White noise excited non-ideal elasto-plastic oscillator

Abstract

Two sets of 50 samples of the displacement response of the top traverse relative to the second traverse of an experimental shear frame with three traverses subject to white noise base shaking of two different intensities have been recorded at Institut fur Allgemeine Mechanik in 1995, and are in file available for analysis. The column connection between the two top traverses were made of aluminum with a linear-elastic non-ideal plastic behavior, and the columns were therefore renewed after each experiment. The two other connections were made of steel with a purely linear-elastic behavior. By use of the measured displacement-retaining force relation for the aluminum connection the plastic displacement responses were isolated from the sample records. From the obtained samples of plastic displacement records various distributions were estimated as well as the time development of the variance of the plastic displacement process. This paper presents a determination of the experimentally estimated statistical properties of the plastic response by use of Slepian model process theory as the basis for a numerical simulation algorithm. Solely the given defining parameters of the experimental frame are used in the calculations, i.e. the given displacement-retaining force relations, the traverse masses, the modal damping ratios for the vibrations within the elastic domain, and the two white noise excitation intensities, all as measured. First the Slepian model process method is applied to a single degree of freedom oscillator with linear-elastic non-ideal plastic displacement restoring force relation. The method is based on a direct generalization of the Slepian model process method that quite successfully has been developed for the linear-elastic ideal-plastic oscillator. Next the method is modified to be applicable on an oscillator of more than one degree of freedom. Applied to the experimental frame the calculations give excellent predictions of the main distributional properties of the plastic displacement process.