Along wind random vibrations of a slender structure --- modelling by continuous elements

Abstract eng:
Along wind random vibration of a slender structure represents one of the most important aeroelastic effects resulting from wind - structure interaction. The theoretical model being based on one-dimensional elements with continuously distributed mass and stiffness has been introduced in this paper. The system has been considered to be self-adjoint and with strongly non-proportional viscose damping with respect to materials of individual parts of the structure and due to vibration dampers. The random excitation of the linear system is gaussian and of additive type, therefore the response is gaussian as well. Consequently, mathematical mean value and correlation function are satisfactory for the full description of the generalized solution of the respective PDE in the stochastic meaning. The stationary solution has been obtained in generalized coordinates providing transparent results and very fast convergency. Using this procedure, the general results can be obtained in the form of analytical formulae for many important cases of input spectral densities.

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