On the dynamics of rigid-block structures|bapplications to SDOF masonry collapse mechanisms
Author
Prieto Castrillo, FranciscoEntity
UAM. Departamento de Química Física AplicadaDate
2007-01-01Subjects
Mecánica aplicada - Tesis doctorales; Control de estructuras (Ingeniería) - Tesis doctorales; QuímicaNote
Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Química Física. Fecha de lectura: 01-01-2007Abstract
This dissertation proposes a novel formulation for the rocking motion (RM) of rigid-blocks
when no sliding mechanisms are present. Both theoretical and numerical analyses are included.
The results obtained from a new formulation for single block dynamics, which have shown to
be extremely powerful, led to the generalization for many degrees of freedom systems presented
herein. That generalization was possible through a transformation of the Euclidean configuration
space to a complex Riemannian manifold endowed with an Hermitian metric tensor.
The present contribution applies also techniques derived from chaos theory to the RM problem
for the understanding and quantification of the dynamic stability. The probability of overturn of
rocking blocks under random loading is both experimentally and numerically investigated.
Through an intensive use of the Poincaré surface of section technique and bifurcation analysis,
the underlying structure of the phase space is highlighted. Delay coordinated, recurrence plots
and recurrence quantification analysis are used to find the recurrences and patterns present in
the dynamics at different time scales. An estimator for the quantification of chaos in the problem
of rocking blocks under earthquake loading is proposed.
Stochastic analysis is performed through an ensemble of input earthquake samples. The ensemble
limits and other stochastic properties of the relevant physical magnitudes are analyzed.
A set of experiments at a seismic table on four blue granite stones were conducted to validate
the theoretical analyses. The response is investigated under different input actions and block
geometries. Several applications to Earthquake Engineering and structural safety assessment
are therefore derived. In particular, numerical thresholds for the probability of collapse of slender
structures are found by means of different criteria. A model for the probability of collapse
based on the stationary solution of the associated Fokker-Planck equation is proposed.
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