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A STOCHASTIC 2D-MODEL FOR CALCULATING VIBRATIONS IN RANDOM LAYERS

PETER BALAZS

Austrian Academy of Sciences, Acoustic Research Institute, Reichsratsstrasse 17, A-1010 Vienna, Austria

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WOLFGANG KREUZER

Austrian Academy of Sciences, Acoustic Research Institute, Reichsratsstrasse 17, A-1010 Vienna, Austria

Corresponding author.

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, and

HOLGER WAUBKE

Austrian Academy of Sciences, Acoustic Research Institute, Reichsratsstrasse 17, A-1010 Vienna, Austria

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https://doi.org/10.1142/S0218396X07003354Cited by:6 (Source: Crossref)

Abstract

Vibrations induced by machinery and traffic have become of increasing concern in the last years, for example, when constructing buildings near railway lines. In this paper we will present a model designed to predict the vibration level in the ground. Since in practice it is nearly impossible to determine exact material parameters for soil layers, we use a model with a stochastic shear modulus G. Under moderate assumptions G can be split with the Karhunen–Loeve expansion into a mean value G₀ and a stochastic part G_stoch. Using a combination method of finite elements, Fourier transformation and Polynomial Chaos, it is possible to transform the partial differential equation describing the system into a matrix-vector formulation Kx = b which can be split into a deterministic and a stochastic part (K₀ + K_s) x = b analog to the shear modulus. To keep the dimensions of the matrices involved with this system small, we use a Neumann-like iteration to solve it. Finally, results for a small example are presented.

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