An explicit expression for the surface-impedance tensor of a compressible monoclinic material in a state of plane strain

Fu, Yibin; Brookes, D. W.

doi:10.1093/imamat/hxh106

Cited by 9 publications

(9 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This type of constraint belongs to our general case for which (5.1) applies and we are able to reproduce all of the numerical results presented in Destrade and Ogden [32]. We also note that when the x 3 = 0 plane is a plane of symmetry, an even easier method for computing the surface-wave speed is available [41,42].…”

supporting

confidence: 56%

Stroh formulation for a generally constrained and pre-stressed elastic material

Edmondson

2009

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

The Stroh formalism is essentially a spatial Hamiltonian formulation and has been recognized to be a powerful tool for solving elasticity problems involving generally anisotropic elastic materials for which conventional methods developed for isotropic materials become intractable. In this paper we develop the Stroh/Hamiltonian formulation for a generally constrained and prestressed elastic material. We derive the corresponding integral representation for the surface-impedance tensor and explain how it can be used, together with a matrix Riccati equation, to calculate the surface-wave speed. The proposed algorithm can deal with any form of constraint, pre-stress, and direction of wave propagation. As an illustration, previously known results are reproduced for surface waves in a pre-stressed incompressible elastic material and an unstressed inextensible fibre-reinforced composite, and an additional example is included analyzing the effects of pre-stress upon surface waves in an inextensible material.

show abstract

supporting

confidence: 56%

Stroh formulation for a generally constrained and pre-stressed elastic material

Edmondson

2009

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

show abstract

“…The coefficients of a 24 From the approximate secular equation (30) and Lemma 4.6 we immediately obtain Proposition 4.7 The effects that the initial stress T • and the perturbative part A of the incremental elasticity tensor L have on the phase velocity v R , to first order of T • and A, come only from a 22 , a 23 , a 33 , a 44 and T • 22 . This proposition allows us to reduce the case where the perturbative part A is generally anisotropic and the initial stress T • is generally given by Equation (12) to the orthorhombic case with uniaxial stress in the propagation direction, which provides a highly efficient derivation of the perturbation formula (15).…”

Section: A Necessary and Sufficient Condition For The Existence Of Ramentioning

confidence: 88%

“…Therefore, the terms linear in a24 and a 34 included in the components r22 and r 33 vanish, and consequently, the effects of T • and A on r22 and r 33 come only from a 22 , a 23 , a 33 , a44 and T • 22 .…”

mentioning

confidence: 99%

Perturbation of phase velocity of Rayleigh waves in pre-stressed anisotropic media with orthorhombic principal part

Tanuma

Man

2012

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

Herein we derive an explicit first-order perturbation formula for the phase velocity of Rayleigh waves that propagate along the free surface of a homogeneous pre-stressed half-space, the incremental elasticity tensor L of which has a principal part C that is orthorhombic (with two of the axes of two-fold rotational symmetry being normal to the free surface and being the propagation direction, respectively) or transversely isotropic (with the ∞-axis being normal to the free surface). The remaining (perturbative) part A of the incremental elasticity tensor can be arbitrarily anisotropic. As an application of the perturbation formula, we consider the case where C is transversely isotropic and A is given by a contraction of the sixth-order acoustoelastic tensor with the pre-stress, and we examine the possibility of and the problems and issues about determination of the pre-stress by boundary measurement of phase velocities of Rayleigh waves.

show abstract

“…Finally, we note that for a generally prestressed isotropic elastic half-space, smallamplitude perturbations are governed by the incremental equation of motion 14) and the incremental traction-free boundary condition takes the form χ i2 = 0, on x 2 = 0, (4.15) where the incremental stress tensor (χ ij ) is given by χ ij = A jilknm in terms of the strain-energy function and the principal stretches can be found in Ogden (1984) or Appendix A of Fu and Ogden (1999). Thus, with c ijkl and e ijklmn identified with A 1 jilk and A 2 jilknm , respectively, all the results obtained above are also valid for a generally prestressed isotropic elastic half-space or coated half-space.…”

Section: Solitary Waves In a Coated Elastic Half-spacementioning

confidence: 94%

Linear and Nonlinear Wave Propagation in Coated or Uncoated Elastic Half-spaces

Waves in Nonlinear Pre-Stressed Materials

View full text Add to dashboard Cite

In these lectures, we discuss the following three closely related topics.(i) Unification of different methods for deriving evolution equations for surface acoustic waves. Early studies on nonlinear surface acoustic waves were thwarted by very complicated derivation of evolution equations. Worse still, different methods seemed to have given different evolution equations. Later on, it became known that all these methods except one yield the same evolution equation, but even at the time when we started to prepare the current lecture notes, there still existed a method that does not agree with the other methods. Such a situation is unsatisfatory since each method has some following. The purpose of the lectures on this topic is three-fold. Firstly, we aim to show that derviation of the evolution eqution for nonlinear surface waves can be carried out in one A4 page even in the most general case. Secondly, we show that the odd method that used to give a different evolution equation can in fact be used to obtain the same evolution equation if it is properly executed. Thus, we set the record straight: all known methods should and do give the same evolution equation! Thirdly, we express our evolution equation in terms of results from the linear surface-wave theory built on the Stroh formulation, and we explain how the coefficients in the evolution equation can be evaluated efficiently.(ii) Linear wave propagation in a coated elastic half-space. This is partly in preparation for our discussion of the third topic, but the problem is of much interest in its own right. We show how the dispersion relation can be expressed elegantly in terms of the surface-impedance matrices associated with the layer and the half-space. We derive a two-term expression for the wave speed in the long-wavelength limit.(iii) Periodic and solitary waves in a coated elastic half-space. An uncoated elastic half-space cannot in general support solitary waves due to lack of dispersion although it has been argued previously that the nonlocal character of nonlinearity may give rise to the existence of steady travelling waves. We derive the nonlinear evolution equation for small-amplitude long-wavelength travellingThe original publication is available at www.springerlink.com http://www.springerlink.com/content/978-3-211-73571-8/#section=264495&page=2&locus=50 2 waves propagating in a coated elastic half-space where the thin coating induces weak dispersion. When this evolution equation is linearized, we recover the two-term dispersion relation obtained in (ii). We explain a simple method that can be used to compute periodic or solitary travelling-wave solutions.

show abstract

An explicit expression for the surface-impedance tensor of a compressible monoclinic material in a state of plane strain

Cited by 9 publications

References 33 publications

Stroh formulation for a generally constrained and pre-stressed elastic material

Stroh formulation for a generally constrained and pre-stressed elastic material

Perturbation of phase velocity of Rayleigh waves in pre-stressed anisotropic media with orthorhombic principal part

Linear and Nonlinear Wave Propagation in Coated or Uncoated Elastic Half-spaces

Contact Info

Product

Resources

About