes in the elastic continuum, caused by nonstationary force perturbations, on the basis of the operational calculus and the Efros theorem is proposed. It allows taking into consideration the internal viscous friction in the material, described by the Kelvin-Feucht friction model. This approach uses a smoothing linear integral operator with a Gaussian difference kernel and can be applied to any elastic solutions that are represented as Duhamel convolution type integrals. The algebraic properties of this operator are investigated. The examples of calculating for a beam and a plate in elastic and viscoelastic settings are given.