3-D waves in porous piezoelectric materials

•Wave propagation in anisotropic porous piezoelectric materials is studied.•The Christoffel equation is derived for 3D waves in porous piezoelectric medium.•The expressions are deduced for 2, m, 222, 2mm, 4, 32, 6mm and 4¯3m crystal classes.•Study of effects of frequency, porosity and piezoelectricity on stiffened quasi waves. Wave propagation in porous piezoelectric materials, possessing crystal symmetries monoclinic (2,m), orthorhombic (222, 2mm), tetragonal (4), trigonal (32), hexagonal (6mm) and cubic (4¯3m), is studied. The Christoffel equation is derived for 3D waves in an anisotropic porous piezoelectric medium. The four roots of the biquadratic equation give the complex wave velocities of four waves propagating in such a medium. These complex wave velocities are resolved to obtain the phase velocities and attenuation factors of waves. The algebraic implicit expressions are derived for monoclinic (2,m), orthorhombic (222, 2mm), tetragonal (4), trigonal (32), hexagonal (6mm) and cubic (4¯3m) crystal classes. The characteristics of waves in porous piezoelectric materials are studied in terms of the velocity surfaces and attenuation surfaces. The effects of phase direction, frequency, piezoelectricity, porosity and crystal symmetry on the velocity surfaces and attenuation surfaces are investigated for these crystal classes. The effects of phase direction and crystal symmetry on the skewing angles and wave fronts of quasi waves are also studied.