An identification of nonlinear dissipative properties of constructional materials at dynamical impact loads conditions

Abstract

The dissipative properties of most structural materials are usually described by a viscous damping parameter determining the rate of energy dissipation. The parameter stem from the traditionally adopted rheological Kelvin model. However, the analytical description of the dynamic properties of modern structural materials, including biological materials, often poses difficulties, due to the fact that the stress–strain dependence in these materials is not linear. Therefore a method of determining of nonlinear form of dissipative characteristic $$ D\left( {x,\dot{x}} \right) $$ (is presented. As it is assumed, mathematical function of the characteristic consist of nonlinear term g(x) of arbitrary form and so called mixed term κ(x)v where κ(x) is a function of deformation x and v—velocity of deformation. The deformation of a viscoelastic element which is made of tested material can be measured as displacement x of a single mass m in relative to a point of a complex vibratory system. The proper analysis of the mass m movement allows to evaluate the form of the functions g(x) and κ(x) what is a fundamental aim of the presented method. Beside of analytical method description some computer examples are presented. The method can be useful in evaluation of modern structural material properties (e.g. composites).