Abstracts:A method to synthesize the modal characteristics of a system from the modal characteristics of its subsystems is proposed. The interest is focused on those systems with elastic links between the parts which is the main feature of the proposed method. An algebraic proof is provided for the case of arbitrary number of connections. The solution is a system of equations with a reduced number of degrees of freedom that correspond to the number of elastic links between the subsystems. In addition the method is also interpreted from a physical point of view (equilibrium of the interaction forces). An application to plates linked by means of springs shows how the global eigenfrequencies and eigenmodes are properly computed by means of the subsystems eigenfrequencies and eigenmodes.

Abstracts:Identifying the bearing fault-induced impulsive components in the frequency domain is a key step in the corresponding fault detection. However, gearbox vibration signals often significant interrupt the rolling bearing fault diagnosis, particularly in the detection of planet bearing faults under the background noise of the planetary gearbox. Except in the case of a high amplitude, a gear meshing-related vibration may also affect the identification of the planet bearing fault-induced resonance frequency band. To solve this problem, a meshing frequency modulation index (indexMFM)-based kurtogram utilizing a particular gearbox related phenomenon is proposed. The underlying mechanism is such that although the gear meshing-related spectral components are always more prominent in relatively higher-frequency band than the planet bearing-induced resonance frequency band in impulsiveness, the gear meshing-related impulsive components modulate the gear meshing frequency, yet the faulty bearing-induced one does not. Exploiting this difference, the planet bearing fault-induced impulsive components can be directly identified from the strong gear vibration interruption by determining the bearing fault-related resonance frequency band in the indexMFM-based kurtogram. The effectiveness of the proposed method is separately verified using simulated and experimental data.

Abstracts:In lightweight structures, there is increasing evidence of the existence of interaction between pedestrians and structures, now commonly termed pedestrian-structure interaction. The presence of a walker can alter the dynamic characteristics of the human-structure system compared with those inherent to the empty structure. Conversely, the response of the structure can influence human behaviour and hence alter the applied loading. In the past, most effort on determining the imparted footfall-induced vertical forces to the walking surface has been conducted using rigid, non-flexible surfaces such as treadmills. However, should the walking surface be vibrating, the characteristics of human walking could change to maximize comfort. Knowledge of pedestrian-structure interaction effects is currently limited, and it is often quoted as a reason for our inability to predict vibration response accurately. This work aims to quantify the magnitude of human-structure interaction through an experimental-numerical programme on a full-scale lively footbridge. An insole pressure measurement system was used to measure the human-imparted force on both rigid and lively surfaces. Test subjects, walking at different pacing frequencies, took part in the test programme to infer the existence of the two forms of human-structure interaction. Parametric statistical hypothesis testing provides evidence on the existence of human-structure interaction. In addition, a non-parametric test (Monte Carlo simulation) is employed to quantify the effects of numerical model error on the identified human-structure interaction forms. It is concluded that human-structure interaction is an important phenomenon that should be considered in the design and assessment of vibration-sensitive structures.

Abstracts:Flywheel energy storage systems (FESSs) with active and passive magnetic bearings are generating interest due to their increasing energy-storing potential caused by advances in motor, bearing and fibre-composite technology. Magnetically suspended FESS are used commercially on static foundations while vehicle applications pose challenges due to manoeuvring, impacts, and other outer perturbations and have thus only seen successful experimental application in a few research projects where the FESS has been mounted in a passive gimbal to avoid gyroscopic forces. Although experimentally implemented, a mathematical model is still missing that determines motions and forces when the FESS is suspended in magnetic bearings, gimbal-mounted, and subject to outer perturbations. This work thoroughly describes how to set up a mathematical model that couples the multi-body dynamics of a flywheel rotor, housing, and gimbal-mount with the magnetic forces of the bearings. The model is used to simulate the behaviour of a FESS with and without gimbal and subject to various perturbations. The results demonstrate how the gimbal mount effectively removes gyroscopic forces but introduces other potential challenges such as large rotor and housing displacements due to dynamical interactions between the rotor, active magnetic bearings, housing, and gimbal.

Abstracts:This paper presents a new approach, referred to here as the two-dimensional spectral-Tchebychev (2D-ST) technique, to predict the dynamics of thick plates having arbitrary geometries under different boundary conditions. The integral boundary value problem governing the dynamics of plate-like structures is obtained using the Mindlin plate theory and following an energy-based approach. To solve the boundary value problem numerically, a spectral-Tchebychev based solution technique is developed. To simplify the calculation of integral and derivative operations and thus to increase the numerical efficiency of the solution approach, a one-to-one coordinate mapping technique is used to map the arbitrary geometry onto an equivalent rectangular in-plane shape of the plate. The proposed solution technique is applied to various different plate problems to assess the accuracy and show the applicability of the technique. In each case, the convergence of the solution is analyzed, and the predicted (non-dimensional) natural frequencies are compared to those found in the literature or to those found using finite element modeling. It is shown that the calculated natural frequencies converge exponentially with increasing number of Tchebychev polynomials used and are in excellent agreement with those found in the literature and found form a finite elements solution. Therefore, it is concluded that the presented spectral-Tchebychev solution technique can accurately and efficiently capture the dynamics of thick plates having arbitrary geometries. Furthermore, the utility of the 2D-ST is demonstrated by comparing the results obtained using a three-dimensional solution approach.

