Abstract
The Slepian model process method has turned out to be a powerful
tool to obtain accurate approximations to the probability
distributions of the plastic displacements of a one degree of
freedom linear elastic-ideal plastic oscillator subject to
Gaussian white noise excitation, Ditlevsen and Bognar (1993). In
the present paper the Slepian method is applied to obtain
approximate distributions on closed analytical form of the plastic
displacements of the top floor of an n-floor shear wall building.
The top floor is modelled as an elasto-plastic oscillator whereas
all the other floors are modelled as linear elastic modally damped
oscillators. The excitation is stationary Gaussian white noise
acting at the bottom floor. This model setup is an attempt to
model a one-floor shear wall building as an elasto-plastic
oscillator subject to a stationary non-white Gaussian excitation
represented by the random vibration of the (n-1)th floor. Moreover
the model simulates the soil-structure interaction through the
exchange of energy between the top floor and the elastic structure
below the top floor. The obtained distribution approximations are
checked by comparison with direct simulation results using an
autoregressive approximate representation of the response. It is
thereby revealed that the neglect of dependency in the sequence of
displacements causes some error in the predicted distribution of
the second and the following plastic displacements in a clump of
consequtive plastic displacements of opposite sign. However, in
the derivation of the distribution of the first plastic
displacement in a clump there is no neglect of dependency and the
approximation is observed to be satisfactory. It is possible to
take the dependency into account by a simulation procedure of
weighted outcomes. However, this topic is not treated in the
present paper. Keywords: Random vihrations, Slepian models, MDOF
elasto-plastic oscillator, Earth quake induced vibrations, Random
plastic displacements.
Original language | English |
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Journal | Prob. Engng Mech. |
Volume | 12 |
Issue number | 1 |
Pages (from-to) | 49-56 |
Publication status | Published - 1997 |