Modelling of circumferential waves in cylindrical thermoelastic plates with voids

Abstract

The propagation of thermoelastic waves along circumferential direction in homogeneous, isotropic, cylindrical curved solid plates with voids has been investigated in the context of linear generalized theory of thermoelasticity. The plate is subjected to stress free or rigidly fixed, thermally insulated or isothermal boundary conditions. Mathematical modeling of the problem for the considered cylindrical curved plate with voids leads to a system of coupled partial differential equations. The model has been simplified by using the Helmholtz decomposition technique and the resulting equations are solved by using the method of separation of variables. The formal solution obtained by using Bessel’s functions with complex arguments is utilized to derive the secular equations which govern the wave motion in the plate with voids. The longitudinal shear motion and axially symmetric shear vibration modes get decoupled from the rest of the motion in contrast to non-axially symmetric plane strain vibrations. These modes remain unaffected due to thermal variations and presence of voids. In order to illustrate theoretical developments, numerical solutions have been carried out for a stress free, thermally insulated or isothermal magnesium plate and are presented graphically. The obtained results are also compared with those available in the literature.