In this paper the effects of heat conduction upon the propagation of Rayleigh surface waves in a semi-infinite elastic solid are studied theoretically in two special cases: (i) when the surface of the solid is maintained at constant temperature (case 1); and (ii) when the surface is thermally insulated (case 2). The investigation is carried out within the framework of the linear theory of thermoelasticity, a principal objective being the clarification of the relation between so-called thermoelastic Rayleigh waves and the Rayleigh waves of classical elastokinetics. The secular equation for thermoelastic Rayleigh waves is shown to define a many-valued algebraic function
μ
(
X
) (
X
being a dimensionless frequency) the branches of which represent possible modes of surface wave propagation. Two different types of surface mode are recognized:
E
-modes, which resemble classical Rayleigh waves but are subject to damping and dispersion; and
T
-modes, which are essentially diffusive in character. Necessary and sufficient conditions for the existence of a surface wave are formulated, and questions of the existence and multiplicity of Rayleigh
E
- and
T-modes in particular situations are resolved by submitting the branches of
μ
(
X
) to these requirements. The algebraic function
μ
(
X
) has singular points at
X
= 0 and
X
= ∞, and approximations, valid at sufficiently low or at sufficiently high frequencies, to the speed of propagation
v
and the attenuation coefficient
q
of a given surface mode are obtainable from series representations of the appropriate branch of
μ
(
X
) in neighbourhoods of these singularities. The singular point
X
= 0 is associated with adiabatic deformations of the solid, and hence with classical Rayleigh waves, and the singularity at
X
= ∞ with isothermal deformations. Particular attention is devoted to the Rayleigh
E
-modes and the main conclusions reached are as follows. In case 1 there exists a single
E
-mode (mode 2) at low frequencies and two distinct
E
-modes (modes 1 and 2) at high frequencies. For mode 2,
v
/
v
R
= 1 +
O
(
X
½
),
q
=
O
(
X
3/2
)
X
distinct 0 (
v
R
being the speed of propagation of classical Rayleigh waves), and for both modes
v
and
q
approach finite limits as
X
→ ∞. In case 2 the converse situation applies, there being two distinct
E
-modes (modes 1 and 2) at low frequencies and only one (mode 1) at high frequencies. For both modes,
v
/
v
R
= 1 +
O
(
X
3/2
),
q
=
O
(
X
2
) as
X
→ 0, and for mode 1,
v
and
q
approach finite limits as
X
→ ∞. Detailed numerical results referring to a medium of worked pure copper at a reference temperature of 20 °C are given. In particular the frequency dependence of the speeds of propagation and attenuation coefficients of the various
E
-modes are exhibited, and the frequencies at which mode 1 appears in case 1 and at which mode 2 disappears in case 2 are determined.
The influence of exchange interaction and dynamic demagnetizing field on dispersion properties of Damon-Eshbach surface wave. Part 3. Special cases of dispersion.
