Lamb Waves-Based Computation of Impact Echo Thickness Resonant Frequency: Theory Development and Case Study - Yujin Wang; Gang Zhang; Shibin Lin; Yong Cheng; Xi Liu; Yan Zhu; Zexiang Qin; Hajin Choi; Guochen Zhao (Advances in Civil Engineering)
The traditional equation of impact echo (IE) thickness resonant frequency upon P-wave reflections is developed based on P-wave velocity and thickness of the plate and a geometric correction factor. The thickness resonant frequency of the IE testing is traditionally considered owing to multiple reflections of P waves among the plate surfaces. However, recent studies have proved that the thickness resonance is because of standing waves caused by the first symmetric mode of Lamb waves at zero group velocity (S1ZGV). This study derives the equation for resonant frequency computation based on the Rayleigh–Lamb equation. Factors affecting the frequency are systematically examined using a range of Poisson’s ratios, thicknesses, densities, and moduli for concrete plates. Numerical simulations of one Portland cement concrete plate and one asphalt concrete plate are employed to validate the new equation. Results indicate that the resonant frequency can be expressed based on the P-wave velocity when the Poisson’s ratio is less than 1/3. It can be expressed based on the S-wave velocity when the Poisson’s ratio is greater than 1/3. A solid physical and theoretical explanation is provided to the correction factor, that is, the ratio of the resonant frequency of S1ZGV waves to that of body waves. Results of case studies indicate that the new equations can significantly improve the accuracy of the estimated frequencies with their errors one order of magnitude less than those from the traditional equation.