This paper focuses on parametric model order reduction (PMOR) of guided ultrasonic wave propagation and its interaction with damage in a fiber metal laminate (FML). Structural health monitoring in FML seeks to detect, localize and characterize the damage with high accuracy and minimal use of sensors. This can be achieved by the inverse problem analysis approach, which employs the signal measurement data recorded by the embedded sensors in the structure. The inverse analysis requires us to solve the forward simulation of the underlying system several thousand times. These simulations are often exorbitantly expensive and trigger the need for improving their computational efficiency. A PMOR approach hinged on the proper orthogonal decomposition method is presented in this paper. An adaptive parameter sampling technique is established with the aid of a surrogate model to efficiently update the reduced-order basis in a greedy fashion. A numerical experiment is conducted to illustrate the parametric training of the reduced-order model. The results show that the reduced-order solution based on the PMOR approach is accurately complying with that of the high fidelity solution.

Guided ultrasonic waves are suitable for use in the context of structural health monitoring of thin-walled, plate-like structures. Hence, observing the wave propagation in the plates can provide an indication of whether damage has occurred in the structure. In this work, the wave propagation in fiber metal laminate consisting of thin steel foils and layers of carbon fiber-reinforced polymer is studied, focusing on the main propagation characteristics like dispersion diagrams and displacement fields. For this purpose, the dispersion diagrams derived from the analytical framework and numerical simulations are first determined and compared to each other. Next, the displacement fields are computed using the global matrix method for two excitation frequencies. The results derived from the analytical framework is used to validate the numerically determined displacement fields based on a 2D and a 3D modeling approach. For both investigations the results of the analytical treatment and the numerical simulation show good agreement. Furthermore, the displacement field reveals the typical and well-known characteristics of the propagation of guided waves in thin-walled structures. Since the use of full 3D models involves a very high computational cost, this work also successfully investigates the possibility for model order reduction to decrease the computational time and costs of the simulation without the loss of accuracy.

Structural health monitoring systems for composite laminates using guided ultrasonic waves become more versatile with the structural integration of sensors. However, the data generated within these sensors have to be transmitted from the laminate to the outside, where polyimide-based printed circuit boards play a major role. This study investigates, to what extent integrated polyimide inlays with applied sensor bodies influence the guided ultrasonic wave propagation in glass fiber-reinforced polymer specimens. For reasons of resource efficiency, narrow specimens are used. Numerical simulations of a damping-free specimen indicate reflections of the $S_0$-mode at the integrated inlay. This is validated experimentally with an air-coupled ultrasonic technique and a 3D laser Doppler vibrometry measurement. The experimental data are evaluated with a method including temporal and spatial continuous wavelet transformations to clearly identify periodically occurring wave packages as edge reflections and distinguish them from possible inlay reflections. However, even when separating in-plane and out-of-plane movements using the 3D measurement, no reflections at the inlays are detected. This leads to the conclusion that polyimide inlays are well suited as substrates for printed circuit boards integrated into fiber-reinforced polymer structures for structural health monitoring, since they do not significantly influence the wave propagation.

Lamb waves occur in thin-walled structures in two wave modes—the symmetric and the antisymmetric mode. Their oscillation on the structures‘ surfaces is either in phase (symmetric) or shifted by a phase angle of $\pi$ (antisymmetric). In this work, a method is developed by which to compare the surfaces’ oscillation phase relation to answer the question of whether fiber metal laminates show the same surface oscillation behavior as described for metals. The evaluation of time signals regarding the instantaneous phase angle is performed by using the continuous wavelet transformation and the short-time Fourier transformation. Numerical simulations utilizing the finite element method provide time signals from the top and bottom surface of different thin-walled structures of different material settings and configurations. The numerically obtained time signals are evaluated by the developed methods with respect to the oscillation phase. Subsequently, the oscillation phase is evaluated experimentally for the wave propagation in a fiber metal laminate. It is shown that the method based on the continuous wavelet transformation is suitable for the evaluation of oscillation phase relations in time signals. Additionally, it is proven that fiber metal laminates show only two phase relations, which indicates the occurrence of Lamb waves.

Motivated by their functional conformity, micro-cantilever-based MEMS oscillators are investigated in this study as structure-integrable transducers for the acquisition of guided ultrasonic waves in fiber–metal laminates. While acceleration-sensitive oscillators are limited in their maximum frequency, the presented displacement-sensitive oscillator is operated quasi-free in the fashion of a seismometer, making it particularly sensitive for high-frequency displacements above the sensor’s resonance frequency. The potential of this non-traditional application of a seismometer for the acquisition of structure-borne ultrasound is demonstrated experimentally. Therefore, MEMS oscillators are formed from the membrane of established pressure sensors by femtosecond laser micro-machining and mounted onto a setup for stimulation by structure-borne ultrasound. Experimental results indicate the targeted proportionality of the high-frequency stimulus and the sensor response. In conclusion, MEMS oscillators enable acquisition of high-frequency displacements and could therefore serve as structure-integrable sensors for guided ultrasonic waves.

This work investigates how integrated polyimide inlays with applied sensor bodies influence the guided ultrasonic wave propagation in narrow glass fiber-reinforced polymer specimens. Preliminary numerical simulations indicate that in a damping-free specimen, the inlays show reflections for the S0-mode propagation. Hence, an air-coupled ultrasonic technique and a 3D laser Doppler vibrometer measurement are used to measure different parts of the propagating waves’ displacement field after burst excitation at different frequencies. No significant reflections on the inlay can be seen in the experiments. However, it is shown that the reflections from the strip specimen’s narrow width cause periodical reflections that superimpose with the excited wave fronts. A continuous wavelet transformation in the time-frequency domain filters discontinuities from the measurement signal and is used for reconstruction of the time signals. The reconstructed signals are used in a spatial continuous wavelet transformation to identify the occurring wavelengths and hence to prove the assumption of reflections from the narrow edges. Since the amplitude of the reflections identified in the numerical data at the polyimide inlays are an order of magnitude smaller than the excited wave packages, it is concluded that material damping of the epoxy resin matrix extincts possible reflections from the inlays.