Stoneley waves at the generalized Wiechert condition
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Zeitschrift f¨ ur angewandte Mathematik und Physik ZAMP
Stoneley waves at the generalized Wiechert condition S. V. Kuznetsov Abstract. A generalization of the Wiechert condition by introducing two independent dimensionless parameters instead of one parameter in the original Wiechert condition is proposed. Variation of Stoneley wave velocity at varying two parameters of the generalized Wiechert condition at different Poisson’s ratios is studied revealing a substantial discrepancy in Stoneley wave velocity profiles. Mathematics Subject Classification. 35Q74, 74J15. Keywords. Stoneley wave, Secular equation, Wiechert condition, Velocity.
1. Introduction Herein, propagation of the interfacial Stoneley waves in layered media satisfying a more general condition, than the original Wiechert condition, is analyzed. (In more details, Wiechert condition is discussed in the next subsection.) The Wiechert condition [1,2] plays an important role in various applications in acoustics and, especially in studies of the interfacial Stoneley waves. In this respect, in the pioneering Stoneley work [3] existence of Stoneley waves propagating on an interface between two dissimilar isotropic halfspaces was studied at an assumption that physical properties of the halfspaces obey Wiechert condition; in [3] an explicit algebraic secular equation for Stoneley wave velocity was also derived. The vast majority of the subsequent studies on Stoneley wave propagation in layered isotropic media were concerned with the Wiechert condition [4–16]. In [4,5], regions of existence for Stoneley waves plotted in terms of their relative physical parameters were constructed numerically, revealing that the Wiechert line belongs to the region of existence. Various forms of secular equations for Stoneley wave velocity were constructed in [6–12]. Several analytical methods for solving secular equations for Stoneley wave velocity were suggested in [13–15]. In [16], it was demonstrated that the studied regions of existence for Stoneley waves are multiply connected, instead of the previously assumed simply connected ones. Appearance of high-frequency Stoneley waves generated by propagation of Lamb waves in layered plates was studied numerically in [17–19] and by constructing high-frequency asymptotics in [20,21]. Stoneley waves propagating on an interface between anisotropic halfspaces were mainly studied by applying either three-dimensional formalism [22] or by complex sextic formalisms [23–25]. 1.1. Wiechert condition The original Wiechert condition asserts that the dimensionless physical parameters responsible for acoustic properties of the contacting media are proportional to a single parameter q. Consider inhomogeneous space consisting of two isotropic homogeneous halfspaces in a contact. Acoustical properties of the contacting halfspaces can be described by the following dimensionless parameters μ1 ρ1 ˜ = λ1 , ˜= , λ (1.1) ρ˜ = , μ ρ2 μ2 λ2 0123456789().: V,-vol
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where ρk are the material densities, and μk , λk , k =
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