Propagation Characteristics Of Guided Waves In Fractional Order Thermoelastic Structures

Compared with the normal temperature environment,high temperature environment will increase the probability of thermal stress,corrosion and crack.This reduces the function and lifetime of the device.Accident occur frequently in high temperature structure such as in-service steam boiler and pipeline.This leads to an increasing demand for on-line inspection of high-temperature structures.As a rapidly developing emerging structural health inspection technology,ultrasonic guided wave can avoid the defect of traditional methods.It has been widely used in the non-destructive testing of high pressure vessel and pipeline.As an effective approach to solve the guided wave propagation,the Legendre orthogonal polynomial transform the differential equation to the complex eigenvalue problem.The obtained complex eigenvalue represents the guided wave propagation and attenuation,which is suitable for dealing with dissipative structure problems.However,in the solving process of the Legendre polynomial approach,the Legendre polynomials and their derivatives are included in the integral kernel functions,the calculation amount difficult and consumes lots of CPU time.In order to overcome these defects,this paper deduces the analytic expression of the correlation integral based on the orthogonality of the Legendre polynomial by summarizing the integral type to improve the computational efficiency.This study can provide theoretical basis for high-temperature structural health detection.The main research contents of this paper are as follows:(1)Based on the fractional order Lord-Shulman(L-S)thermoelastic theory,the wave dynamics models of anisotropic plate and functionally graded material(FGM)plate under isothermal boundary condition are established.An analytical integration Legendre polynomial approach(AILPA)is proposed,which is improve the computational efficiency enormously.Comparative studies demonstrate the effectiveness and efficiency of AILPA.The influences of fractional orders,relaxation time and gradient on phase velocity dispersion curves,attenuation curves,the displacement and temperature distributions in thermoelastic dissipative plates are analyzed.The results demonstrate that the phase velocity of thermal wave is larger with a smaller α,relaxation time have considerable influence both on the elastic mode and thermal wave mode attenuation.(2)The guided wave propagation models of fractional order anisotropic and FGM hollow cylinder in cylindrical coordinate system are established,which expands solve area of AILPA.Comparison with existing results shows the effectiveness of AILPA.The phase velocity dispersion curves,attenuation curves,the displacement and temperature distributions for thermoelastic dissipative hollow cylinders with different fractional orders,radius-thickness ratio and gradient are analyzed.The flexural modal dispersion and attenuation characteristics under different flexural orders are analyzed.This study demonstrates that the phase velocity of thermal wave is larger with a smaller α than that a bigger α,relaxation time have considerable influence both on the elastic mode and thermal wave mode attenuation.Meanwhile,the study of longitudinal wave in hollow cylindrical structures show that the attenuation rapidly decrease to zero when the bending longitudinal mode and bending torsional mode approach.(3)In order to verify the correctness of the theoretical analysis,a theoretical solution of longitudinal wave propagation model in a thermoelastic solid cylindrical rod under isothermal boundary conditions is calculated,and an experimental system for thermoelastic guided wave is established.Results show that the theoretical and experimental group velocities with different temperature are consistent.