Autoencoder-based anomaly detector for gear tooth bending fatigue cracks

The article reports on anomaly detection performance of data-driven models based on a few selected autoencoder topologies and compares them to the performance of a set of popular classical vibration-based condition indicators. The evaluation of these models employed data that consisted of baseline gearbox runs and the associated runs with seeded bending cracks in the root of the gear teeth for eight different gear pairings. The analyses showed that the data-driven models, trained on a subset of baseline data outperformed classical CIs as anomaly detectors.

Free and Forced Wave Vibration Analysis of a Timoshenko Beam/Frame Carrying a Two-Degree-of-Freedom Spring-Mass System

In this paper, free and forced vibrations of a transversely vibrating Timoshenko beam/frame carrying a discrete two-degree-of-freedom spring-mass system are analyzed using the wave vibration approach, in which vibrations are described as waves that propagate along uniform structural elements and are reflected and transmitted at structural discontinuities. From the wave vibration standpoint, external excitations applied to a structure have the effect of injecting vibration waves to the structure. In the combined beam/frame and two-degree-of-freedom spring-mass system, the vibrating discrete spring-mass system injects waves into the distributed beam/frame through the spring forces at the two spring attached points. Assembling the propagation, reflection, transmission, and external force injected wave relations in the beam/frame provides an analytical solution to vibrations of the combined system. In this study, the effects of rotary inertia and shear deformation on bending vibrations are taken into account, which is important when the combined structure involves short beam element or when higher frequency modes are of interest. Numerical examples are given, with comparisons to available results based on classical vibration theories. The wave vibration approach is seen to provide a systematic and concise solution to both free and forced vibration problems in hybrid distributed and discrete systems.

An analysis method of the vortex-induced vibrations of a tethered sphere

Vortex-induced vibrations (VIV) in systems with more than one degree of freedom often present complex synchronization among the motion components, also hidden by the randomness that characterizes the motion itself. A phase average method has been here developed and applied to the displacements of a tethered sphere, at low mass and damping, to analyze its xy trajectories over a wide range of reduced velocities, 5 ≤ U* ≤ 25 (Reynolds numbers, 5.1 × 103 ≤ Re ≤ 2.67 × 104). This method has allowed the identification of both the periodic and chaotic contribution of each motion component, accurately reconstructing the underlying trajectory periodic pattern. The two classical vibration modes, I and II, have been also observed. The method developed here was able to better rebuild the experimental data compared to other methods found in the relevant literature, providing useful insights into the study of the dynamic response of a freely-oscillating tethered sphere immersed in a steady flow.

In-Plane Vibration of a Deployable Segmented Ring

The in-plane vibrations of regular polygonal rings composed of rigid segments joined by torsional springs are studied for the first time. The nonlinear dynamical difference equations are formulated and solved by perturbation about the equilibrium state. As the number of segments increase, the frequencies, if aptly normalized, converge to the classical vibration frequencies of a continuous elastic ring. The vibration mode shapes are illustrated. The tiling of many identical polygons is discussed. Possible applications include the vibrations of space structures and graphene sheets.

Mathematical study of the small oscillations of a finite cylindrical column liquid-gas under zero gravity

This paper deals with the mathematical study of the small motions of a system formed by a cylindrical liquid column bounded by two parallel circular rings and an internal cylindrical column constituted by a barotropic gas under zero gravity. From the equations of motion, the authors deduce a variational equation. Then, the study of the small oscillations depends on the coerciveness of a hermitian form that appears in this equation. It is proved that this last problem is reduced to an auxiliary eigenvalues problem. The discussion shows that, under a simple geometric condition, the problem is a classical vibration problem.

Simulation and Characterization of a Nonlinear Dual-Frequency Piezoelectric Energy Harvester

In this paper, we present a concept, simulation and characterization results of a dual-frequency piezoelectric energy harvester with magnetic frequency tuning capabilities. We demonstrate that the frequency-agile multi-mode capability enables the device to harvest on a wider range of operating frequencies than classical vibration harvesters.

Complete and Simplified Models for Estimating Vibration Instability of Cyclically Symmetric Ring Structures: Comparison and Verification

In-plane vibration of cyclically symmetric ring structures is examined with emphasis on the comparison of instabilities estimated by complete and simplified models. The aim of this paper is to understand under what conditions and to what degree the simplified models can approach the complete model. Previous studies develop time-variant models and employ perturbation method by assuming weak support. This work casts the rotating-load problem into a nonrotating load problem. A complete model with time-invariant coefficients is developed in rotating-support-fixed frame, where the bending and extensional deformations are incorporated. It is then reduced into two simplified ones based on different deformation restrictions. Due to the time-invariant effect observed in the rotating-support-fixed frame, the eigenvalues are formulated directly by using classical vibration theory and compared based on a sample structure. The comparisons verify that the two types of models are comparable only for weak support. Furthermore, the simplified models cannot accurately predict all unstable behaviors in particular for strong support. The eigenvalues are different even in comparable regions. For verification purpose, the time-invariant models are transformed into time-variant ones in the inertial frame, based on which instabilities are estimated by using Floquét theory. Consistence between the time-invariant and -variant models verifies the comparisons.

Thermodynamic Variational Formulations of Subordinate Oscillator Arrays (SOA) With Linear Piezoelectrics

It has been shown theoretically that by prescribing the mass and stiffness distributions of a subordinate oscillator array (SOA) that is attached to a host structure, significant vibration attenuation of a host can be obtained over a finite frequency range. This case stands in stark contrast to classical vibration isolator designs for two degree of freedom systems that achieve exact vibration cancellation at a single isolated frequency. Despite the attractiveness of SOAs for the design of broader band vibration suppression, the theoretically desired result can deteriorate rapidly due to small fabrication imperfections in the SOA. This paper introduces and compares variational thermodynamic formulations of composite piezoelectric SOA that are designed to be adjustable in real-time to ameliorate the effects of disorder due to fabrication in a SOA.