Quantum fidelity susceptibility in excited state quantum phase transitions: application to the bending spectra of nonrigid molecules

We characterize excited state quantum phase transitions in the two dimensional limit of the vibron model with the quantum fidelity susceptibility, comparing the obtained results with the information provided by the participation ratio. As an application, we locate the eigenstate closest to the barrier to linearity and determine the linear or bent character of the different overtones for particular bending modes of six molecular species. We perform a fit and use the optimized eigenvalues and eigenstates in three cases and make use of recently published results for the other three cases.

Magnetoelastic Ribbons as Vibration Sensors for Real-Time Health Monitoring of Rotating Metal Beams

In the current work, magnetoelastic material ribbons are used as vibration sensors to monitor, in real time and non-destructively, the mechanical health state of rotating beam blades. The magnetoelastic material has the form of a thin ribbon and is composed of Metglas alloy 2826 MB. The study was conducted in two stages. In the first stage, an experiment was performed to test the ability of the ribbon to detect and transmit the vibration behavior of four rotating blades, while the second stage was the same as the first but with minor damages introduced to the blades. As far as the first stage is concerned, the results show that the sensor can detect and transmit with great accuracy the vibratory behavior of the rotating blades, through which important information about the mechanical health state of the blade can be extracted. Specifically, the fast Fourier transform (FFT) spectrum of the recorded signal revealed five dominant peaks in the frequency range 0–3 kHz, corresponding to the first five bending modes of the blades. The identification process was accomplished using ANSYS modal analysis, and the comparison results showed deviation values of less than 1% between ANSYS and the experimental values. In the second stage, two types of damages were introduced to the rotating blades, an edge cut and a hole. The damages were scaled in number from one blade to another, with the first blade having only one side cut while the last blade had two side cuts and two holes. The results, as was expected, show a measurable shifting on the frequency values of the bending modes, thus proving the ability of the proposed magnetoelastic sensors to detect and transmit changes of the mechanical state of rotating blades in real time.

Self-updated four-node finite element using deep learning

This paper introduces a new concept called self-updated finite element (SUFE). The finite element (FE) is activated through an iterative procedure to improve the solution accuracy without mesh refinement. A mode-based finite element formulation is devised for a four-node finite element and the assumed modal strain is employed for bending modes. A search procedure for optimal bending directions is implemented through deep learning for a given element deformation to minimize shear locking. The proposed element is called a self-updated four-node finite element, for which an iterative solution procedure is developed. The element passes the patch and zero-energy mode tests. As the number of iterations increases, the finite element solutions become more and more accurate, resulting in significantly accurate solutions with a few iterations. The SUFE concept is very effective, especially when the meshes are coarse and severely distorted. Its excellent performance is demonstrated through various numerical examples.

Split Cantilever Multi-Resonant Piezoelectric Energy Harvester for Low-Frequency Application

This paper presents a new way to design a broadband harvester for harvesting high energy over a low-frequency range of 10–15 Hz. The design comprises a cantilever beam with two parallel grooves to form three dissimilar length parallel branches, each with an unequal concentrated tip mass. The piezoelectric material covers the whole length on both sides of the beam to form a bimorph. Appropriate geometry and mass magnitudes are obtained by a parametric study using the Finite Element Method. The design was simulated in COMSOL Multiphysics to study its response. The first three bending modes were utilized in energy harvesting, resulting in three power peaks at their respective fundamental frequencies. The adequate load resistance determined was 5.62 kΩ, at which maximum power can be harvested. The proposed harvester was compared to two other harvesters presented in the literature for validation: First, an optimized conventional harvester while the proposed harvester is operating at adequate load resistance. Second, a multimodal harvester, while the proposed harvester is operating at a 10 kΩ load. The suggested harvester proved to be more efficient by harvesting sufficiently higher broadband energy and is applicable in a wide range of vibration environments because of its adaptability in design.

Vibration transmission across fractured beam-to-column junctions of reinforced concrete

To detect human survivors trapped in buildings after earthquakes by using structure-borne sound it is necessary to have knowledge of vibration transmission in collapsed and fragmented reinforced-concrete buildings. In this paper, Statistical Energy Analysis (SEA) is used to model the vibration transmission in seismic damaged reinforced concrete beam-to-column junctions where the connection between the beam and the column is made only via the steel reinforcement. An ensemble of 30 randomly damaged beam-to-column junctions was generated using a Monte Carlo simulation with FEM. Experimental SEA (ESEA) is then considered with two or three subsystems to determine the CLFs between the beam and the column with either bending modes or the combination of all mode types. It is shown that bending modes dominate the dynamic response and that the uncertainty of predicting the CLFs using FEM with ESEA is sufficiently low that it should be feasible to estimate the coupling even when the exact angle between the beam and the column is unknown. In addition, the use of two rather than three subsystems for the junction significantly decreases the number of negative coupling loss factors with ESEA.

