| Author | Wu, Chi-chin |
| Call Number | AIT Thesis no.1030 |
| Subject(s) | Seismology
|
| Note | A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering of the Asian Institute of Technology,
Bangkok, Thailand. |
| Publisher | Asian Institute of Technology |
| Abstract | A linearization technique is developed to obtain the statistical response of a nonlinear system subjected to an earthquake which is assumed
to be a finite order Markov process. The system exhibits nonlinearity due to its bilinear hysteretic restoring force-deformation relationship. The
study is carried out first for a single-degree-of-freedom system, in which the restoring force is characterized by a linear spring, a viscous damper and a Coulomb stiffness element, in parallel. A Fokker-Planck equation is derived containing a nonlinear term of a product of the displacements of the
mass and the Coulomb spring. An equivalent linear model is proposed by replacing the slider in the Coulomb stiffness element by a viscous damper , i.e., re
placing the Coulomb spring by a Maxwell model . Thus the analysis involves a single coefficient characterizing this new viscous damper. For each time, this coefficient is obtained by minimizing the statistical mean square error between the
Fokker-Planck equation of the nonlinear model and that of the equivalent linear model. The system is assumed to be subjected to a gaussian white noise excitation. The analysis is then extended to a multi-degree-of- freedom system
whose adjacent masses are linked by a stiffness element of a bilinear hysteretic restoring force-deformation relationship. A linear equivalent system is proposed by replacing each slider in each Coulomb stiffness element by a viscous damper. The single coefficient involved for each stiffness element is determined in the same manner as in the SOF system. This
MOF system is subjected to a nonstationary filtered shot noise excitation, and its statistical response can be obtained by uncoupling the equations
of motion by means of a complex eigenvalue computer program. Results by the proposed single-coefficient method agree well with
those by the 2-coefficient method and other existing methods, specially for
the common case that the statistical response is not exceeding the yielding
level much . As conclusions , the former method is more at tractive, since it is explained by real physical models, involves a simpler analysis and needs a
simpler numerical computation. In addition, the proposed single-coefficient method can be applied with more convenience to a system with multi
linear hysteretic stiffness elements. |
| Year | 1977 |
| Type | Thesis |
| School | Student Research Before 1979 |
| Department | Other Field of Studies (No Department) |
| Academic Program/FoS | Thesis (Year <=1979) |
| Chairperson(s) | Karasudhi, Pisidhi : Takemiya, Hirokazu
|
| Scholarship Donor(s) | The Keidanren Foundation, Japan |
| Degree | Thesis (M.Eng.) - Asian Institute of Technology, 1977 |