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Experimental modal analysis and damage detection on an ancient masonry building
No full textProcedures and results are presented relative to the modal identification of an old masonry building from two sets of experimentally determined frequency response functions. Both tests were performed by exciting the structure with low intensity forces produced by a vibrodyne, before and after high intensity shakes comparable to a destructive earthquake, in order to detect and quantify the damage suffered by the masonry. In spite of nonlinearities appearing in the frequency response functions, a significant modal model is obtained in both cases, provided that a non-proportional damping model, yielding complex modes, is adopted. The decreasing of natural frequencies, in addition to the increasing of damping factors between the two low intensity tests, indicate remarkable structural damage. In order to obtain useful quantities for the identification of a finite element model, which is the most suited for damage localization and quantification, real modes have been extracted by filtering out the damping effects from the complex modes derived by appropriately curve-fitting the frequency response functions
Poincarè Map-Based Continuation of Periodic Orbits in Dynamic Discontinuous and Hysteretic Systems
No full textA numerical algorithm is proposed to compute variation of periodic solutions and their codimension-one bifurcations in discontinuous and hysteretic systems. For general nonsmooth systems such as those exhibiting hysteresis, the nondifferentiable nature of the vector field makes the Poincaré map method one of the viable numerical strategy for continuation and stability analysis. Here the Jacobian of the map is evaluated via a finite-difference approach. The continuation scheme is based on arclength parameterization. The eigenvalues of the Jacobian of the map - Floquet multipliers - are computed to ascertain the stability of the periodic orbits and the associated bifurcations. The procedure is used to investigate the response of a class of one-dof systems with different representative restoring forces. The objective of the investigation is twofold: (i) to show the effectiveness of the procedure in dealing with various typical bifurcation scenarios of nonlinear dynamic systems and (ii) to investigate more in-depth some peculiar characteristics of softening-type oscillators having multi-linear and hysteretic restoring forces. Specifically, a bilinear system with either a sharp or a smooth transition in the force-displacement curve, Masing-type, and Bouc-Wen hysteretic systems are analyzed. A rich class of solutions and bifurcations - including jump phenomena, pitchfork, and period-doubling - are captured effectively by the procedure. Therefore, the implemented numerical strategy proves to be a powerful tool for analyzing the bifurcation behavior of general hysteretic systems shedding light onto some nonthoroughly explored nonlinear phenomena in these systems
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