Investigation on the Robustness of Rotor/Stator Contact Interactions with Respect to Small Mistuning

In this work, the impact of small mistuning on rotor/stator contact interactions is investigated. First, a detailed study of a rotor/stator interaction between the first bending modes and the second engine order is presented in the tuned case. Then, a numerical investigation on the effect of mistuning on the studied rotor/stator contact interaction is carried out. In particular, a stochastic analysis is performed to evaluate the robustness of the interaction with respect to the mistuning level. Simulations are conducted using a reduced order model (ROM) of an industrial bladed disk that combines both physical degrees of freedom (along blades tip for contact treatment) and modal coordinates. Mistuning is introduced in the tuned ROM by means of a modified version of the component mode mistuning method that allows to keep physical degrees of freedom within the reduced basis. Nonlinear amplification factors, i.e. the amplification factors in the context of contact nonlinearities, are compared with their linear counterparts, the latter are computed using a linear forcing on each blade using a two nodal diameters traveling wave excitation on the mistuned and the tuned bladed disk. The comparison between the linear and nonlinear amplification factor for each sample highlights that no correlation exists between a mistuning pattern leading to high amplifications in a linear context or when contact nonlinearities are taken into account. Therefore, dedicated analyses on the effect of mistuning should be undertaken with contact nonlinearities considerations at the design stage especially if intentional mistuning is considered.

Using the Nonlinear Duffing Effect of Piezoelectric Micro-Oscillators for Wide-Range Pressure Sensing

This paper investigates the resonant behaviour of silicon-based micro-oscillators with a length of 3600 µm, a width of 1800 µm and a thickness of 10 µm over a wide range of ambient gas (N2) pressures, extending over six orders of magnitude from 10−3 mbar to 900 mbar. The oscillators are actuated piezoelectrically by a thin-film aluminium-nitride (AlN) layer, with the cantilever coverage area being varied from 33% up to 100%. The central focus is on nonlinear Duffing effects, occurring at higher oscillation amplitudes. A theoretical background is provided. All relevant parameters describing a Duffing oscillator, such as stiffness parameters for each coverage size as well as for different bending modes and more complex modes, are extracted from the experimental data. The so-called 2nd roof-tile-shaped mode showed the highest stiffness value of −97.3∙107 m−2s−2. Thus, it was chosen as being optimal for extended range pressure measurements. Interestingly, both a spring softening effect and a spring hardening effect were observed in this mode, depending on the percentage of the AlN coverage area. The Duffing-effect-induced frequency shift was found to be optimal for obtaining the highest pressure sensitivity, while the size of the hysteresis loop is also a very useful parameter because of the possibility of eliminating the temperature influences and long-term drift effects of the resonance frequency. An reasonable application-specific compromise between the sensitivity and the measurement range can be selected by adjusting the excitation voltage, offering much flexibility. This novel approach turns out to be very promising for compact, cost-effective, wide-range pressure measurements in the vacuum range.

An experimental modal analysis of clavicle bending modes

Clavicle fractures are common medical emergencies; their prevention through design of protection systems depends upon understanding injury mechanisms. This work analyzes the bending natural frequencies and mode shapes of the human cadaver clavicles in situ. The method applied includes experimental modal analysis (EMA) techniques on cadaver clavicles and correlates results with previous analyses. The clavicle response to shock depends on mechanical energy transmission between load and bone and requires an understanding of modal characteristics of the clavicle as well as the frequency range of the shock. The loads acting upon the clavicle may be represented by hard impacts (i.e. sport-related hits) or loads with short durations which can excite a wide frequency spectrum. Modal analyses of clavicles have been reported in literature, but those studies were performed on the clavicles isolated from the body. As a result, those analyses found mode shapes dependent upon different boundary conditions than those found in nature. In our study, EMA employed triaxial accelerometers and a force hammer, a testing procedure was developed, and data was analyzed. The EMA was performed with the clavicle supported in situ, and results include the coronal and axial plane first bending modes. Modal parameters obtained serve to design shock mitigation systems.