Résumé:
When a structure is subjected to a dynamic excitation, a quantity of energy is diffused into the structure. This latter absorbs and dissipates this energy by transforming it to kinetic and potential energy; this inherent damping which consists in a combination of strength, deformability, and flexibility allows the input energy to be extinguished. The technological evolution in the last decades allowed the use of innovative systems that improve the structural capacity to dissipate the energy. Two distinctive approaches are available to evaluate the response under dynamic excitations, deterministic and non-deterministic. These two methods can be adopted in a time or a frequency domain, it is quickly seen that a probabilistic method is much simpler to execute in the frequency domain using Spectral Analysis. Additional energy dissipation devices may achieve a better structural behavior and improvement. To consider all parameters involved in terms of their statistical properties, the Stochastic Analysis had to be developed. As more information is regarded, loading and the response are characterized in probabilistic terms. Therefore, it will be concentrated on the prediction response of a deterministic linear system subjected to stochastic excitation, i.e., wind load. Fluid viscous dampers are widely used in civil structures. So much effort was done in order to make the concept of additional damping as a workable technology. The nonlinear behavior of these devices however, makes it more complicated to estimate the response using spectral analysis, and to predict the damping properties of the additional devices. The stochastic Linearization technique is used to overcome this nonlinear problem and facilitate the calculation of the covariance matrices, and extends the applicability of the spectral analysis. The design process of this type of devices can be restricted into the selection of appropriate parameters values (damping coefficient, damping exponent) and their location along the structure. This process is a time-consuming task (numerically expensive), and it is more complicated for a nonlinear case, as it requires nonlinear time history analysis. Within the available design methods, many speculative assumptions are made in order to simplify the task, which may lead to inaccurate results. In the spirit of simplifying the process, this work proposes a procedure based on the concept of a target damping ratio and the equivalent energy-consumption approach, to determine an approximate nonlinear damping coefficient for the FV dampers. This work also describes the stochastic response of deterministic structures equipped by nonlinear FVD under random excitation i.e. Wind. Stochastic analysis of a single degree of freedom system and a multiple degree of freedom system is developed. The application of the stochastic linearization technique is realized, where the difficulty resides in defining a formulation to evaluate the equivalent damping matrix. Results prove the accuracy of the proposed method, which does not require an important computational time, allowing the designer to do multiple analyses in a small period, respecting the randomness aspect of the excitation
