Analysis of axisymmetric cylindrical problem with fractional order derivative via Moore-Gibson-Thompson model

Abstract Present study investigates the thermoelastic behavior of a semi-infinite axisymmetric cylindrical structure using the Moore-Gibson-Thompson model with a fractional-order derivative. The fundamental equations, governing the system are employed to analyze an axisymmetric problem in a half-space cylindrical domain subjected to mechanical point load and thermal point heat source. The field variables, including normal/shear stresses, radial/axial displacements and temperature variations, are examined for different time instants, fractional orders, and generalized thermoelastic models. To solve the problem, harmonic variations and the Hankel transform techniques are utilized to express the unknown functions in the transformed domain. The physical quantities are obtained by applying the inverse Hankel transform integral, evaluated using Romberg’s integration through an extended Simpson’s one-third rule, followed by a limiting process as the step size approaches zero. The system of fundamental equations is solved using the Gauss elimination method under well-posed conditions, yielding significant results for the field functions. Numerical results for stresses, displacements, and temperature variations are presented graphically concerning radial distance, fractional order derivatives, time instants and different thermoelastic models.