Stochastic Dynamics Theory and Viscoelasticity

Research focus

The Peer review has evaluated this group as Average

A1: CLOSURE METODS FOR MOMENT EQUATIONS OF MARKOV DYNAMIC SYSTEMS RESEARCH SIGNIFICANCE: in various fields of engineering, it has been recognized that the excitations are random processes. This impies that analyses ought to be done by using the tools of stochastic dynamics. However, there is still a lack of analytical solutions and a little certainty on the efficacy of the available methods. This research is aimed on improving the workability of stochastic dynamics in engineering. SUMMARY: the probabilistic evolution of Markov systems of random dynamics is governed by a partial differential equation, the so called Fokker-Planck-Kolmogorov (FPK) equation. Unfortunately, this has an analytical solution in few cases, most of which for the steady state only. Moreover, in some cases the solution exists under strict relationships among system and excitation parameters, which diminishes the practical importance of the solution. Finally, with the exception of very few cases, the excitation must belong to the class of Gaussian delta-correlated processes, that is Gaussian or Poisson white noise processes. Alternatively, the problem can be tackled by means of Itô's stochastic differential calculus. In this way, the ordinary differential equations governing the evolution of the response statistical moments can be written even for the case in which the excitation is given by a non-Gaussian delta-correlated process. Much work in this field has been accomplished by Prof. Di Paola and his collaborators. However, even the moment equation method (ME) has serious drawbacks: (1) the number of the equations becomes very large rapidly as the number of problem variables increase; (2) even in the case in which the FPK equation is solvable, the ME equation constitute an infinite hierarchy, since the equations written for the moments of order r contain moments of order larger than r. therefore, beginningin the 1980’s various closure methods for the ME have been proposed: the Hermite moment closure method, the central moment closure method, the cumulant neglect closure method and the iterative closure method for dynamic systems excited by polynomial forms of Gaussian filtered processes (Di Paola and Floris, to be published). Nevertheless, presently some aspects of the closure methods have not yet studied thoroughly, and will be object of the present research project: (1) performance of the different methods for dynamic systems with 2 or more state variables; (2) significance of the multiple solutions of the ME, which become algebraic in the steady state, especially when the corresponding deterministic system can exhibit chaotic behavior; (3) application of the closure methods to the ME of dynamic systems excited by non-Gaussian delta-correlated processes. A2: RANDOM DYNAMICS OF BRIDGES RESEARCH SIGNIFICANCE: nowadays longer and longer bridges are constructed for both vehicles and trains. The loads exerted on them including wind loads are random processes so that a correct dynamic of bridges must be performed in a stochastic context. SUMMARY: this research theme is in its first steps. Presently, the random dynamics of externally prestressed bridges is considered. With a linear model it has been found that external prestress is not favourable to the dynamic characteristic of a bridge. A nonlinear model will be adopted next. A problem that will be considered in the near future regards the random dynamics of suspended bridges. B: VISCOELASTICITY OF STRUCTURES RESEARCH SIGNIFICANCE: In the past, the development of viscous strains was taken into account only under static loading of long duration. This assumption however is certainly not valid for bridges, because traffic increase causes dynamic loads of long duration and new materials, which are used to damp the vibrations, develop viscous strain in very short times. Consequently, viscous 122 strains are to be considered in dynamic analyses through the nonlinear stress-strain relationships which characterize new materials. Moreover, the coupling problems which arise in the analysis of structures composed of elements with different rheological behavior become increasingly important. SUMMARY: the following research subthemes are studied: (1) dynamic response in the presence of viscous forces with an aging law (in the literature there many papers in which the hereditary law is adopted, while there is a lack of results with an aging stress-strain relationship, which is more suitable to describe the behaviour of concrete); (2) coupling problems in which some elements are elastic and others viscous; (3) structural analyses using nonlinear viscous relationships with fractional powers.

Dipartimento di afferenza

Dipartimento di Ingegneria Strutturale (DIS)

Docenti afferenti

Associate Professors
Claudio Floris