The spectral methods for the propagation of thermoelastic waves in multilayer cylinders based on nonlocal strain gradient elasticity

Based on the nonlocal strain gradient elasticity and thermoelasticity, the longitudinal and torsional guided waves in an infinite multilayered cylindrical rod are studied. A generalized thermoelastic mathematical model with dual-phase lag and fractional-order derivatives is utilized. A solution approach based on the Legendre polynomial series is proposed for approximating the displacement and temperature fields of guided waves. The problem of solving complex wave numbers in a complex domain is ultimately transformed into a complex eigenvalue problem to avoid the difficulty of root-seeking in a complex domain. In contrast to traditional methods, this spectral method makes intricate iterative processes unnecessary and avoids the missing root and false root in the numerical root-seeking process. Subsequently, a comprehensive parameter study is conducted to examine the influence of nonlocal parameters, strain gradient parameters, and fractional-order parameters on the propagation characteristics of guided waves. The investigation reveals that strain gradient effects and nonlocal effects have opposite impacts on propagation behavior. The fractional order primarily manifests its influence on wave attenuation.