Vol. 13, No. 3, 2018

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Formulas for the H$/$V ratio of Rayleigh waves in compressible prestressed hyperelastic half-spaces

Pham Chi Vinh, Thanh Tuan Tran, Vu Thi Ngoc Anh and Le Thi Hue

Vol. 13 (2018), No. 3, 247–261
Abstract

This paper concerns the propagation of Rayleigh waves in compressible prestressed elastic half-spaces. The main aim is to derive formulas for the HV ratio (ellipticity), which is the ratio of the amplitude of the horizontal displacement to the amplitude of the vertical displacement of Rayleigh waves. First, the equation for the HV ratio is obtained using the secular equation and the relation between the HV ratio and the Rayleigh wave velocity. Then, formulas for the HV ratio are derived for a general strain-energy function. They are then specified for some strain-energy functions. Since the HV ratio is a good tool for nondestructively evaluating the prestresses of structures before and during loading, the obtained formulas will be very useful in practical applications.

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Keywords
Rayleigh waves, prestressed half-spaces, H/V ratio, H/V ratio formulas
Milestones
Received: 25 October 2017
Revised: 8 April 2018
Accepted: 28 April 2018
Published: 31 August 2018
Authors
Pham Chi Vinh
Faculty of Mathematics, Mechanics and Informatics
Hanoi University of Science
Hanoi
Vietnam
Thanh Tuan Tran
Faculty of Mathematics, Mechanics and Informatics Hanoi University of Science
Hanoi
Vietnam
Vu Thi Ngoc Anh
Faculty of Mathematics, Mechanics and Informatics
Hanoi University of Science
Hanoi
Vietnam
Le Thi Hue
Vietnam National University of Forestry
Hanoi
Vietnam