As thin-walled structural components are widely used in the aerospace field, it is necessary to evaluate their mechanical properties, particularly the elastic modulus. The traditional methods for measuring the elastic modulus include the tensile and indentation methods; however, these methods are not suitable for the detection of formed structural components because they are destructive. By contrast, laser ultrasound is a nondestructive testing method with the characteristics of high resolution, flexible sound source, multiple modes, and noncontact; therefore, this method is appropriate for measuring the elastic modulus of thin-walled structures. The primary advantage of measuring the elastic modulus using laser ultrasound is the accurate detection of the velocities of compressional and shear waves. For bulk structures, compressional and shear waves can be motivated simultaneously and measured accurately. Several scholars have used this method to calculate the elastic moduli of various materials. However, in thin-walled structures, ultrasonic waves propagate in the form of Lamb waves, and it is difficult to directly measure the velocities of compressional and shear waves. Therefore, the velocities must be inversed using the Lamb wave data. Dispersion curve inversion is a commonly used inversion method; however, it obtains signals by scanning a large area. In this case, the results would be affected by the uneven thickness of the sample. A local detection method is required to accurately measure the local elastic modulus of thin-walled structures. In this paper, the Lamb wave dual-modal resonance method is proposed based on the zero group velocity (ZGV) resonance and thickness resonance of the plates. In this method, the local Poisson's ratio and the local bulk wave velocity of the thin plate are calculated using the S₁ modal ZGV resonance peaks and any other resonance peak in the spectrum through single-point detection without scanning, and the local elastic modulus is determined by combining the measured densities. This method provides a theoretical basis for the online monitoring of the elastic modulus of thin-walled structures.

The dual-modal resonance method uses resonance peaks to calculate the velocity of ultrasonic waves and Poisson's ratio and then combines the densities measured to detect the local elastic modulus. First, the relationship curve between the correction factor and the Poisson's ratio is calculated (Fig. 5). Then, the spectra of aluminum, copper, and titanium plates by single-point detection are obtained using laser ultrasound (Fig. 8). Subsequently, the S₁ modal ZGV resonance peaks with large amplitude and any other resonance peak in the spectrum are selected to calculate the local Poisson's ratio and the local bulk wave velocity of the thin plate using the dual-mode resonance method, and the local elastic modulus is obtained by combining the measured densities (Table 3). Finally, the measured compressional wave velocity and elastic modulus are verified using a 50-MHz compressional wave probe and a nano-indenter.

Laser ultrasound experiments are performed to detect the resonance peaks and calculate the elastic modulus using the dual-modal resonance method. The results show that there are multiple resonance peaks in the spectrum, and the amplitude of the S₁ modal ZGV resonance peak is the largest. In the spectrum of the titanium plate, the A₃ resonance peaks are disturbed by noise and are difficult to identify (Fig. 8). In this case, the calculation can be completed by combining the S₁ modal ZGV resonance peaks with any other resonance peak, without A₃ resonance peaks. The results show that the difference in the velocities between the calculated and measured values is within 20 m/s, and the difference in the elastic moduli between the calculated and measured values is within 2 GPa. Therefore, the Lamb wave dual-modal resonance method is reliable for accurately calculating the elastic modulus of thin-walled structures.

In this paper, a local detection method, namely, the Lamb wave dual-modal resonance method, for measuring the elastic modulus is proposed. In this method, the local Poisson's ratio and the local bulk wave velocity of the thin plate can be calculated using the S₁ modal ZGV resonance and any other modal resonance in the spectrum, and the local elastic modulus can be determined by combining the measured densities. The measurement results by the compressional wave probe and the nanoindentation instrument prove the accuracy of the proposed method. Compared with the traditional methods used for measuring the elastic modulus, this method is nondestructive, efficient, and noncontact, and is suitable for detecting the elastic modulus of thin-walled structural components. In addition, compared with the inversion method using the dispersion curve, this method is more efficient because it identifies signals through single-point detection. Finally, when some resonance peaks cannot be identified in the spectrum owing to noise, the calculation can be completed using other resonance peaks that are not affected by noise through this novel method.