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 x; _ x ð Þ(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 j(x)v where j(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 j(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).
This paper presents the application of the energy balance equation to the identification of nonlinear damping in complex multi-degree-of-freedom systems subjected to excitations in the form of a random series of impulses. It is proven that the proposed procedure makes it possible to determine damping characteristics irrespective of the form of purely elastic interactions and the occurrence of the so-called mixed term. The procedure was verified experimentally, using a system with two degrees of freedom. The effect of the intensity with which impulses appear (pulse rate) on the quality of the obtained results is examined. The presented method can be applied to investigate the damping of vibrations of selected elastodamping elements in real vibrating systems.
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