How intrusive are accelerometers for measuring nonlinear vibrations? A case study on a compressor blade subjected to vibro-impact dynamics

A characteristic feature of nonlinear vibrations is the energy transfer among different parts or modes of a mechanical system. Moreover, nonlinear vibrations are often non-periodic, even at steady state. To analyze these phenomena experimentally, the vibration response must be measured at multiple locations in a time-synchronous way. For this task, piezoelectric accelerometers are by far the most popular technology. While the effect of attached sensors on linear vibration properties is well-known (mass loading in particular), the purpose of the present work is to assess their intrusiveness on nonlinear vibrations. To this end, we consider a compressor blade that undergoes impacts near the tip for sufficiently large vibrations. We consider two configurations, one in which five triaxial piezoelectric accelerometers are glued to the blade surface and one without sensors attached. In both configurations, the vibration response is measured using a multi-point laser Doppler vibrometer. In the linear case without impacts, the lowest-frequency bending mode merely sees the expected slight frequency shift due to mass loading. In the nonlinear vibro-impact case, unexpectedly, the near-resonant response to harmonic base excitation changes severely both quantitatively and qualitatively. In particular, pronounced strongly modulated responses and period doubling are observed only in the case without attached sensors. We conjecture that this is due to a considerable increase of damping, caused by the sensor cables, affecting mainly the higher-frequency modes.

Prediction of Vertical Tail Buffet Using CFD/CSD Coupling Method

The vertical tail buffet induced by the vortex breakdown flow is numerically investigated. The unsteady flow is calculated by solving the RANS equations. The structural dynamic equations are decoupled in the modal coordinates. The radial basis functions (RBFs) are employed to generate the deformation mesh. The buffet response of the flexible tail is predicted by coupling the three sets of equations. The results show that the presence of asymmetry flow on the inner and outer surface of the tail forced the structural deflection offsetting the outboard. The frequency of the 2nd bending mode of the tail structure meets the peak frequency of the pressure fluctuation upon the tail surface, and the resonance phenomenon was observed. Therefore, the 2nd bending responses govern the flow field surrounding the vertical tail. Finally, the displacement of the vertical tail is small, while the acceleration with a large quantitation forces the vertical tail undergoing severe addition inertial loads.

Enhanced Energy Harvesting of Flexural Waves in Elastic Beams by Bending Mode of Graded Resonators

We show efficient elastic energy transfer and wave confinement through a graded array of resonators attached to an elastic beam. Experiments demonstrate that flexural resonators of increasing lengths allow to reduce wave scattering and to achieve the rainbow effect with local wavefield amplifications. We show that the definition of a monotonically decreasing distribution of the natural frequencies of the resonators along the wave propagation direction, is the preferable choice to increase the energy efficiency of the system. The proposed configuration is suitable for micro-fabrication, envisaging practical applications for micro-scale vibration energy harvesting.

Behavior of cracked Euler–Bernoulli beam and inverse problem for assessing crack severity

In this present study, natural frequencies of the first two modes of bending vibration for the cracked simply supported Euler–Bernoulli beam is determined using finite element analysis (FEA). FEA natural frequencies for the cracked beam are used to investigate the behavior of the cracked beam and also used in the inverse problem of crack depth detection. Dynamic behavior of the cracked simply supported beam is observed, and it is found that normalized mode shape at crack location has great effect on amount of decreasing of natural frequencies. When normalized mode shape at crack location is increased, then natural frequencies decrease. In this study, pattern of mode shape played a vital role in decreasing or increasing natural frequencies. At the midpoint of the beam, there is largest bending moment in first bending mode and there is nodal point in second bending mode. Harmonic analysis for the cracked simply supported beam is carried out to find von Mises stress responses and appearance of peaks at frequency of first bending mode is noticed in graphs of von Mises stress response, expressing high values of von Mises stress at crack tip. Inverse problem of assessing the crack depth is performed using results of FEA first mode frequency ratio and published experimental results and the method showed good results in case of high crack depth ratios.

Strain Acquisition Framework and Novel Bending Evaluation Formulation for Compression-Loaded Composites Using Digital Image Correlation

Consistent and reproducible data are key for material characterization. This work presents digital image correlation (DIC) strain acquisition guidelines for compression-loaded carbon fiber composites. Additionally, a novel bending criterion is formulated which builds up on the DIC strain data so that it is able to completely replace state-of-the-art tactile strain devices. These guidelines are derived from a custom test setup that simultaneously investigates the front and side view of the specimen. They reflect both an observation and post-processing standpoint. It is found that the DIC-based strain progress matches closely with state-of-the-art strain gauges up to failure initiation. The new bending evaluation criterion allows the bending state—and therefore, the validity of the compression test—to be monitored analogously to the methodology defined in the standards. Furthermore, the new bending criterion eliminates a specific bending mode, caused by an offset of clamps, which cannot be detected by the traditional strain gauge-based monitoring approach.

Influence of Bending Vibration on the Vertical Vibration Behaviour of Railway Vehicles Carbody

The topic of reducing structural vibrations in the case of flexible carbodies of railway vehicles has been intensively studied, but it is still an active research topic thanks to the importance of the perspective of improving the ride comfort. However, no study has been identified in the specialty literature to feature the contribution of the vibration structural modes upon the vibration behaviour of the railway vehicle carbody. The structural vibration modes of the flexible carbodies are particularly complex; however, the first vertical bending mode holds great significance in terms of the ride comfort. This paper analyses the influence of the first vertical bending mode on the vibration behaviour in three reference points of the railway vehicle carbody in correlation with the carbody flexibility, the vehicle velocity and the suspension damping. This study relies on comparisons between the results of the numerical simulations obtained for a ‘flexible carbody’ type model of the vehicle and the ones obtained for a ‘rigid carbody’ type model. The first part of this study analyses the characteristics of the vertical vibrations behaviour of the flexible carbody based on the dynamic response of the vehicle and expressed as the acceleration power spectral density. In the second part, the influence of the vertical bending on the vertical vibrations level of the carbody is analysed using the root mean square of the vertical acceleration.

Efficient Use of Carbon Fibers as Heating Elements for Curing of Epoxy Matrix Composites

The aim of this study is to achieve a fully cured thermoset matrix that is heated by a direct electric current passing through the reinforcement fibers i.e., the Joule heating effect. Two types of fibers were used as heating elements for curing the epoxy resins. Kanthal resistance fibers were used as reference heating elements and subsequently, they were replaced by a Torayca Carbon Tow of the same radius. The specimens were cured by the heat produced by a direct electric current passing through the fibers and achieving temperatures of 50 °C and 70 °C. Specimens cured in a conventional oven were also manufactured, to compare the resistance heating method to the conventional one. Next, all specimens were mechanically characterized in a quasi-static three-point bending mode of loading and experimental results were compared to derive useful conclusions concerning the applicability of the technique to polymer/composite materials mass production. Finally, a preliminary economical study concerning power consumption needed for the application of both the traditional oven curing and the carbon fibers heating elements use for the manufacturing of the same amounts of materials is presented, showing a maximum financial benefit that can be achieved, on the order of 68%.