The effect of inextensibility on elastic surface waves

Whitworth, A. M.; Chadwick, P.

doi:10.1016/0165-2125(84)90032-5

Cited by 5 publications

(6 citation statements)

References 12 publications

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“…This is very similar to the case of inextensible materials examined by Whitworth and Chadwick [34] and Captain and Chadwick [35]. We expect the other eigenvalues to be complex.…”

Section: Accepted Manuscript Subsection Is Not Valid supporting

confidence: 66%

“…Such a constraint is very often used to model strongly anisotropic fibre-reinforced composites. Surface-wave propagation in such a constrained elastic material has previously been examined by Whitworth and Chadwick [34] and Captain and Chadwick [35]. If we assume that the fibre direction e is given by e = m m + n n + l l, where l = m ∧ n, As remarked earlier, the constraint of inextensibility belongs to our special case φ = kθ.…”

mentioning

confidence: 93%

“…Over the past five decades, such constrained material models have frequently been used in the study of acceleration waves, shock waves, and body waves [17][18][19][20][21][22][23][24][25]. They have also been used in the study of surface waves [26][27][28][29][30][31][32][33][34][35][36][37]. In this paper, we shall consider a generally constrained and prestressed elastic material.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

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

Edmondson

2009

International Journal of Non-Linear Mechanics

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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.

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“…This is very similar to the case of inextensible materials examined by Whitworth and Chadwick [34] and Captain and Chadwick [35]. We expect the other eigenvalues to be complex.…”

Section: Accepted Manuscript Subsection Is Not Valid supporting

confidence: 66%

mentioning

confidence: 93%

Section: Accepted Manuscriptmentioning

confidence: 99%

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

Edmondson

2009

International Journal of Non-Linear Mechanics

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“…In another paper (24), the propagation of plane harmonic waves of small amplitude was examined without any restriction on the material symmetry and without the assumption that the undisturbed state is stress free. The secular equation was derived in a form that made clear the association of low-and high-frequency behaviour with isentropic and isothermal conditions, respectively.…”

Section: Wave Propagation In Heat-conducting Elastic Mediamentioning

confidence: 99%

“…In two papers (26, 27) conditions were identified under which an interfacial wave can propagate along the boundary between two adjoined half-spaces of neo-Hookean elastic material subjected to triaxial extensions of different magnitudes in directions in and normal to the interface. In the first (26), the in-plane stretches (in directions parallel to the interface) were taken to be equal in each of the constituent half-spaces, while in the second (27) the two half-spaces were subjected to different stretches along common axes, one of them normal to the interface, without restriction on the magnitudes of the in-plane stretches. The domains of existence of interfacial waves were catalogued in detail.…”

Section: Scientific Workmentioning

confidence: 99%

Peter Chadwick. 23 March 1931—12 August 2018

Ogden

2020

Biogr. Mems Fell. R. Soc.

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Peter Chadwick studied mathematics as an undergraduate at the University of Manchester, graduating with first-class honours in 1952, from where he moved to Cambridge and completed a PhD on the thermal history of the Earth in the Department of Geodesy and Geophysics under the supervision of Dr Robert Stoneley. His research then developed to focus primarily on the propagation of waves, and he made a major contribution to the mathematical theory of elastic wave propagation and became a world-leading authority in this area. He also made fundamental advances in the modelling of the thermo-elastic properties of rubberlike materials. At the University of East Anglia, where he was a professor for 26 years, he was the driving force behind the development of a research group in theoretical mechanics in the School of Mathematics and Physics, leading by example and supporting and encouraging fellow faculty members, especially the younger staff, academic visitors and students. He gave considerable service to the University of East Anglia in a number of capacities, including a period as Dean of the School, and to the scientific community, through substantial journal editorial activities and as a member of several national and international committees.

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