A.L. Shuvalov

Nonlinear shear wave interaction at a frictional interface: Energy dissipation and generation of harmonics

Analytical and numerical modeling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and the influence on interface behavior is investigated: Coulombs law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and the dependence on the contact dynamics (friction law, sliding, and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface.

Transmission of acoustic waves through piezoelectric plates: modeling and experiment

The transmission of acoustic waves through a piezoelectric plate is dealt with theoretically and experimentally. The analytical treatment engages the octet formalism of anisotropic piezoacoustics. A specific version of the plate admittance matrix is introduced, which incorporates the electric boundary conditions for a non-metallized or metallized plate. In consequence, expressions for the reflection and transmission coefficients are reduced to explicitly the same form as in the case of pure elasticity. This theoretical model is then applied for material characterization. Material constants of a Pz27 plate are inferred from the numerical simulations and the experimental results of ultrasonic-transmission measurements. Good agreement is observed with another method based on electrical-impedance measurements. The impact of electrical boundary conditions is visualized by presenting the numerical and experimental transmission spectra through the Pz27 plate with non-metallized and metallized faces.

Converging Bounds for the Effective Shear Speed in 2D Phononic Crystals

Calculation of the effective quasistatic shear speed c in 2D solid phononic crystals is analyzed. The plane-wave expansion (PWE) and the monodromy-matrix (MM) methods are considered. For each method, the stepwise sequence of upper and lower bounds is obtained which monotonically converges to the exact value of c. It is proved that the two-sided MM bounds of c are tighter and their convergence to c is uniformly faster than that of the PWE bounds. Examples of the PWE and MM bounds of effective speed versus concentration of high-contrast inclusions are demonstrated.

Dispersion spectrum of acoustoelectric waves in 1D piezoelectric crystal coupled with 2D infinite network of capacitors

A one-dimensional piezoelectric crystal coupled through periodically embedded electrodes with a two-dimensional semi-infinite periodic network of capacitors is considered. The unit cell of the network contains two capacitors with capacitances C1 and C2 which are in parallel and in series, respectively, with the electrodes. The dispersion spectrum of the longitudinal acoustoelectric wave in the piezoelectric crystal coupled with the electric wave of potentials and charges in the network of capacitors is investigated. It is shown that when C1 and C2 are of the same sign, the dispersion spectrum consists of a discrete set of curves, for which the electric wave exponentially decays into the depth of the network of capacitors. In contrast, if C1 and C2 are of the opposite sign and |C1/C2|<1, then the spectrum simultaneously includes the discrete set of dispersion curves, corresponding to the localized waves, and the continuous band, which admits a finite but not localized (not decaying into the depth) wave field at any frequency and wavenumber within the band. Finally, when C1 and C2 are of the opposite sign and |C1/C2|≥1, the whole dispersion spectrum is a continuous band. The width of the continuous band and the equation describing the dispersion curves are found explicitly; the equation for the wave field is also obtained. Another interesting spectral feature is the unusual non-monotonic shape of the dispersion curves for a certain range of C1(<0), C2. This shape is due to the hybridization of the individual spectra of the crystal and of the network of capacitors.A one-dimensional piezoelectric crystal coupled through periodically embedded electrodes with a two-dimensional semi-infinite periodic network of capacitors is considered. The unit cell of the network contains two capacitors with capacitances C1 and C2 which are in parallel and in series, respectively, with the electrodes. The dispersion spectrum of the longitudinal acoustoelectric wave in the piezoelectric crystal coupled with the electric wave of potentials and charges in the network of capacitors is investigated. It is shown that when C1 and C2 are of the same sign, the dispersion spectrum consists of a discrete set of curves, for which the electric wave exponentially decays into the depth of the network of capacitors. In contrast, if C1 and C2 are of the opposite sign and |C1/C2|<1, then the spectrum simultaneously includes the discrete set of dispersion curves, corresponding to the localized waves, and the continuous band, which admits a finite but not localized (not decaying into the depth) wave fi...