Effect of Initial Stress on the Behavior of Love Waves in an Elastic Half-Space with a Functionally Graded Layer

2008 ◽  
Vol 33-37 ◽  
pp. 669-674 ◽  
Author(s):  
Zheng Hua Qian ◽  
Feng Jin ◽  
Kikuo Kishimoto
Keyword(s):  
Initial Stress ◽  
Half Space ◽  
Love Wave ◽  
Dispersion Relations ◽  
Functionally Graded ◽  
Love Waves ◽  
Shear Stresses ◽  
Thickness Direction ◽  
Mechanical Displacement ◽  
Graded Structures

The propagation behavior of Love waves in a functionally graded material layered half-space with initial stress is taken into account. The Wentzel-Kramers-Brillouin (WKB) asymptotic technique is adopted for the theoretical derivations. The analytical solutions are obtained for the dispersion relations and the distributions of mechanical displacement and stress along thickness direction in the layered structure. Firstly, these solutions are used to study effects of the initial stress on the dispersion relations and phase velocities, then influences of the initial stress on the distributions of mechanical displacement and shear stresses along thickness direction are discussed in detail. Numerical results obtained indicate that the phase velocity of Love wave increases with the increase of the magnitude of the initial tensile stress, while decreases with the increase of the magnitude of the initial compression stress. The effects on the dispersion relations of the Love wave propagation are negligible as the magnitudes of the initial stress are less than 100MPa. Some other results are shown for distributions of field quantities along thickness direction. The results obtained are not only meaningful for the design of functionally graded structures with high performance but also effective for the evaluation of residual stress distribution in the layered structures.

Love Wave in an Isotropic Half-Space with a Graded Layer

2013 ◽  
Vol 325-326 ◽  
pp. 252-255
Author(s):  
Li Gang Zhang ◽  
Hong Zhu ◽  
Hong Biao Xie ◽  
Jian Wang
Keyword(s):  
Shear Modulus ◽  
Half Space ◽  
Analytical Solutions ◽  
Love Wave ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Vibration Model ◽  
General Dispersion ◽  
Functionally Graded Layer

This work addresses the dispersion of Love wave in an isotropic homogeneous elastic half-space covered with a functionally graded layer. First, the general dispersion equations are given. Then, the approximation analytical solutions of displacement, stress and the general dispersion relations of Love wave in both media are derived by the WKBJ approximation method. The solutions are checked against numerical calculations taking an example of functionally graded layer with exponentially varying shear modulus and density along the thickness direction. The dispersion curves obtained show that a cut-off frequency arises in the lowest order vibration model.

scholarly journals Group and Phase Velocity of Love Waves Propagating in Elastic Functionally Graded Materials

2015 ◽  
Vol 40 (2) ◽  
pp. 273-281 ◽  
Author(s):  
Piotr Kiełczyński ◽  
Marek Szalewski ◽  
Andrzej Balcerzak ◽  
Krzysztof Wieja
Keyword(s):  
Group Velocity ◽  
Half Space ◽  
Functionally Graded Materials ◽  
Integral Formula ◽  
Liouville Problem ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Love Waves ◽  
Graded Materials ◽  
Sturm Liouville

AbstractThis paper presents a theoretical study of the propagation behaviour of surface Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in acoustics. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). Two Love wave waveguide structures are analyzed: 1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and 2) a semi-infinite nonhomogeneous elastic half-space. The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved 1) analytically in the case of the step profile, exponential profile and 1cosh2type profile, and 2) numerically in the case of the power type profiles (i.e. linear and quadratic), by using two numerical methods: i.e. a) Finite Difference Method, and b) Haskell-Thompson Transfer Matrix Method.The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The results obtained in this paper can give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials.

A Combined Fourier Series–Galerkin Method for the Analysis of Functionally Graded Beams

2004 ◽  
Vol 71 (3) ◽  
pp. 421-424 ◽  
Author(s):  
H. Zhu ◽  
B. V. Sankar
Keyword(s):  
Fourier Series ◽  
Differential Equations ◽  
Galerkin Method ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Beam ◽  
Fourier Series Method ◽  
Bending Stresses ◽  
The Galerkin Method ◽  
Graded Structures

The method of Fourier analysis is combined with the Galerkin method for solving the two-dimensional elasticity equations for a functionally graded beam subjected to transverse loads. The variation of the Young’s modulus through the thickness is given by a polynomial in the thickness coordinate and the Poisson’s ratio is assumed to be constant. The Fourier series method is used to reduce the partial differential equations to a pair of ordinary differential equations, which are solved using the Galerkin method. Results for bending stresses and transverse shear stresses in various beams show excellent agreement with available exact solutions. The method will be useful in analyzing functionally graded structures with arbitrary variation of properties.

