Identification of Non-Linear Vibration Parameters of a Nuclear Fuel Rod

In Pressurized Water Reactors (PWR), fuel assemblies are composed of fuel rods, long slender tubes filled with uranium pellets, bundled together using spacer grids. These structures are subjected to fluid-structure interactions, due to the flowing coolant surrounding the fuel assemblies inside the core, coupled with large-amplitude vibrations in case of external seismic excitation. Therefore, understanding the non-linear response of the structure and, particularly, its dissipation, is of paramount importance for the choice of safety margins. To model the nonlinear dynamic response of fuel rods, the identification of nonlinear stiffness and damping parameters is required. The case of a single fuel rod with clamped-clamped boundary conditions was investigated by applying harmonic excitation at various force levels. Different configurations were implemented testing the fuel rod in air and in still water; the effect of metal pellets simulating nuclear fuel pellets inside the rods was also recorded. Non-linear parameters were extracted from some of the experimental response curves by means of a numerical tool based on the harmonic balance method. The axisymmetric geometry of fuel rods resulted in the presence of a one-to-one internal resonance phenomenon, which has to be taken into account modifying accordingly the numerical identification tool. The internal motion of fuel pellets is a cause of friction and impacts, complicating further the linear and non-linear dynamic behavior of the system. An increase of the equivalent viscous-based modal damping with excitation amplitude is often shown during geometrically non-linear vibrations, thus confirming previous experimental findings in the literature.

Dynamical Modeling of Gear Transmission Considering Gearbox Casing

Much research has been carried out to investigate the dynamical response of a gear system because of its importance on vibration feature analysis. It is well known that the gearbox casing is one of the most important components of the gear system and plays an important role in signal propagation. However, its effects have widely been neglected within the dynamic simulations and few dynamic models have considered the gearbox casing when modeling a gear transmission. This paper proposes a gear transmission dynamical model with the consideration of the effects of gearbox casing. The proposed dynamical model incorporates TVMS, a time-varying load sharing ratio, as well as dynamic tooth contact friction forces, friction moments and dynamic mesh damping coefficients. The proposed gear dynamical model is validated by comparison with responses obtained from experimental test rigs under different speed conditions. Comparisons indicate that the responses of the proposed dynamical model are consistent with experimental results, in both time and frequency domains under different rotation speeds.

Selective Wave Filtering in Time-Modulated Elastic Metamaterials

We implement periodic stiffness time-modulation in a beam with piezoelectric patches and switchable shunted negative capacitance. The shunted negative capacitance circuits, connected in series with each piezoelectric patch through a switch, soften the structure. By alternatively opening and closing the switch, the beam’s stiffness effectively oscillates periodically between two values. We present a simplified theoretical model of time-periodic beams and describe the occurrence of flat bands in the dispersion diagrams. We show that a narrowband reflection from a time-modulated domain can be obtained for a broadband incident wave, hence qualifying the modulated domain as a single-port system with tunable response. We validate our theoretical findings by comparing time-domain simulations with experimental measurements of transient wavefields through scanning Doppler laser vibrometry.

Two-Dimensional Contact Analysis Using Trigonometric Polynomials: Some Early Verification Problems

A discretization strategy for elastic contact on a half plane has been devised to explore the significance of different friction models on joint-like interface mechanics. It is necessary to verify that discretization and accompanying contact algorithm on known solutions. An extensive comparison of numerical predictions of this model with corresponding 2-D elastic, frictional contact solutions from the literature is presented.

Vibrational Analysis of Human Femur Bone

Femur bone is the longest and largest bone in the human skeleton. This bone connects the pelvic bone to the knee and carries most of the body weight. The static behavior of femur bone has been a center of investigation for many years while little attention has been given to its dynamic and vibrational behavior, which is of great importance in sports activities, car crashes and elderly falls. Investigation of natural frequencies and mode shapes of bone structures are important to understand the dynamic and vibrating behaviors. Vibrational analysis of femoral bones is presented using finite element method. In the analysis, the bone was modeled with isotropic and orthotropic mechanical properties. The effect of surrounding bone muscles has also been accounted for as a viscoelastic medium embedding the femur bone. Natural frequencies extracted considering the effects of age aggravated by weakening the elastic modulus and density loss. The effects of real complex bone geometry on natural frequencies are studied and are compared with a simple circular cross-sectional model.

