Conventional finite-difference operators for numerical differentiation become progressively inaccurate at higher frequencies and therefore require very fine computational grids. This problem is avoided when the derivatives are computed by multiplication in the Fourier domain. However, because matrix transpositions are involved, efficient application of this method is restricted to computational environments where the complete data volume required by each computational step can be kept in random access memory. To circumvent these problems a generalized numerical dispersion analysis for wave equation computations is developed. Operators for spatial differentiation can then be designed by minimizing the corresponding peak relative error in group velocity within a spatial frequency band. For specified levels of maximum relative error in group velocity ranging from 0.03% to 3%, differentiators have been designed that have the largest possible bandwidth for a given operator length. The relation between operator length and the required number of grid points per shortest wavelength, for a required accuracy, provides a useful starting point for the design of cost-effective numerical schemes. To illustrate this, different alternatives for numerical simulation of the time evolution of acoustic waves in three-dimensional inhomogeneous media are investigated. It is demonstrated that algorithms can be implemented that require fewer arithmetic and I/O operations by orders of magnitude compared to conventional second-order finite-difference schemes to yield results with a specified minimum accuracy.

Computational Aspects of the Choice of Operator And Sampling Interval For Numerical Differentiation In Large-Scale Simulation of Wave Phenomena

In one-dimensional hexagonal piezoelectric quasi-crystals, there exist the phonon–phason, electro–phonon, and electro–phason couplings. Therefore, the phonon–phason coupling and piezoelectric effec...

Axial guided wave characteristics in functionally graded one-dimensional hexagonal piezoelectric quasi-crystal cylinders:

Anatomy of flexoelectricity in micro plates with dielectrically highly/weakly and mechanically complaint interface

In the present article, a theoretical investigation has been carried out to analyze the propagation of shear horizontal surface waves (SH-waves) in a structure consisting of a functionally graded p...

Mathematical analysis of surface wave transference through imperfect interface in FGPM bedded structure

In this article, the generalized model for thermoelastic waves with two relaxation times is utilized to compute the increment of temperature, the displacement components, the stress components, and the changes in the volume fraction field in a two-dimensional porous medium. By using the Fourier-Laplace transform and the eigenvalue method, the considered variables are obtained analytically. The derived approach is estimated with numerical outcomes which are applied to the porous media with a geometrical simplification. The numerical results for the considered variables are performed and presented graphically. Finally, the outcomes are represented graphically to display the difference among the classical dynamical (CD) coupled, the Lord-Shulman (LS), and the Green-Lindsay (GL) models.

Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux

Analysis of mechanical vibration (SH wave) in Piezo-composite plates

The frequency of the Love-type surface waves in a bedded structure consisting of a porous piezoelectric (PP) medium and a functionally graded material (FGM) substrate is approximated. The FGM layer is assumed to have a constant initial stress. The Wentzel-Kramers-Brillouin (WKB) approximation technique is used for the wave solution in the FGM layer, and the method of separation of variables is applied for the solution in the porous piezoelectric medium. The dependence of the wave frequency on the wave number is obtained for both electrically open and short cases. The effects of the gradient coefficient of the FGM layer, the initial stresses (tensile stress and compressive stress), and the width of the FGM layer are marked distinctly and shown graphically. The findings may contribute towards the design and optimization of acoustic wave devices.

Transference of Love-type waves in a bedded structure containing a functionally graded material and a porous piezoelectric medium

A mathematical model is presented to describe the propagation of torsional surface waves in a corrugated loosely bonded orthotropic layer sandwiched between two initially stressed viscoelastic half-spaces. The dispersion relation in a closed form is obtained for the analytical model. It is found that the initial stress, hydrostatic stress, viscoelasticity, and the bonding and flatness parameters have a great effect on the phase velocity of torsional surface waves. The method of separation of variables is employed to obtain an analytical solution in the present study. Some particular cases are discussed, and it is found that the results obtained well agree with the classical Love wave equation. Numerical simulations have also been performed to show results of the present analytical study graphically.

Analysis of Torsional Waves in a Prestressed Composite Structure with Loosely Bonded and Corrugated Boundaries

The present study presents the propagation of horizontally polarized shear waves (SH-waves) in highly anisotropic layered media under the effect of horizontal and vertical initial stresses. Following Biot’s theory of incremental stresses, the present problem has been formulated. The dispersion equation has been derived using the Thomson–Haskell matrix method. Closed form expressions for phase and group velocities have been obtained using finite difference schemes. Also, the stability condition of using this finite difference scheme has been achieved. Substantial influence of the Courant number (stability ratio), tensile and compressive stress on both phase and group velocities has been observed and depicted through graphs.

Modeling of SH-Wave Propagation in a Pre-stressed Highly Anisotropic Layered Structure

The present study deals with the propagation of a polarized shear horizontal (SH) wave in a pre-stressed piezoelectric cylinder circumscribed by a self-reinforced cylinder. The interface of the two media is assumed mechanically imperfect. For obtaining the dispersion relation, the mathematical formulation has been developed and solved by an analytical treatment. The effects of various parameters, i.e., the thickness ratio, the imperfect interface, the initial stress, the reinforcement, and the piezoelectric and dielectric constants, on the dispersion curve are observed prominently. The dispersion curves for different modes have been also plotted. The consequences of the study may be used for achieving optimum efficiency of acoustic wave devices.

Kamlesh K. Pankaj

Papers

Analysis of mechanical vibration (SH wave) in Piezo-composite plates

Transference of Love-type waves in a bedded structure containing a functionally graded material and a porous piezoelectric medium

Analysis of Torsional Waves in a Prestressed Composite Structure with Loosely Bonded and Corrugated Boundaries

Modeling of SH-Wave Propagation in a Pre-stressed Highly Anisotropic Layered Structure

Surface wave transference in a piezoelectric cylinder coated with reinforced material