Uniqueness, reciprocity theorem and variational principle in fractional order theory of thermoelasticity with voids

In this work, a new theory of thermoelasticity with voids is discussed by using the methodology of fractional calculus. The governing equations for particle motion in a homogeneous anisotropic fractional order thermoelastic medium with voids are presented. A variational principle, uniqueness theorem and reciprocity theorem are proved. The plane wave propagation in orthotropic thermoelastic material with fractional order derivative and voids is studied. For two-dimensional problem there exist quasi-longitudinal (qP) wave, quasi-transverse (qS) wave, quasi-longitudinal thermal (qT) wave and a quasi-longitudinal volume fractional (qV) wave. From the obtained results the different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically.