System Identification Of Structures Based On A Linearly Tapered Shear Beam

Simple beam models have been very useful in earthquake engineering to model the response of both structural elements and a structure as a whole.For example,the shear beam model has been found to be appropriate for modeling the response of frame buildings for longer wavelengths,while,for buildings with shear walls,the Timoshenko beam model has been found to be more appropriate.Because real structures are three-dimensional and consist of many structural elements boned together,while the beam models are one-dimensional and are made of a continuum,the beam models are appropriate to represent real structures only for long-wavelength waves,which are not sensitive to the details of the structural design and reflections of the lateral boundaries of the structure.The model simplicity has been an advantage for the use of beam models in parametric structural system identification and health monitoring because they are defined by a smaller number of parameters,which can be estimated from the observed response with less uncertainty.The objective of this thesis work is to add to the family of simple beam models for use in structural system identification and health monitoring another model that is appropriate for structures that are linearly tapered（e.g.truncated pyramid）and deform predominantly in shear.It also presents an application to system identification of a unique pyramid-shaped building using earthquake records.This thesis presents the development of an analytical solution for the response of a homogenous,linearly tapered,cantilever shear-beam,excited by base motion,in terms of Bessel functions of fractional order.This solution is then used to derive the propagator matrix（also called transfer-matrix）for a homogeneous tapered shear beam,which is then used as a building block to derive the propagator for a nonhomogeneous beam,such that has piecewise constant material properties,or a layered tapered shear beam.The equation of motion was solved analytically in terms of Bessel function for dynamic response.The analytical solution for a homogeneous beam is used for a parametric study of the natural frequencies of vibration,their ratios,and mode shapes,in terms of dimensionless model parameters and as a function of the degree of tapering.The appropriateness of the model for representing real buildings is validated by its application to the Transamerica building,a 48-story steel structure with a pyramid shape,located in San Francisco,California,U.S.A.,which is the symbol of the city.Above the 49^th floor,there is a spire,which hives the structure a visual impression of a full pyramid.The building has been instrumented and recorded the Loma Prieta earthquake of October 18,1989.The distance between the ground floor and the 49^th floor is 199.3 m.Analysis of the observed response shows that the first five observed modes of vibrations are within bands 0-1.7Hz for EW and NS,and 0-1.9Hz for a torsional response.The observed fundamental frequency for both NS and EW directions is 0.28 Hz,and that the ratio of the frequencies of the higher modes to the fundamental mode frequency is 1:1.96:2.91:3.36:4.83..,which is significantly different from 1:3:5:7….,which corresponds to a uniform cross-section shear beam.The observed pulse travel time from the basement to the 49^th floor was 1.35 sec for NS and 1.44 sec for EW responses.The building is first modeled as a homogeneous truncated pyramid,with shear wave velocity is determined from the observed fundamental frequency and geometry.The model frequency ratios are 1:2.1:3.3:4.5:5.7..,These ratios are much closer to the observed ones,both differing significantly from the frequency ratios for a uniform cross-section shear beam model.This comparison shows that the tapered shear beam model is an appropriate physical model for this building.The transfer-functions and impulse response functions of the model are also studied for the model for the virtual source pulse at the base and the roof.The impulse response functions represent the model response to a virtual input pulse.The propagator for a multi-layer tapered shear beam was implemented in a Mat lab code for system identification of buildings by the least-squares fit of a layered shear beam model with a uniform cross-section,which has been developed earlier by Rahmani and Todorovska at the University of Southern California.What is matched in this method are impulse responses on the floors where the earthquake response has been recorded.Results are presented for fitted 1-layer,3-layer and 4-layer tapered shear beam.It is concluded that the linearly tapered shear beam model can be a useful modelfor structural system identification and health monitoring of pyramid shapes structures.