Stoneley waves at the Wiechert condition
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Zeitschrift f¨ ur angewandte Mathematik und Physik ZAMP
Stoneley waves at the Wiechert condition S. V. Kuznetsov
Abstract. The interfacial Stoneley waves at the Wiechert condition imposed on physical properties of the adjacent isotropic and homogeneous halfspaces are analyzed. It is shown both theoretically and numerically that the speed of propagation of Stoneley waves along the Wiechert line is a monotonically decreasing function of the dimensionless Wiechert parameter. It is also found that such a monotonic behavior takes place at the nonnegative values of Poisson’s ratio. The observed monotonic behavior delivers the unique possibility for applying acoustic methods to nondestructive evaluation of physical parameters of media satisfying the Wiechert condition. Mathematics Subject Classification. 35Q72, 74J15. Keywords. Guided wave, Stoneley wave, Dispersion, Wiechert condition.
1. Introduction Stoneley waves propagating along an interface between two dissimilar isotropic and homogeneous halfspaces in a contact are analyzed by applying Cauchy sextic formalism coupled with the exponential fundamental matrix method [1,2]. That formalism was initially developed for study of guided wave propagation in stratified plates, and later on, it was modified for application to acoustics of functionally graded (FG) plates [3]. In the current research, the main attention is paid to the case when physical properties of the contacted halfspaces satisfy the Wiechert condition [4,5] with relation to velocities of the interfacial Stoneley waves [6]. In [7–9], it was observed that at high frequencies Lamb waves propagating in stratified media are transformed into Stoneley waves, if the adjacent layers satisfy Wiechert condition. It was also observed that the number of different Stoneley waves propagating in stratified plates with periodic structure depends upon symmetric (with the odd number of alternating layers) or asymmetric layout of layers (with the even number of layers) [9]. Herein, it is shown both theoretically and numerically that the speed of propagation of Stoneley waves along Wiechert line is monotonically decreasing in the range q ∈ (1, ∞) where q is the dimensionless Wiechert parameter; for the definition, see Sect. 2. The observed monotonic variation delivers the unique possibility for applying acoustic methods to nondestructive evaluation of physical parameters of contacting media obeying Wiechert condition; see Remark 3.2. Moreover, the observed monotonic variation of Stoneley wave velocity takes place for all studied (nonnegative) values of Poisson’s ratio; see Sect. 3.3. It should be noted that the Wiechert condition was originally proposed to describe the physical properties of the layered structure of the Earth’s crust [4,5]; since that time, the Wiechert condition plays an important role in the problems of Stoneley wave existence [7–17]. In this respect, the Wiechert line plays an important role in deriving conditions of existence. The Wiechert line is defined as the straight 0123456789().: V,-vol
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