On Waves Propagated along the Plane Surface of an Elastic Solid
John W. Strutt, Lord Rayleigh, D.C.L., F.R.S., 2007. "On Waves Propagated along the Plane Surface of an Elastic Solid", Classics of Elastic Wave Theory, Michael A. Pelissier, Henning Hoeber, Norbert van de Coevering, Ian F. Jones
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It is proposed to investigate the behaviour of waves upon the plane free surface of an infinite homogeneous isotropic elastic solid, their character being such that the disturbance is confined to a superficial region, of thickness comparable with the wave-length. The case is thus analogous to that of deep-water waves, only that the potential energy here depends upon elastic resilience instead of upon gravity.
Denoting the displacements by α, β, γ, and the dilatation by θ, we have the usual equations
Figures & Tables
In this chapter, we give a brief synopsis of each of the classic papers referred to in this collection. Where relevant, we reproduce the basic equations, recast in modern notation. Supporting works also are referred to. They are listed in the “General References” section.
Table 1 is a quick outline of the key contributions of each paper reprinted in this book.
Robert Hooke, “Potentia Restitutiva, or Spring” (Oxford, 1678)
The article by Robert Hooke, “Potentia Restitutiva, or Spring,” contains the statement of the proportional relation between stress and strain universally referred to as Hooke’s law. Although the English language has evolved somewhat since 1678, the article does not require translation. Hooke describes a variety of experiments, accompanied by illustrations, confirming the stress/strain relation over a wide range of applied loads. He emphasizes the great generality of his results.
Based on his experimental work from 1660 onward, Hooke first published his law in 1676 in the form of an anagram in Latin,
which he later revealed to be “ut tensio sic vis.” Roughly translated, this means “as the force, so is the displacement” (Love, 1911; Boyce and DiPrima, 1976).
In his treatise, Hooke examined the behavior of springs, so his first casting of the equations dealt with the restoring force on a spring, for a given displacement: