Nonlinear Wave Propagation in Complex Structures Modelled by Random Media with Self-Stresses
General modelling for complex engineering structures is proposed. In order to describe such intrinsic properties of complex structures as vibration localisation and parameter uncertainty, complex structures are modelled by random media with self-stresses, the role of the latter being played by the internal degrees of freedom of structural members. The rheological model is composed of an infinite number of elastic-plastic elements in parallel. The Dyson integral equation is applied to solve the problem of wave propagation in essentially heterogeneous random media. It is shown that the considerable spatial decay of the propagating wave is caused by (i) dispersion and scattering, (ii) resonant absorption in secondary systems attached to the primary structure and (iii) nonlinear material damping and dry friction between the structural members. The latter causes various nonlinear effects, e.g. the vibration saturation in complex structures. Structures are also shown to exhibit another nonlinear effect, namely, maximum distance which the wave propagates down the structure.
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