Simple vibration modeling of structural fuzzy with continuous boundary by including two-dimensional spatial memory

Abstract

Many complicated systems of practical interest consist basically of a well-defined outer shell-like master structure and a complicated internal structure with uncertain dynamic properties. Using the “fuzzy structure theory” for predicting audible frequency vibration, the internal structure is considered as one or more fuzzy substructures that are known in some statistical sense only. Experiments have shown that such fuzzy substructures often introduce a damping in the master which is much higher than the structural losses account for. A special method for modeling fuzzy substructures with a one-dimensional continuous boundary was examined in a companion paper [L. Friis and M. Ohlrich, “Vibration modeling of structural fuzzy with continuous boundary,” J. Acoust. Soc. Am. 123, 718–728 (2008)]. In the present paper, this method is extended, such that it allows modeling of fuzzy substructures with a two-dimensional continuous boundary. Additionally, a simple method for determining the so-called equivalent coupling factor is presented. The validity of this method is demonstrated by numerical simulations of the vibration response of a master plate structure with fuzzy attachments. It is revealed that the method performs very well above a nondimensional frequency of 500 of the master, and it is shown that errors below this frequency are caused mainly by simplifying assumptions concerning the shape of the master vibration displacement.

A Multi Scale Approach for the Ground Motion Modelling in Urban Areas

“…where = (m str m f ⁄ ) and ω f are assumed as identical for each of the buildings, for simplicity sake. The aim of this formulation is to derive an equivalent local oscillator (Soize, [17], Friis and Ohlrich, [19]) as an average of the building impedances over the whole ERB (Boutin and Rousillon, [13]). Closed-form evaluation of Eq.…”

“…In this paper, a hierarchical multi-scale approach to model the ground motion in urban areas is proposed. At mesoscale level, the effect of each cluster of buildings is derived through a homogenization approach based on the strategy used in acoustic to determine the perturbations induced in a large main structure by several small substructures attached to it (Soize [17], Strass and Feit, [18], Friis and Ohlrich, [19] and [20]). Then, at macroscale level, the ground motion in the urban environment is derived through a wave propagation model (Morse and Ingard, [21]).…”