Research on Longitudinal Thermoelastic Waves in an Orthotropic Anisotropic Hollow Cylinder Based on the Thermoelastic Theory of Green–Naghdi

Abstract

At present, many high-temperature pipelines need to carry out non-stop detection under high-temperature conditions, and an ultrasonic guided wave is undoubtedly one of the solutions with the highest potential to solve the problem. However, there is a lack of research on the propagation characteristics of longitudinal guided wave modes in high-temperature pipelines. Based on the Green–Naghdi (GN) generalized thermoelastic theory, a theoretical model of thermoelastic guided waves in an orthotropic hollow cylinder with a temperature field is established by using the Legendre polynomial series expansion method. Firstly, based on the GN thermoelastic theory, the coupling equations expressed by displacement and temperature are established by introducing the rectangular window function. The curves of dispersion, displacement, and temperature of the guided wave are numerically solved by using this equation. Subsequently, the influence of the diameter-to-thickness ratio on the dispersion of the longitudinal thermoelastic guided wave is analyzed at the same temperature. Finally, the effect of temperature field variation on the phase velocity dispersion is discussed, which provides a theoretical basis for the study of the dispersion characteristics of hollow cylindrical pipes containing temperature fields.

Keywords

• longitudinal thermoelastic
• waveguide
• Legendre orthogonal polynomials
• dispersion curve
• temperature field