| Prestressed reinforced concrete structure is widely used in bridge construction because of its excellent mechanical properties.As one of the core components,prestressed steel bars will inevitably suffer from prestress drop and section damage during the long-term operation,which will lead to irreversible damage to the whole bridge.Considering the key role of prestressed reinforcement in the structure,it is urgent to carry out non-destructive testing research on its residual prestress and damage degree.Most of the research results in the field of ultrasonic guided wave nondestructive testing are based on experiments,and there is still a lack of theoretical research on the propagation characteristics of guided waves in complex structures.This paper takes the study of single-layer medium(bare steel)as the starting point,and then expands the research object to multi-layer medium(grouting steel).Theoretical analysis and semi-analytical finite element method simulation are used to study the basic wave characteristics of guided waves in single steel bar and grouted steel bar.Considering the influence of material damping and initial stress effect,the simulation analysis is closer to the actual project.The main research contents and conclusions are as follows :(1)Based on the semi-analytical finite element method,the fluctuation characteristics of bare steel are studied and analyzed.The semi-analytical finite element method in Cartesian coordinate system is used to solve and draw the dispersion curve of guided wave propagation in bare steel.The results are in good agreement with the solutions of Pochhammer-Chree equation.Then,the full-wavenumber-frequency domain three-dimensional curves of longitudinal wave,flexural wave and torsional wave in bare steel are solved by the semi-analytical finite element method in cylindrical coordinate system,and the complex wave number domain is emphatically analyzed.The propagation and attenuation of each mode of guided wave can be reflected in the complex wave number domain.(2)The influence of material damping on guided wave propagation characteristics in bare steel is investigated by improved semi-analytical method.The material damping is characterized by introducing a hysteresis model.For bare steel with damping,the fluctuation characteristics will be characterized by energy velocity and attenuation factor.The regional energy velocity curve after the cut-off frequency almost coincides with the group velocity of fully elastic bare steel.The characteristic that the amplitude of the guided wave gradually decreases with the increase of the propagation distance can be characterized by the attenuation factor.The attenuation factor curve will decrease to a minimum value as the frequency increases,and then gradually increase and eventually converge to a linear trend.(3)The influence of initial stress on the fluctuation characteristics of bare steel was explored by improved semi-analytical method.The semi-analytical finite element model of bare steel under initial stress is derived from strain nonlinear theory and virtual work equation,and solved.The energy velocity curve and attenuation curve under different initial stress are analyzed.The results show that in the same mode,the energy velocity change curve caused by initial stress changes with the change of energy velocity curve,so do the attenuation factor change curve and attenuation curve.The absolute value of the energy velocity change caused by the initial stress is positively correlated with the initial stress.(4)The improved semi-analytical method is used to study the fluctuation characteristics of grouting reinforcement,and the influence of material damping and initial stress is analyzed.The wave dispersion curve of grouting steel bar is calculated,and the result is consistent with the solution obtained by the software PCdisp based on the global matrix method.Compared with bare steel,the number of modes increases exponentially with the increase of frequency,and the change of single mode becomes more complicated.The full wavenumber-frequency curve of grouting steel bar is similar to that of bare steel as a whole,but there are also some changes.After considering the effect of material damping and initial stress,the change trend of the dispersion curve is roughly the same as that of the bare steel,but in the same trend,the absolute value of the energy velocity change of the grouting steel bar caused by the initial stress is greater than the corresponding value of the single rebar. |
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