Modal Parameter Tracking in a Carbon Fiber-Reinforced Structure over Different Carbon Fiber Angles

Abstract

The dynamics of carbon fiber-reinforced plastic (CFRP) change according to the carbon fiber angle, and a mode order shift may occur in CFRP specimens. The variation trends in modal parameters differ in each mode; thus, an efficient mode-tracking method is needed to identify the reliable dynamic behavior of the CFRP structure. The mode-tracking method was assumed to be applicable for the same configuration of the tested specimen except for the differences in carbon fiber angle of the CFRP specimen. Simple rectangular specimens were prepared for one isotropic material, SS275, and five anisotropic CFRP specimens with five carbon fiber angles ranging from 0° to 90°. An experimental impact test was conducted to obtain all the modal parameters. The proposed mode-tracking method was applied using three indicators: the modal assurance criterion (MAC) and two modal parameters (resonance frequency and modal damping ratio). The MAC value was valid for the three bending modes at 0°, 30°, and 90°, but not for the two torsional modes. However, the variation in the resonance frequencies was a more efficient indicator with which to track all the modes of interest, except for the second torsional mode. The variation in the modal damping ratio was also a valid indicator for the two torsional modes. Therefore, the proposed three indicators were all required to derive reliable mode tracking for the CFRP specimens considering the mode order shift.

Integrated fault diagnosis of rolling bearings based on improved multichannel singular spectrum analysis and frequency–spatial domain decomposition

“…where c m is a real constant, λ m = −σ m + iω dm denotes the pole corresponding to the mth-order mode and ω dm denotes the natural frequency of the mth-order mode. Using all frequency points near the eigenfrequency, equation (10) was solved using the least-squares method, and the modal parameters were obtained using equation (11),…”

“…MAC is a modal metric designed to determine whether the mode shapes used in the calculations correspond to the same model [33]. In addition, it has been applied to modal estimation comparisons between different system identification procedures [11], damage detection [13], and several other applications involving modal vector comparisons. MAC can be expressed as follows:…”

“…MAC refers to the correlation coefficient of the modal shapes before and after damage. In practical applications, two-mode shapes are considered related when the MAC is greater than 0.9, whereas they are considered unrelated when the MAC is less than 0.05 [11].…”

“…It is worth noting that in recent years, some novel theories were introduced into the field of fault diagnosis successively, such as operational modal analysis (OMA) [9] and singular spectrum analysis (SSA) [10]. The modal parameters extracted from the vibration signal can identify the damage to the system structure [11]. OMA is the primary approach to obtaining modal parameters [12].…”