Abstracts:Frequency contents have been widely investigated to understand the vibration behaviors of planetary gearboxes. Appearances of certain sideband peaks in the frequency spectrum may indicate the occurrence of gear fault. However, analyzing too many sidebands will create problems and uncertainty of fault diagnoses. To this end, it is of vital importance to focus on those sidebands, as well as their amplitudes, which are directly induced by the gear faults. The Sideband Energy Ratio (SER) method, which synthesize the amplitudes of characteristic frequencies and meshing frequency, has shown its effectiveness in fault diagnosis of fixed-shaft gearboxes. However, for planetary gearboxes, the effectiveness and theoretical explanation behind this method still needs to be explored. In this paper, we first explored the amplitudes of characteristic frequencies based on a phenomenological model. Our investigation demonstrated that monitoring the amplitude of a single frequency component is inadequate for fault diagnosis of planetary gearbox. Second, the theoretical explanation of SER for a planetary gearbox is explored. Finally, a modified SER, namely the Modified Sideband Energy Ratio, is proposed to deal with the problem of rotating speed fluctuation. Experimental studies are provided to demonstrate the effectiveness of the proposed method.

Abstracts:A theoretical model is proposed in the current work to shed light on the noise-reduction mechanisms of trailing-edge serrations, which have been shown to suppress noise generated at the trailing edge due to the scattering of boundary layer pressure fluctuations. The current analytical model, which is developed by incorporating Fourier series expansions and the Wiener-Hopf method, can quickly predict noise reductions due to various types of trailing-edge serrations at low Mach numbers. The present model is validated by comparing its predictions with relevant published theoretical and experimental results. Moreover, from the Winer-Hopf analysis, an effective method based on Fourier series expansion is proposed to approximately evaluate the noise-reduction performance of different serrated geometries under various working conditions. The current work shows that trailing-edge serrations reduce noise by producing scattered waves with spanwise modes which could be evanescent, and explains why some serrated geometries are more effective than others in suppressing noise. The efficient noise prediction capability of the proposed model makes it very suitable to be used in the trailing-edge designs and evaluations of low-noise aircraft components such as wings and aero-engine fan, compressor and turbine cascades.

Abstracts:We study the effects of structural properties distributions on the sound radiation of a thin elastic airfoil. Focusing on flapping-flight in a high-Reynolds and low-Mach regime, we seek optimal conditions to mitigate flapping-sound while maintaining aerodynamic efficiency. The airfoil is immersed in a two-dimensional potential flow field, and is subjected to leading-edge actuation in the form of a small-amplitude periodic heaving motion. The near-field dynamics is governed by Euler-Bernoulli's beam equation of motion and analyzed using thin airfoil theory in conjunction with a discrete-vortex wake model. The near-field results are introduced as an effective dipole-type source term to the right-hand-side of the Powell-Howe acoustic wave equation, and the associated far-field sound is calculated using Green's function formulation. Considering the elastic flapping configuration, we seek optimal material properties and a linear thickness distribution to reduce the sound of an otherwise rigid airfoil while retaining the lift amplitude of the rigid configuration. To this end, the aeroacoustic model is introduced into an optimization scheme, where minimal sound amplitude is sought in the lift direction, subjected to the aforementioned lift force constraint with a 33% assigned tolerance value. The relatively wide tolerance produces in turn an effective Pareto front, reflecting the trade-off between the competing objectives of lower sound levels and aerodynamic efficiency. Compared with the rigid heaving airfoil, over 10 [dB] sound reduction was obtained for the optimal flexible configuration producing the same lift amplitude. The Pareto front also displays a linear relation between sound reduction ratio and lift amplitude ratio, indicating a further substantial sound reduction of up to 30 [dB] for smaller lift ratio values. The effect of optimal structure thickness distribution on the equi-lift sound reduction mechanism is two-fold: The motion and wake dipoles are shifted to an antiphased mode thus reducing the total sound signal, and the motion dipole which represents the unsteady forces, exerted by the airfoil on the fluid while transversing, is fixed in magnitude, thus retaining the lift amplitude value. The system dynamics leading to the opposing sound dipoles is evoked by phase-locking the airfoil motion and circulation, and following Kelvin's theorem, antiphase-locking the airfoil motion and wake circulation. Implications on flapping flags and streamers is briefly discussed as well.

Abstracts:In most previous studies of sound radiation from railway rails, the rail has been regarded as located in free space, disregarding the influence of the ground. However, in order to predict the noise from the rail more precisely, the effect of the ground should be included in rolling noise predictions. In this study, the rail noise is investigated by means of a wavenumber domain numerical method, including the presence of the ground. For rails attached to a rigid ground or located at a certain distance above it, the influence of the ground is examined in terms of the radiation ratio and longitudinal directivity. From the prediction of radiated power, it is found that the vertical and lateral bending waves of the rail radiate most of the noise for the corresponding direction. Hence, a simplified calculation is proposed that only includes these waves, instead of a full three-dimensional analysis. An absorptive ground is also modelled by applying impedance boundary conditions at the ground surface to investigate the influence of the ground on the rail noise. Finally, for the vertical and lateral bending waves in the rail, the cross-sectional directivity of the noise is predicted for various surface impedances of the ground. It is found that the simplified calculation proposed in this study is valid for the prediction of noise from the rail. Also the presence of the ground and its impedance condition have considerable effects on the level and directivity patterns of the noise radiated from the rail.

Abstracts:A new method for input signal reconstruction is presented. This approach utilizes the convolution relationship of inputs and outputs of linear systems. A linear discretization of sampled points was assumed in formulating the discrete convolution integral. Subsequently, the resulting equation was modified via a linear constraint to facilitate solution by the least square method. This improves the conditioning of discrete deconvolution. The method was validated numerically on a single degree of freedom dynamic system. Inputs reconstructed matched the applied input very well for a low noise case. A methodology for multiple inputs and outputs was developed. The single input-multiple output formulation was validated using experimental strain measurements of hammer pulse tests. Pulse areas and peak magnitudes were reconstructed with good accuracy.