#### Vol. 13, No. 3, 2018

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1559-3959 Author Index To Appear Other MSP Journals
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 H$∕$V 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 H$∕$V ratio is obtained using the secular equation and the relation between the H$∕$V ratio and the Rayleigh wave velocity. Then, formulas for the H$∕$V ratio are derived for a general strain-energy function. They are then specified for some strain-energy functions. Since the H$∕$V 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.

##### 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