10-10-2014, 02:00 PM
The thesis deals with the seismic response analysis of structural systems which
axe supported multiple points. In this type of structures, the distance between
the supports axe comparable to the characteristic seismic wavelength and,
consequently, the supports suffer differential ground motions. Examples for this
type of structures can be either land based structures like long span bridges,
large dams, petroleum pipe lines or they can be secondary parts of primary
system like piping systems, stairways, and multi-span rotors.
A review of literature on the methods for seismic response analysis of multisupport
structures and on method of critical excitations has been presented in
Chapter 1. A review of literature on the models for spatial variability and models
for individual components of ground motions axe discussed. Also, the scope
and limitations of currently available methods for seismic response analysis of
multi-support structures namely, time history method, response spectrum
method and random vibration method is presented.
The development of vector critical random earthquake excitation models is
presented in Chapter 2. The input is modeled as a vector of non-stationary
random processes. Each of components of this vector is obtained as a product of
a deterministic envelope and a stationary Gaussian random process. It is
assumed that the knowledge on auto-power spectral density functions is
available; the cross spectral density functions are unknowns. These unknown
functions axe determined, that, the variance of a specified response variable is
maximized over time. The methodology developed is illustrated with reference
to a Euler-Bernoulli beam supported on two linear springs. Two alternatives
critical cross power spectral density function models are developed.
The dynamics of nonlinearly supported beam structures which axe subjected to
differential random support motions is considered in Chapter 3. The beam is
taken to be a linear Euler- Bernoulli beam and the support springs axe modeled
as Duffing springs with cubic nonlinearity. The support excitations are modeled
as a vector of stationary Gaussian random processes. The response analysis is
carried out using the method of equivalent lineaxisation in conjunction with
dynamic stiffness matrix method of structural analysis. The approximate results
thus obtained axe validated by comparing them with corresponding results from
Monte Carlo simulations based on finite element structural analysis.
Furthermore, the problem of determination of critical cross power spectral
density functions is also considered. The two models for critical cross spectra
described in Chapter 2 are extended to account for system non-linearitys.
The conclusions resulting from the above studies and a few suggestions for
further research have been presented in Chapter 4.
Appendix A describes three methods that are available to analyze the response
of multiply sup- ported structures subjected to differential support motions.
Brief description of simulation of vector Gaussian random processes with
specified power spectral density matrix axe presented in Appendix B. Some
useful terminologies on the description of vector random processes axe given in
Appendix C.