Force mobility of an elastic stratum over a rigid base: Part I. Approximate solution
2006 (English)In: Acta Acoustica united with Acustica, ISSN 1610-1928, E-ISSN 1861-9959, Vol. 92, no 3, 378-389 p.Article in journal (Refereed) Published
An approximate approach to derive the input mobility of an infinite elastic stratum on a rigid base is investigated. The excitation is due to a vertical force, which is applied via a small massless indenter with a circular base, fixed to the stratum. Two cases are investigated: a stratum with a fixed base and a stratum with a frictionless base. General expressions for the mobilities are derived from the equations of motion of an isotropic elastic medium. Using a numerical approach, the analytical results are evaluated up to a Helmholtz number k(L)d = 10, where k(L) is the wave number of the P- wave and d is the stratum depth. For small Helmholtz numbers, asymptotic expressions are derived analytically; the two evaluations agree well up to a Helmholtz number of 0.2 for the frictionless base and to 0.5 for the fixed base. It is shown that the mobilities for the two cases differ significantly at small Helmholtz numbers. This is mainly due to the influence of a propagating wave, which can exist only in the case of a frictionless base. It is also shown that the local deformations in the vicinity of the indenter are built up by low-frequency, non-propagating Lamb modes. Finally, the dispersion relations are evaluated up to a Helmholtz number k(L)d = 16.
Place, publisher, year, edition, pages
2006. Vol. 92, no 3, 378-389 p.
IdentifiersURN: urn:nbn:se:kth:diva-152148ISI: 000238264600005ScopusID: 2-s2.0-33745365265OAI: oai:DiVA.org:kth-152148DiVA: diva2:749221
QC 201409232014-09-232014-09-232014-09-23Bibliographically approved