NEHRP Clearinghouse
- Title
- Earthquake Waves in a Random Medium.
- File
- PB80104862.pdf
- Author(s)
- Chu, L.; Askar, A.; Cakmak, A. S.
- Source
- National Science Foundation, Washington, DC. Engineering and Applied Science., June 30, 1979, 46 p.
- Identifying Number(s)
- 79/SM/3
- Abstract
- Measurements are conducted with small samples in the laboratory and thus for all practical purposes the medium is macroscopically homogeneous. On the other hand, the uncertainties and the irregular changes in situ are macroscopic inhomogeneities. This work is an effort for accounting for these stochastic changes in the elastic properties and density in a rational manner. The method used is that of Karal and Keller which is based on the use of the Green's function and neglect of third order correlations. The resulting integral equations are solved by Laplace transform. The analysis indicates that the energy decay in the mean motion through random mode coupling introduces damping into even a purely elastic medium and enhances the damping in a significant manner in a hysteretic viscoelastic medium. This consideration is important in relating the damping and dispersion characteristics of waves in situ to those measured in the laboratory. The formulation is extended to multilayer systems through transfer matrices and to arbitrary inputs by Fourier transform. Sample calculations are presented for single and multilayer systems to obtain response spectra and for the response to Gaussian and actual earthquake input motions.
- Keywords
- Laplace transformation; Seismic waves; Mechanical hysteresis; Fourier transformation; Dynamic response; Earthquake engineering; Greens function; Elastic properties; Stochastic processes; Earthquakes