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# ADVANCED STRUCTURAL DYNAMICS Homework: Bouc-Wen model

Advanced Structural Dynamics June 27, 2023 Instructor: J. Zhang Due July 7, 2023 1ADV ANCED STRUCTURAL DYNAMICS Homework

A rigid mass of 50960Mg is supported on 300 lead rubber be arings. Recorded force- displacement loops from cyclic testing of the bearings are shown below. Use the Bouc-Wen model to approximate the recorded force-displacement loop in Figure 2: (1) where the hysteretic parameter, , satisfies the differential equation: (2) Use and adjust parameter to a pproximate the recorded behavior. Figure 1. Force-Displacement Loop of Lead Rubber Bearings a. Calibrate the model parameters to matc h the experimental fo rce-displacement loop shown in Figure 1 and plot the force-displacement of the bear ing using your model when it is subjected to a harmonic displacement time history. b. Use Matlab to write a program to conduct the nonlinear time history an alysis of a SDOF system supported by a nonlinear element that ca n be approximated by Bouc-Wen model. You need to use the state-space formulation and the built-in ODE solver in Matlab.

2c. Using the calibrated model fo r the lead bearings, compute the response of the rigid mass when subjected to the Newhall re cord of the 1994 Northridge earthqu ake. Plot the time history of relative displacement of the rigid mass and the force-displacement loops of bearing during the earthquake.

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