# Wideband Vibro-Acoustic Modulation for Crack Detection in Wind Turbine Blades
## 1 Introduction
One early method employed to assess material cracks is harmonic distortion. This method evaluates the material by measuring the non-linear distortion of a primarily sinusoidal acoustic signal, which represents the harmonic distortion [32; 33]. Since then, significant research has been conducted into techniques and methods using the NA approach. Various NA, NDE, and SHM techniques utilize a broad range of NA effects. A comprehensive summary of current NA, NDE, and SHM research can be found in [34], as well as in [35; 36; 37; 38; 39; 40]. Currently, the method most widely adopted and used to assess damage is VAM. This technique applies the modulation of a high-frequency probe wave by a lower-frequency pump wave. The majority of VAM methods evaluate non-linearity by measuring the level of sideband components with sum and difference frequencies, which are typically quantified as the ratio of sideband peaks to the amplitude of the carrier wave. More recently, the count of sideband peaks has been utilized as a measure of non-linearity [41; 42; 43; 44]. The generation of low-frequency vibrations in VAM techniques has been accomplished through two methods: (1) utilizing harmonic sources and (2) applying mechanical impact. The first method has several options for excitation, such as piezoceramic transducers [45; 46], speakers [47; 48], lasers [49], and loading machines [50]. A limited number of publications have considered VAM applications for WT SHM. The periodic load change due to blade rotation can serve as the low-frequency wave used for the modulation of the high-frequency wave. Refs. [10; 11] presented VAM experiments using actual WT blades. The chosen spot for the fracture was the back edge of the blade, which was 0.3048 m away from the blade's tip, where the highest stress occurs. A quick force was applied to the blade's tip to cause a break while it was held steady at this pre-determined break point. In the tests, high-frequency probe signals were radiated and received using micro fiber composite (MFC) transducers with frequencies ranging from 5 to 10 kHz. At a rotational frequency of 3.1 Hz, the modulation of these signals, along with corresponding harmonic frequencies, was detected. There are many more publications about theoretical study of non-linear vibrations of objects with breathing defects. In [51], the resonant frequency and the non-linear stiffness of the blade with a defect were studied using a finite element model via centrifugal loading. The outcomes revealed that the resonant frequencies of the blade with cracks were greater for the rotating case than for the static case. Furthermore, the distinction between the resonant frequencies of the non-linear and linear cases became more apparent as the crack length increased. Ref. [52] presented the simulation of the non-linear dynamic characteristic of a rotating blade with breathing damage. The results showed that the defect length had a significant effect on the resonant frequency and the vibration behavior contains damping and stiffness. Research presented in [53] used a numerical model to analyze the forced response of the blade under alternating loads. The model considers the impacts of the crack on the blade's natural frequencies, mode shapes, and damping characteristics and calculates the resulting vibrations. The results of the study indicate that the resonant frequencies of the blade are significantly affected by the presence of a crack, with the natural frequencies decreasing and the damping ratio increasing as a result of the crack. Also, the vibration response of the blade is highly dependent on the increase in the alternating loads. In this study, we explore the VAM technique, in which the harmonic or broad-spectrum vibrations of the probe blade are influenced by the rotation of the blades. The simulation of this effect is conducted based on the oscillator model, in which the resonance frequency and attenuation vary under altered loads produced via the rotation of the WT blades.