Abstract
Lamb wave is a type of ultrasonic guided wave, which can propagate in plates, shells and other structures. Lamb waves have been widely used in non-destructive testing (NDT) and structural health monitoring (SHM) for damage detection due to their sensitivity to small defects and ability to travel long distances. This paper introduces the basic theory of Lamb waves, including their generation, propagation and sensing mechanism. Several commonly used techniques for Lamb wave-based NDT and SHM are also discussed.
Introduction
Structural integrity is a critical issue in many fields, such as aerospace, civil engineering and mechanical engineering. The ability to detect early-stage damage or defects in these structures is important for ensuring safety, reducing maintenance costs and prolonging service life. Non-destructive testing (NDT) and structural health monitoring (SHM) are two effective approaches for detecting damage or defects without disrupting normal operation of the structure. Among various NDT/SHM methods, ultrasonic guided waves have shown great potential due to their unique properties such as long-range inspection capability, high sensitivity to small defects and multi-mode propagation.
Lamb wave is one type of ultrasonic guided waves that has attracted significant attention in recent years. It was first discovered by Horace Lamb in 1917 [1]. Unlike bulk waves that propagate through the entire thickness of a structure, Lamb waves can travel along the surface of plates or shells with a certain depth penetration into the material. This feature makes Lamb waves particularly suitable for inspecting thin-walled structures or composite materials.
Basic Theory of Lamb Waves
Theoretical analysis of Lamb waves involves solving the dispersion equation that describes the relationship between frequency, wavelength and phase velocity. The dispersion equation varies depending on the plate geometry (e.g., rectangular or circular), material properties (e.g., elastic modulus and density) and mode order (e.g., symmetric or anti-symmetric). For example, the fundamental symmetric (S0) mode in a rectangular plate can be described by the following dispersion equation [2]:
tan(kd) = ±[k/(k^2 - k0^2)]1⁄2
where k is the wave number, d is the plate thickness, and k0 is a constant determined by material properties. The positive and negative signs correspond to two different propagation directions along the plate length.
Lamb waves can be generated by various methods, such as piezoelectric transducers, magnetostrictive sensors or laser sources. The choice of generation method depends on the frequency range of interest, inspection area and accessibility. Typically, a pair of transducers are used to generate and receive Lamb waves. When an AC voltage is applied to the transmitting transducer, it generates a mechanical vibration that propagates through the plate as a Lamb wave. The receiving transducer detects the induced electrical signal caused by the wave motion.
Applications of Lamb Waves in NDT/SHM
Lamb waves have been widely used in NDT/SHM for damage detection due to their sensitivity to small defects and ability to travel long distances. Several commonly used techniques based on Lamb waves are introduced below:
Time-of-flight diffraction (TOFD): TOFD is a technique that measures the time difference between two echoes from opposite ends of a defect in order to determine its size and position. It relies on the fact that Lamb waves diffract at sharp edges or discontinuities in a structure.
Pitch-catch method: In this method, two pairs of transducers are placed on opposite sides of a specimen. One pair acts as transmitter while another pair acts as receiver. The distance between two pairs can be varied to control which mode(s) of Lamb wave will be excited and received.
Scanning laser Doppler vibrometry (SLDV): SLDV uses laser interferometry to measure the surface displacement of a structure caused by Lamb waves. By scanning the laser spot across the surface, a 2D or 3D image of wave propagation can be obtained.
Conclusion
Lamb wave-based NDT/SHM is a promising approach for detecting early-stage damage or defects in thin-walled structures or composite materials. The basic theory of Lamb waves and several commonly used techniques have been introduced in this paper. Future research can focus on developing advanced signal processing algorithms to extract more information from Lamb wave signals, as well as exploring new applications of Lamb waves in other fields such as biomedical imaging and underwater acoustics.
References
[1] H. Lamb, “On Waves in an Elastic Plate,” Proceedings of the Royal Society A, vol.93, pp.114-128, 1917.
[2] Y.-S. Kim and L.J. Jacobs, Ultrasonic Guided Waves in Solid Media, Cambridge University Press, 2009.
