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MODAL ANALYSIS OF SOFT‐SOIL SITES INCLUDING RADIATION DAMPING
Author(s) -
ZHAO J. X.
Publication year - 1997
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/(sici)1096-9845(199701)26:1<93::aid-eqe625>3.0.co;2-a
Subject(s) - modal , radiation damping , modal testing , damping ratio , half space , modal analysis , rigidity (electromagnetism) , homogeneous , radiation , physics , mechanics , finite element method , mathematical analysis , materials science , mathematics , optics , structural engineering , acoustics , engineering , vibration , particle physics , polymer chemistry , thermodynamics
For the one‐dimensional analysis of soft‐soil layers on an elastic half‐space, a general form of analytical solution is developed for converting radiation damping due to energy leaking back to the half‐space into equivalent modal damping, allowing the modal analysis technique to be extended to a site where radiation damping has to be accounted for. Closed‐form solutions for equivalent modal damping ratios and effective modal participation factors are developed for a single layer with a shear wave velocity distribution varying from constant to linearly increasing with depth. Compact and recursive forms of solutions for equivalent modal damping ratios are developed for a system with an arbitrary number of homogeneous layers on an elastic half‐space. Comparisons with numerical solutions show that the modal solutions are accurate. The nominal frequency of a site, i.e. the inverse of four times the total shear wave travel time through the layers, is an important parameter for estimating the high mode frequencies. A parameter study shows that for the same impedance ratio of the bottom layer to the elastic half‐space, a system of soil layers with an increasing soil rigidity with depth has, in general, larger peak modal amplifications at the ground surface than does a single homogeneous layer on an elastic half‐space, while a system with a decreasing soil rigidity with depth has smaller modal peak amplifications. © 1997 by John Wiley & Sons, Ltd.