Hybrid-Bistable Vibration Energy Harvester With Adaptive Potential Well

Many common environmental vibration sources exhibit low and broad frequency spectra. In order to exploit such excitations, energy harvesting architectures utilizing nonlinearity, especially bistability, have been widely studied since the energetic interwell oscillations between their stable equilibria can provide enhanced power harvesting capability over a wider bandwidth compared to the linear counterpart. However, one of the limitations of these nonlinear architectures is that the interwell oscillation regime may not be activated for a low excitation level that is not strong enough to overcome the potential energy barrier, thus resulting in low amplitude intrawell response which provides poor energy harvesting performance. While the strategic integration of bistability and additional dynamic elements has shown potential to improve broadband energy harvesting performance by lowering the potential barrier, there is a clear opportunity to further improve the energy harvesting performance by extracting electrical power from the kinetic energy in the additional element that is induced when the potential barrier is lowered. To explore this opportunity and advance the state of the art, this research develops a novel hybrid bistable vibration energy harvesting system with a passive mechanism that not only adaptively lowers the potential energy barrier level to improve broadband performance but also exploits additional means to capture more usable electrical power. The proposed harvester is comprised of a cantilever beam with repulsive magnets, one attached at the free end and the other attached to a linear spring that is axially aligned with the cantilever (a spring-loaded magnet oscillator). This new approach capitalizes on the adaptive bistable potential that is passively realized by the spring-loaded magnet oscillator, which lowers the double-well potential energy barrier thereby facilitating the interwell oscillations of the cantilever across a broad range of excitation conditions, especially for low excitation amplitudes and frequencies. The interwell oscillation of the cantilever beam enhances not only the piezoelectric energy harvesting from the beam but also the electromagnetic energy harvesting from the spring-loaded magnet oscillator by inducing large amplitude vibrations of the magnet oscillator. Numerical investigations found that the proposed architecture yields significantly enhanced energy harvesting performance compared to the conventional bistable harvester with fixed magnet.

Current-Aided Time-Frequency Analysis of Vibration Signals for Gearbox Fault Diagnosis

Vibration monitoring is an effective method for mechanical fault diagnosis. Wind turbines usually operated under varying-speed condition. Time-frequency analysis (TFA) is a reliable technique to handle such kind of nonstationary signal. In this paper, a new scheme, called current-aided TFA, is proposed to diagnose the planetary gearbox. This new technique acquires necessary information required by TFA from a current signal. The current signal is firstly used to estimate the rotating speed of the shaft. These parameters are applied to the demodulation transform to obtain a rough time-frequency distribution (TFD). Finally, the synchrosqueezing method further enhances the concentration of the obtained TFD. The validation and application of the proposed method are presented by a simulated signal and a vibration signal captured from a test rig.

A Round Robin Study: Detection of Damage in a Composite Plate With a Real-Time Moving Sensor Measurement Technique

A worldwide round robin study is sponsored by the Society of Experimental Mechanics to detect damage in a composite plate with a scanning laser Doppler vibrometer (SLDV). The aim of this round robin study is to explore the potential of a SLDV for detection of damage in composite plates. In this work, a curvature-based damage detection method with use of a continuously SLDV (CSLDV) is proposed. A CSLDV can be regarded as a real-time moving sensor, since the laser spot from the CSLDV continuously moves on a structure surface and measures velocity response. An operating deflection shape (ODS) of the damaged composite plate can be obtained from velocity response by the demodulation method. The ODS of the associated undamaged composite plate is obtained by using polynomials to fit the ODS of the damaged plate. A curvature damage index (CDI) using differences between curvatures of ODSs (CODSs) associated with the ODSs from the demodulation method and the polynomial fit is proposed to detect damage. With the proposed curvature-based damage detection method, locations of two possible damage are detected in areas with consistently high CDI values at two excitation frequencies, which are in good agreement with prescribed damage locations.

Modal Analysis of Magnetic Resonance Imaging (MRI) Scanner Support Structure

Experimental and computational modal analysis has been completed as part of a larger project with the ultimate goal of understanding MRI vibration and implementing passive vibration isolation in the MRI machine support structure. The specific purpose of the modal analysis is to extract natural frequencies (eigenvalues) and mode shapes (eigenvectors) of the MRI support structure in order to validate the computational model of the base against the experimental results so that the former may be used as an analysis and design tool. From the model, the resonance points of the MRI support structure are determined within the expected frequency ranges of excitation.

Voltage Response of Superharmonic Resonance of Electrostatically Actuated MEMS Resonators: Comparison Between Boundary Value Problem Model and Reduced Order Model

This paper deals with the voltage response of electrostatically actuated NEMS resonators at superharmonic resonance. In this work a comparison between Boundary Value Problem (BVP) model, and Reduced Order Model (ROM) is conducted for this type of resonance. BVP model is developed from the partial differential equation by replacing the time derivatives with finite differences. So, the partial differential equation is replaced by a sequence of boundary value problems, one for each step in time. Matlab’s function bvp4c is used to numerically integrate the BVPs. ROMs are based on Galerkin procedure and use the mode shapes of the resonator as a basis of functions. Therefore, the partial differential equation is replaced by a system of differential equations in time. The number of the equations in the system is equal to the number of mode shapes (or modes of vibration) used in the ROM. One mode of vibration ROM is solved using the method of multiple scales. Two modes of vibration ROM is numerically integrated using Matlab’s function ode15s in order to obtain time responses, and a continuation and bifurcation analysis is conducted using AUTO 07P. The effects of different nonlinearities in the system on the voltage response are reported. This work shows that BVP model is a valid method to predict the voltage response of a micro/nano cantilevers.