Self-orthogonal sextic formalism for anisotropic elastic media: spaces of simple reflection and two component surface waves

Stroh Formalism and Rayleigh Waves

“…The existence of surface waves for which Stroh's eigenvalue problem (3.14) is degenerate is considered in [37,79,83,86]. For supersonic surface waves, we refer, for example, to [32,44] and the references therein. Theorem 3.12, which we have used to find the secular equations for Rayleigh waves in Sections 3.4 and 3.5, goes back to the work in [14].…”

“…44) In this case, by (1.18) and (1.26), the general form of the basic solution to (1.17) which describes two-dimensional 5 deformations in the half-space n · x ≤ 0, satisfies the condition u = a e − √ −1 ξ m·x on n · x = 0 for some complex vector a, and decays to zero as n · x −→ −∞ is written as…”

“…A necessary and sufficient condition for the existence of the Rayleigh waves in the halfspace n · x ≤ 0 which propagate along the surface n · x = 0 in the direction of m with 44 The positive definiteness of S 2 (v) (0 ≤ v < v L ) and that of d dv S 3 (0 < v < v L ) are proved under the strong ellipticity condition (1.79) because only the positive definiteness of T(φ) for all φ is needed there (see Lemma 3.5 and Lemma 3.15). On the other hand, the more stringent strong convexity condition (1.7) is needed for the negative definiteness of S 3 (0) (cf.…”

“…For the proof, which is long, we refer to Section 5.C of [22], [31,76] and Section 7.6 of [77]. 44 Since the negative definiteness of S 3 (0) implies that all its eigenvalues are negative, it follows from (2) of Lemma 3.15 that all the eigenvalues of S 3 (v) increase monotonically with v in the interval 0 ≤ v < v L from their negative values at v = 0. Now we give a criterion for the existence of Rayleigh waves based on the behavior of S 3 (v) in the transonic limit v ↑ v L .…”

Pseudo surface acoustic waves in&#x03B1;-quartz

“…I NTENSIVE numerical studies of the properties of surface (SAW ) and leaky (L SA W) acoustic waves on symmetric planes of elastic crystals [1][2][3] show that in some propagation direction of LSA W its energy leakage vanishes into the medium, and the wave becomes as two partial pseudo surface acoustic wave (PSA W), called also as an isolated (genuine ) surface wave [4][5] or secluded supersonic acoustic surface wave [6][7][8][9][10]. Three necessary conditions, which provide the existence of PSA W on anisotropic elastic crystals, were obtained analytically in explicit form [4].…”