Generalized Rayleigh waves in a multi-layered structure of porous piezoelectric materials overlying a functionally graded porous piezoelectric base

Functionally graded materials (FGM) are materials in which there is a gradual variation in functional properties of the material so as to make it useful for different purposes. The life span and efficiency of Surface Acoustic Waves (SAW) devices can be increased by taking FGM into consideration. Further, FGM as a substrate can help to improve the structural integrity of a component or device. FGM substrates offer flexibility in design, enabling engineers to tailor the substrate's characteristics for specific functions within a device or system. Rayleigh-type surface waves, known for their numerous advantageous attributes, find extensive applications in various functional devices, and Rayleigh waves in functionally graded porous piezoelectric medium have not been studied so far and for more accurate simulation of field conditions, porous layers should be taken into account when determining the excitation and propagation processes of Rayleigh surface waves. Taking these considerations into account, this paper introduces a new model of composites of 'n' porous piezoelectric layers over functionally graded porous piezoelectric half-space (FGPPHS) and different characteristics of generalized Rayleigh waves in this model are studied. The material properties of the FGPPHS are taken to vary along the vertical direction (thickness). Closed form frequency equations are obtained for electrically short and open boundaries. Computing the model numerically, the impacts of gradation and wavenumber on the phase velocity and group velocity of generalized Rayleigh waves are examined. Also, lateral and vertical fluctuations of the electric potentials, stresses, mechanical displacements and electrical displacements are depicted by plotting 3D surface and contour graphs. In acoustic devices, a crucial measure that reflects the impact of piezoelectricity on wave phase velocity is the electromechanical coupling factor, therefore, the numerical analysis in terms of the electromechanical coupling factor is done and it is observed that the gradation coefficient can be adjusted to produce fairly high electromechanical coupling factor for the structure at a particular wave number. Numerical results are presented for alternating layers of Barium Titanate Crystal, PZT-5H, and PZT-7H and it is found that phase velocity decreases as the number of porous piezoelectric layers above FGPPHS increases for a particular wavenumber. The particle motion, in the layers and the half-space, is also determined and is found to be elliptic, in general, but its eccentricity changes with layer to FGPPHS and with depth. The outcome of the study provides a deeper understanding of the nature of generalized Rayleigh wave propagation in non-homogeneous functionally graded porous materials and may find applications in designing high performance SAW devices and also in the optimization of Rayleigh wave based devices for engineering applications.