Elsevier

Ultrasonics

Volume 111, March 2021, 106336
Ultrasonics

Improved spectrum method for impact damage characterization in the composite beam using Lamb waves

https://doi.org/10.1016/j.ultras.2020.106336Get rights and content

Highlights

  • Cepstrum based filtering method is proposed to separate the spectral components related to reflections.

  • Spectrum features regarding intensity and distribution are sensitive to the impact damage.

  • The relation curves between the impact energy and proposed damage indices indicate the evolution of the impact damage.

Abstract

Lamb wave spectral methods are one candidate to characterize invisible damages in composite structures. Unfortunately, multiple reflections resulting from geometric boundaries could distort the Lamb wave spectrum, which may cover the important signatures concerning structural integrity. To eliminate spectral interference, a cepstrum based filtering method is proposed to separate various reflection features. In particular, the fundamental spectrum contributing to structural integrity can be extracted smoothly by removing harmonic fluctuations regarding wave reflections with an optimized filter. Subsequently, to establish the quantitative relationships between fundamental spectrum features and the impact energies, damage indices involving spectrum energy mean and median frequency shift are introduced to quantify the change of spectrum intensity and distribution respectively, which shows good performance on impact damage characterization. Finally, the experiment was carried out on a T300 composite beam, in which strong reflections come after direct waves. Meanwhile, the severity of impact damage was simulated by the free droppings of a steel ball with different heights. The results show the effectiveness of the proposed method for characterizing impact damages with improved sensitivity.

Introduction

The beam-like composite structures are widely used in the form of “T” and “I” type of plate, flanged beams, and stiffened plate in various high-end manufacturing fields due to their outstanding mechanical and structural performance [1]. However, structural failures resulting from invisible damages may be induced accordingly due to abrupt impacts, fatigues, and thermal loadings during the manufacturing and in-service process. Therefore, a high-level reliability system is urgently needed to identify, locate, and evaluate the damages for the sake of ensuring structural safety [2]. Traditional nondestructive evaluation (NDE) and structural health monitoring (SHM) methods using X-ray [3], ultrasonic CT [4], and thermography [5] have shown many benefits in improving the structural reliability in various practical applications. Nevertheless, the higher demands of testing methods with fast speed, high efficiency, and large covering range for various thin-walled composite structures are getting more attention.

Lamb wave technique is one of the most promising methods for damage detection in the plate- and pipe-like structures due to many advantages including the capacity of long propagation distance and sensitivity to various kinds of damages [6]. Recently, the utilization of Lamb waves for damage characterization in composite structures has also been addressed by many researchers. For instance, the propagation of Lamb waves in composite laminates with piezoelectric detection systems has been studied numerically and experimentally in [7], [8], [9], thereby providing the principles for excitation waveform design, mode selection, and damage localization. To further identify the damages in the composite structures, various state of art methods have been reported [10], [11]. A series of analyses including signal processing, feature extraction, and data fusion is reported so that the damage-related features can be identified and quantified. In terms of impact damage assessment, the correlation between the impact energy and damage indices like Root Mean Square Deviation [12] and relative acoustic nonlinear parameters [13], wave energy [14], and energy-based root mean square [15] has been investigated, thereby showing the potential for the quantitative prediction of damage severity. Hence, the strong applicability of the Lamb wave method for impact damage characterization in composite structures has been validated. Although Lamb waves are available for damage identification, localization, and evaluation in different kinds of composite structures, it remains a challenge to highlight damage features when the temporal signals are overlapped by strong reflections.

To reveal damage singularities which may not be recognized in time or time-frequency domain, spectrum analysis is an appealing alternative for damage detection in composite structures. For instance, Charles et al. [16] investigated piezo-induced dynamic forced response changing with delamination. The results show that the amplitude spectrum can be used to predict the delamination. Kim et al. [17] proposed a spectral analysis method to assess damage severity in layered composites using Lamb waves. The result shows that the power spectrum density is proportional to the delamination size. However, the detection of the defect in the beam is much harder than that in larger-scale plates because the boundary scattering covers the features related to the damage. The spectral features may be easily masked and interfered by the strong reflections caused by geometric boundaries and structural discontinuities, it is still a challenge to improve the accuracy of the extracted spectral features. Benefiting from cepstrum based method adopting for mode decomposition reported in the [18], [19], decoupling the fundamental spectrum from multiple scattering components is promising for dealing with the superposition problem for Lamb waves in composite structures.

The objective of this paper is to characterize impact damages quantitatively in a composite beam with Lamb wave spectral features. To decouple the superposition of multiple components resulting from geometric boundaries and discontinuities, a cepstrum based filtering method is proposed. Benefiting from the cepstrum filter designed according to the effective frequency band of excitations, the fundamental spectrum for structural integrity can be extracted without losing global spectrum features. To quantify the spectral changes induced by impacts with increasing energies, the spectrum energy mean and median frequency shift are adopted as damage signatures, which shows a good correlation with the impact energies. On this basis, the growth of impact damage can be monitored and predicted with Lamb wave signals.

The organization of this paper is as follows. In Section 2, the propagating background of Lamb waves in the beam is theoretically presented. In Section 3, the cepstrum based filtering method is proposed and the quantitative damage indices are established based on the fundamental spectrum. Experimental investigations are carried out in Section 4. Finally, conclusions are drawn in Section 5.

Section snippets

Scattering model of Lamb waves in the beam

Lamb waves are two families of symmetric and anti-symmetric modes resulting from a superposition of longitudinal and shear waves in thin structures [20], [21]. The propagating properties of Lamb waves vary with the excitation and structural geometry, namely the production of frequency and thickness. Compared with ultrasonic bulk waves, Lamb waves are multimodal and dispersive which means each Lamb wave mode will spread out in time during the propagation, thereby increasing the complexity of

Cepstrum based filtering method for spectral features extraction

To reveal the singularities induced by damages that cannot be easily identified in the time domain, the method of finding damage features through the Lamb wave spectrum may provide an alternative solution. Since the interaction of Lamb waves with the defect would dissipate the wave energy and change the system response [23], [24], spectral amplitude features related to energy intensity and distribution can be adapted to estimate the perturbation of signals. In this section, the filtering

Experimental setup

The composite plate was fabricated by unidirectional T300/3231 prepregs with a layup of [+45,−45,0,90]2s. The dimension of the composite beam is 300 mm × 30 mm × 2 mm. The schematic diagram of the experimental setup is shown in Fig. 4. Two PZTs (P-51 with main constants shown in Table 1) with a diameter of 8 mm and thickness of 0.5 mm are bonded permanently with epoxy resin adhesive on the top surface of the beam acting as actuator and sensor, respectively. Chirp signal with a bandwidth of

Conclusions

In this paper, a spectral characterization method for impact damages in a composite beam is proposed to reveal the spectral features varying with impact energy. Due to the modulation of strong reflections in the spectrum, damage related features may be masked in the raw Lamb wave response. To solve this problem, a cepstrum based filtering method is proposed to extract the fundamental spectrum that is more sensitive to structural integrity. On this basis, the damage indices regarding spectrum

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

The work is supported by the National Natural Science Foundation of China (Grant No. 51905016, 91860205) and the China Postdoctoral Science Foundation (Grant No.2019M660394), which are highly appreciated by the authors.

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