Abstract
This paper investigates the influence of a temperature field on the dynamics of nonlinear systems, focusing on the vibrations and stability of rotating drill strings with initial curvature and finite deformations in a fluid flow. The thermal environment is modeled through variations in the elastic modulus of the drill string material based on the thermoelasticity theory. This approach is validated using the Euler–Bernoulli beam model, demonstrating that heating the beam reduces both its bending stiffness and natural frequencies. The proposed method is subsequently applied to study nonlinear vibrations and the stability of the drill string. The behavior of its small perturbations is examined by analyzing the equation of the perturbed state using the method of partial discretization. The results show strong agreement with the obtained stability zones and phase portrait behaviors. The quantitative effect of the temperature field on the dynamics and stability of the drill string is established.