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

Reflection and transmission of waves at the common interface of piezoelectric half-spaces with microstructure

Dynamic analysis of piezoelectric materials with an elliptical hole under the action of shear horizontal waves

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

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.

Surface wave transference in a piezoelectric cylinder coated with reinforced material

Present study primarily focuses on interpreting the propagation pattern of Shear horizontal (SH) wave in a piezo-composite layered cylinder. The structure consists of three concentric cylinders com...

Analysis of SH wave in hollow piezo-composite cylinder with coupled imperfect interface condition

This study concentrates on the propagation pattern of shear horizontal (SH) waves on the conductive liquid-loaded porous piezoelectric media. Porous piezoelectric media is composed of fluid saturated functionally graded porous piezoelectric material (FGPPM) plate and functionally graded piezoelectric material (FGPM) half-space. The functional grading is assumed to be exponential for the FGPPM layer and quadratic for the FGPM layer respectively, along the direction of thickness. The mechanical imperfection is considered at the interface of the two media. The dispersion and the attenuation curve have been plotted to describe the impact of various parameters, namely gradient parameter of both the piezoelectric material, thickness of FGPPM plate, imperfect interface parameter, relative permittivity and conductivity of the liquid medium. Also, different modes for both the dispersion and attenuation curves have been delineated to get a better insight. Dispersion equations for non-conductive liquid loaded piezo-composite have also been obtained for both electrically open and short circuit conditions. To validate the present outcome, the geometry is reduced to special cases and the outcome is matched with pre-existing results. This article may find its application in better understanding of SAW devices incorporated with liquid layer. 

Shreeta Kumari

Papers

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

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

Surface wave transference in a piezoelectric cylinder coated with reinforced material

Analysis of SH wave in hollow piezo-composite cylinder with coupled imperfect interface condition

SH wave vibration in functionally graded porous piezoelectric composite loaded with Newtonian conductive/non-conductive liquid