UNCERTAINTIES PROPAGATION IN THE DYNAMICS OF A CABLE-BEAM SYSTEM

JORGE BALLABEN; MARTA B. ROSALES; RUBENS SAMPAIO

Rouen

Simposio; 2nd International Symposium on Uncertainty Quantification and Stochastic Modeling-UNCERTAINTIES 2014; 2014

French Society of Mechanical Sciences-ABCM (Brazilian Society of Mechanical Sciences)-SBMAC (Brazilian Society of Applied Mathematics)

Cable-stayed bridges and guyed towers are examples of structures extensively used in Civil Engineering. Usually the standards recommend certain ranges of guy tension to avoid overstress or slackness. During the service life of the structure, the tension values are checked during the maintenance procedures and adjusted if necessary. However, and depending on the importance of the structure, this parameter can vary due to various circumstances. The consequences can range from operational difficulties to failure of the structure or some of its components. Thus, an uncertainty study appears desirable to provide a real model of the system dynamics. The nonlinear dynamic behavior of a cable-beam system which constitutes a simplified model of a guyed structure, is stated as a first model. The beam behavior is assumed linear (small deformations) while the cable is modeled with nonlinear equations that account for its extensibility and an initial deformed state due to gravity. First, the deterministic model is stated. The partial differential equations are approximated by the finite element method. A linearized model allows determining the natural frequencies and modes. Using the latter as a basis, a Galerkin projection is employed to construct a reduced order model (ROM) of the nonlinear cable-beam system. The deterministic dynamic response of the system under dynamic loads is found. Afterwards, the cable tension is assumed stochastic and the Principle of Minimum Entropy is employed to derive an appropriate probability density function (PDF). A numerical analysis is carried out to obtain simulations of the random model using Monte Carlo techniques. Additionally, the beam stiffness can be also a varying parameter. Therefore, this parameter is also considered stochastic with an associated PDF. The propagation of this uncertainty is also evaluated for the dynamic response of the structure. Some unexpected features, such as multimodality of the PDFs, are observed in the statistic response of the system. The structural model seems to be more sensitive to the tension uncertainty.