Vol. 15, No. 1, 2020

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An approximate formula of first peak frequency of ellipticity of Rayleigh surface waves in an orthotropic layered half-space model

Truong Thi Thuy Dung, Tran Thanh Tuan, Pham Chi Vinh and Giang Kien Trung

Vol. 15 (2020), No. 1, 61–74
Abstract

The propagation of Rayleigh surface waves in an orthotropic composite layer with fixed bottom is considered by using the transfer matrix method. By considering the critical frequency, an explicit approximate formula of the peak frequency of the fundamental mode of H/V ratio curve is derived. In case the impedance contrast between the half-space and the layer is high, the obtained formula is shown to be the limit of the formula of the resonance frequency of the layers under the excitement of SH body waves, which demonstrates that the peak frequency of the H/V ratio could be interpreted as the resonance frequency of the layer. Since Rayleigh surface waves are easier to be excited than SH body incident waves traveling from the half-space to the surface of the layer, and the H/V ratio is a dimensionless quantity and it is easier to be measured than the response function of SH body waves, the obtained formula is potentially useful in measuring the resonance frequency of thin films deposited on a thick layer of substantially higher rigidity. Finally, some numerical calculations are carried out to illustrate that the obtained approximate formula is a good one for the resonance frequency of a composite layer, especially of a periodic composite layer.

Keywords
Rayleigh waves, SH body waves, orthotropy, H/V technique, resonance frequency, transfer matrix
Milestones
Received: 23 May 2019
Revised: 27 December 2019
Accepted: 29 January 2020
Published: 26 February 2020
Authors
Truong Thi Thuy Dung
Faculty of Mathematics, Mechanics and Informatics
VNU University of Science, Vietnam
Hanoi
Vietnam
Tran Thanh Tuan
Faculty of Mathematics, Mechanics and Informatics
VNU University of Science, Vietnam
Hanoi
Vietnam
Pham Chi Vinh
Faculty of Mathematics, Mechanics and Informatics
VNU University of Science, Vietnam
Hanoi
Vietnam
Giang Kien Trung
Faculty of Physics
VNU University of Science, Vietnam
Hanoi
Vietnam