Linearly dispersive signal construction of Lamb waves with measured relative wavenumber curves

•LDSC is presented for Lamb wave dispersion compensation in unknown structures.•LDSC can be performed with theoretical wavenumber curves or measured relative ones.•A narrowband spectroscopy method is proposed for relative wavenunmber measurement.•A LDSC-based high resolution Lamb wave imaging method is further developed.•LDSC and LDSC-based imaging methods are validated in an unknown composite plate. Dispersion compensation is a vital issue in Lamb wave identification. Except for time reversal process (TRP), the commonly used compensation methods require the priori-knowledge of Lamb wave dispersion characteristics, which is usually derived in theory using the structure material parameters. However, the parameters could be probably unavailable, making the theoretical wavenumber relations hard to be attained. For the practical situation and considering the complexity of absolute wavenumber determination, linearly dispersive signal construction (LDSC) is presented for dispersion compensation of Lamb waves in this paper. LDSC can be performed not only with theoretical wavenumber curves but also with relative wavenumber curves, which can be easily measured without any structure material parameters. Thus, LDSC has high potential in Lamb wave detection for unknown structures. After the basic LDSC principle is fully explored based on the sensing model simplified in frequency domain, the numerical realization for LDSC is discussed. Then, a narrowband spectroscopy method is introduced for relative wavenumber curve measurement, and the applicability of LDSC with the measured relative wavenumber curves is theoretically investigated, which is subsequently validated with an aluminum plate experiment. Finally, associated with the traditional delay-and-sum algorithm, LDSC is used, as a typical application instance, for high spatial resolution Lamb wave imaging. The efficiency of the proposed LDSC and LDSC-based imaging is demonstrated by the experimental study on a glass fiber reinforced composite plate with unknown material parameters.