Love wave in an isotropic homogeneous elastic half-space with a functionally graded cap layer

2014 ◽  
Vol 231 ◽  
pp. 93-99 ◽  
Author(s):  
Hong Zhu ◽  
Ligang Zhang ◽  
Jiecai Han ◽  
Yumin Zhang
Keyword(s):  
Half Space ◽  
Love Wave ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Cap Layer

scholarly journals Propagation of Love-Type Wave in Porous Medium over an Orthotropic Semi-Infinite Medium with Rectangular Irregularity

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Pramod Kumar Vaishnav ◽  
Santimoy Kundu ◽  
Shishir Gupta ◽  
Anup Saha
Keyword(s):  
Porous Medium ◽  
Dispersion Relation ◽  
Initial Stress ◽  
Half Space ◽  
Love Wave ◽  
Separation Of Variables ◽  
Infinite Medium ◽  
Type Wave ◽  
Bounded Below ◽  
Irregular Interface

Propagation of Love-type wave in an initially stressed porous medium over a semi-infinite orthotropic medium with the irregular interface has been studied. The method of separation of variables has been adopted to get the dispersion relation of Love-type wave. The irregularity is assumed to be rectangular at the interface of the layer and half-space. Finally, the dispersion relation of Love wave has been obtained in classical form. The presence of porosity, irregularity, and initial stress in the dispersion equation approves the significant effect of these parameters in the propagation of Love-type waves in porous medium bounded below by an orthotropic half-space. The scientific effect of porosity, irregularity, and initial stress in the phase velocity of the Love-type wave propagation has been studied and shown graphically.

Stresses at the Interface between the Functionally Graded Coating and the Elastic Half-Space Caused by Spherical Indentation

2007 ◽  
Vol 345-346 ◽  
pp. 833-836 ◽  
Author(s):  
S.M. Aizikovich ◽  
L.I. Krenev ◽  
I.S. Trubchik
Keyword(s):  
Half Space ◽  
Elastic Properties ◽  
Layered Structures ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Coating ◽  
Graded Coatings ◽  
Graded Coating ◽  
Functionally Graded Coatings

Recent advances in nanotechnology have revealed numerous new methods of manufacturing functionally graded coatings and materials, but progress in this field is limited by the lack of knowledge about the mechanical behavior of such structures. Existing models of the mechanics of layered structures are not generally adequate for this purpose, since functionally graded structures can exhibit both qualitative and quantitative behavioral differences in comparison with homogeneous or layered structures, particularly if there is a significant gradient of elastic properties in the coating. In applications, interest is focused mainly on the deformation fields and stresses inside the inhomogeneous material caused by the contact tractions. Stresses at the interface between the functionally graded coating and the elastic half-space are of particular interest because of their influence on the propagation of cracks and other defects on this interface. Shear stresses at this interface associated with rapid variation in elastic properties with depth are particularly dangerous because of potential delaminations. In their work the authors: • develop a precise mathematical model and of the computational methods which makes it possible to achieve stable numerical results while analyzing the mechanical properties of functionally graded coatings; • study the variation effect in elastic properties on the maximum stresses in the surface layers of materials with functionally graded coatings caused by indentation.

Love Wave Propagation in Prestressed Piezoelectric Layered Structure

2016 ◽  
Vol 08 (04) ◽  
pp. 1650045 ◽  
Author(s):  
Shishir Gupta ◽  
Abhijit Pramanik ◽  
Mostaid Ahmed ◽  
Arun Kumar Verma
Keyword(s):  
Wave Propagation ◽  
Initial Stress ◽  
Layered Structure ◽  
Love Wave ◽  
Love Waves ◽  
Piezoelectric Film ◽  
Elastic Substrate ◽  
Open Case ◽  
Piezoelectric Layered Structure ◽  
General Dispersion

In this paper, the effect of initial stress on the propagation of Love waves in a layered structure with a thin piezoelectric film bonded perfectly to an elastic substrate has been investigated. General dispersion equations, describing the properties of Love waves in both cases, electrically open case and electrically shorted case of the piezoelectric layer, have been obtained. The effects of inhomogeneity parameters in the substrate and the initial stress in both, the layer and the substrate on the phase velocity of Love waves, are analyzed and presented graphically. The analytical method and obtained results may find applications for designing the resonators and sensors.

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