Generalized thermoelastic wave propagation in circumferential direction of transversely isotropic cylindrical curved plates

The propagation of thermoelastic waves along circumferential direction in homogeneous, transversely isotropic, cylindrical curved plates has been investigated in the context of theories of thermoelasticity. This type of study is important for ultrasonic non-destructive inspection of large-diameter pipes, which helps in the health monitoring of ailing infrastructure. Longitudinal stress-corrosion cracks are usually temperature dependent and can be detected more efficiently by inducing circumferential waves; hence the study of generalized thermoelastic wave propagation in the circumferential direction in a pipe wall is essential. Mathematical modeling of the problem of obtaining dispersion curves for curved transversely isotropic thermally conducting elastic plates leads to coupled differential equations. The model has been simplified by using the Helmholtz decomposition technique and the resulting equations have been solved by using separation of variable method to obtain the secular equations in isolated mathematical conditions for the plates with stress-free or rigidly fixed, thermally insulated and isothermal boundary surfaces. The closed form solutions are also obtained under different situations and conditions. The longitudinal shear motion and axially symmetric shear vibration modes get decoupled from the rest of the motion and are not affected by thermal variations, whereas for the non-axially symmetric case of plane strain vibrations, these modes remain coupled and are affected by temperature changes. Moreover, these vibration modes are found to be dispersive and dissipative in character. In order to illustrate theoretical development, numerical solutions are obtained and presented graphically for a zinc plate. The obtained results are also compared with those available in the literature in case of waves in cylindrical shell/circular annulus in the absence of thermomechanical coupling and thermal relaxation times.