Antiplane (SH) Waves Diffraction by a Semicircular Cylindrical Hill Revisited: An Improved Analytic Wave Series Solution

Surface motion of a semi-elliptical hill for incident plane SH waves

“…It can be seen that they agree very well with each other. Figure 8 illustrates the comparison of our result of nearly semi-circular hill (M =0.99) for incident frequency ETA=5.0 with those of semi-circular hill by Lee et al (2006) and Liang and Ba (2008). It is observed that there is nearly no difference among them.…”

“…So equation (14) cannot be solved directly and the nonorthogonal terms must be replaced by the orthogonal ones. Cosine series {cosnη, n∈integer} satisfy this requirement, and a sine function, after even extension, can be expanded as (Lee et al, 2006) …”

“…Then the solutions were improved to higher incident frequency by sine and cosine series expansion technique (Lee et al, 2006). Compared with a semi-cylindrical hill or a shallow circular hill, a semi-elliptical hill is more approximate for natural convex topography, and especially it can simulate a very prolate hill.…”

“…Compared with a semi-cylindrical hill or a shallow circular hill, a semi-elliptical hill is more approximate for natural convex topography, and especially it can simulate a very prolate hill. This paper presents a closed-form solution of surface motion of semi-elliptical hill for incident plane SH waves by using the sine and cosine series expansion technique proposed by Lee et al (2006), and aims at giving results for some very prolate hills for high incident frequency and explaining some vibrating properties.…”

Anti-plane (SH) waves diffraction by an underground semi-circular cavity: analytical solution

“…Lee et al (2004) used the auxiliary function method to obtain an analytical solution of a semi-circular hill with an inside concentric semi-circular tunnel. Lee et al (2006) adopted a convenient improved Cosine Half-range Expansion (Hinders and Yaghjian, 1991) to obtain an analytical solution for the same semi-circular hill modeled in Yuan and Men (1992), with much less displacement and stress residues, especially at two rims of the hill. Liang et al (2010) solved the same semicircular cavity model as the one presented in this paper by the auxiliary function method of Yuan and Men (1992).…”