Authors' reply to discussion by Chongmin Song and John P. Wolf of ‘numerical evaluation of the damping-solvent extraction method in the frequency domain’ Earthquake Engng. Struct. Dyn. 2002; 31(6):1231–1250

✍ Scribed by Ushnish Basu; Anil K. Chopra

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 35 KB
• Volume: 32
• Category: Article
• ISSN: 0098-8847
• DOI: 10.1002/eqe.281

✦ Synopsis

Discussion by Dr Chongmin Song and Dr John P. Wolf, especially because (i) they clarify their approach towards choosing a ÿnite-element mesh for use in the DSE method; and (ii) provide a complete description of their choice of ÿnite element meshes used in obtaining the results for dynamic sti ness of an embedded foundation in Ref. 8 of our paper (Wolf JP, Song C. Finite-Element Modelling of Unbounded Media. Wiley; Chichester; England, 1996). These results are repeated in the Discussion, which pertains to three questions: (i) What is an adequate domain size? (ii) How does artiÿcial damping in uence accuracy? and (iii) Would a smaller domain su ce if artiÿcial damping is increased? Our comments on these questions follow.

What is an adequate domain size?

To paraphrase the approach of the Discussers, the bounded domain and its ÿnite-element mesh may be chosen as follows:

1. Choose an appropriate artiÿcial damping ratio. 2. Choose a domain size (and mesh density) for the lowest frequency of interest either by trial-and-error-'by comparing the results from meshes of di erent sizes and densities'-or by experience. 3. Determine the highest frequency for which the chosen mesh density is adequate. 4. Reduce the domain size and increase the mesh density for frequencies higher than this frequency.

We recognize that the domain size may be reduced at higher frequencies, having discussed this issue in the last paragraph on page 1238 of our paper.