THERMOELASTIC WAVE PROPAGATION IN PLATES: AN IMPROVED LEGENDRE POLYNOMIAL APPROACH

In recent years, the research of thermoelastic coupled wave has greatly promoted the development of high temperature online detection and laser ultrasonic technology. For its small attenuation, long propagation distance and wide signal coverage, ultrasonic guided wave has become one of the rapid development directions in the field of nondestructive testing. However, the development of guided wave high temperature on-line detection and laser ultrasonic guided wave technology is slow. The key lies in the difficulty in solving the coupled thermoelastic wave equation and the difficulty in studying the propagation and attenuation characteristics. As an effective method, Legendre polynomial approach has been widely used to solve the problem of guided wave propagation since 1999. But there are two shortcomings in this method, which limit its further development and application. Two defects are: (1) Due to the Legendre polynomial and its derivative in integral kernel function, the integrals in the solution process leads to low calculation efficiency; (2) Only the thermoelastic guided wave propagation with isothermal boundary conditions can be treated. In order to solve these two defects, an improved Legendre polynomial method is proposed to solve the fractional thermoelastic guided waves in plates. The analytical integral instead of numerical integration in the available conventional Legendre polynomial approach, which greatly improves the calculation efficiency. A new treatment of the adiabatic boundary condition for the Legendre polynomial is developed by introducing the temperature gradient expansion based on the rectangular window function. Compared with the available data shows the validity of the improved method. Comparison with the CPU time between two approaches indicates the higher efficiency of the presented approach. Finally, the phase velocity dispersion curves, attenuation curves, the stress, displacement and temperature distributions for a plate with different fractional orders are analysed. The fractional order has weak influence on the elastic mode velocity, but it has considerable influence on the elastic mode attenuation.