Natural frequency and damping ratio of a vertically vibrated surface foundation

It is possible and common to obtain equivalent natural frequency and damping for a soil-foundation system from results of experimental or numerical analysis assuming the system has a single degree of freedom. Three approaches to extract natural frequency and damping were applied to the vertically vibrated soil-foundation system. The sensitivity of the computed natural frequency and damping to the soil properties was evaluated through parametric studies. About 10-20% of discrepancy in values of natural frequency was observed due to different approaches. The results help to assess the reliability of equivalent soil properties determined from the reported natural frequency of the system. Finally the results obtained using theoretical predictions with linear soil properties measured in situ were compared to those calculated from experimental data. The prediction and experimental results showed good agreements if the embedment of the foundation is neglected with stepped sine test but considered with impulse test. © 2010 Elsevier Ltd.

Multi-frequency operation of a mems vibration energy harvester by accessing five orders of parametric resonance

The mechanical amplification effect of parametric resonance has the potential to outperform direct resonance by over an order of magnitude in terms of power output. However, the excitation must first overcome the damping-dependent initiation threshold amplitude prior to accessing this more profitable region. In addition to activating the principal (1st order) parametric resonance at twice the natural frequency ω0, higher orders of parametric resonance may be accessed when the excitation frequency is in the vicinity of 2ω0/n for integer n. Together with the passive design approaches previously developed to reduce the initiation threshold to access the principal parametric resonance, vacuum packaging (< 10 torr) is employed to further reduce the threshold and unveil the higher orders. A vacuum packaged MEMS electrostatic harvester (0.278 mm3) exhibited 4 and 5 parametric resonance peaks at room pressure and vacuum respectively when scanned up to 10 g. At 5.1 ms-2, a peak power output of 20.8 nW and 166 nW is recorded for direct and principal parametric resonance respectively at atmospheric pressure; while a peak power output of 60.9 nW and 324 nW is observed for the respective resonant peaks in vacuum. Additionally, unlike direct resonance, the operational frequency bandwidth of parametric resonance broadens with lower damping. © Published under licence by IOP Publishing Ltd.

Forcing of self-excited round jet diffusion flames

In this experimental and numerical study, two types of round jet are examined under acoustic forcing. The first is a non-reacting low density jet (density ratio 0.14). The second is a buoyant jet diffusion flame at a Reynolds number of 1100 (density ratio of unburnt fluids 0.5). Both jets have regions of strong absolute instability at their base and this causes them to exhibit strong self-excited bulging oscillations at welldefined natural frequencies. This study particularly focuses on the heat release of the jet diffusion flame, which oscillates at the same natural frequency as the bulging mode, due to the absolutely unstable shear layer just outside the flame. The jets are forced at several amplitudes around their natural frequencies. In the non-reacting jet, the frequency of the bulging oscillation locks into the forcing frequency relatively easily. In the jet diffusion flame, however, very large forcing amplitudes are required to make the heat release lock into the forcing frequency. Even at these high forcing amplitudes, the natural mode takes over again from the forced mode in the downstream region of the flow, where the perturbation is beginning to saturate non-linearly and where the heat release is high. This raises the possibility that, in a flame with large regions of absolute instability, the strong natural mode could saturate before the forced mode, weakening the coupling between heat release and incident pressure perturbations, hence weakening the feedback loop that causes combustion instability. © 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

The ensemble statistics of the energy of a random system subjected to harmonic excitation

This paper is concerned with the ensemble statistics of the response to harmonic excitation of a single dynamic system such as a plate or an acoustic volume. Random point process theory is employed, and various statistical assumptions regarding the system natural frequencies are compared, namely: (i) Poisson natural frequency spacings, (ii) statistically independent Rayleigh natural frequency spacings, and (iii) natural frequency spacings conforming to the Gaussian orthogonal ensemble (GOE). The GOE is found to be the most realistic assumption, and simple formulae are derived for the variance of the energy of the system under either point loading or rain-on-the-roof excitation. The theoretical results are compared favourably with numerical simulations and experimental data for the case of a mass loaded plate. © 2003 Elsevier Ltd. All rights reserved.

Dynamic properties of superconducting magnetic bearings

The potential use of YBa2j as an active component in a magnetic bearing is being investigated. Although the load bearing capacity is high and increases with the square of the magnetic field trapped, the stiffness is low. Both the stiffness and the lévitation height are a function of the loading history of the bearing. At Cambridge we have been investigating the effects of dynamic loading such as single large excursions from steady state loads and cyclically applied loads such as vibrations. Since a superconducting bearing has little inherent damping cyclic loads applied at or near its natural frequency can have catastrophic effects. The information being gathered at Cambridge will be used to enable these effects to be mitigated in the bearing design process. © 1997 IEEE.

Probabilistic fault identification using vibration data and neural networks

Bayesian formulated neural networks are implemented using hybrid Monte Carlo method for probabilistic fault identification in cylindrical shells. Each of the 20 nominally identical cylindrical shells is divided into three substructures. Holes of (12±2) mm in diameter are introduced in each of the substructures and vibration data are measured. Modal properties and the Coordinate Modal Assurance Criterion (COMAC) are utilized to train the two modal-property-neural-networks. These COMAC are calculated by taking the natural-frequency-vector to be an additional mode. Modal energies are calculated by determining the integrals of the real and imaginary components of the frequency response functions over bandwidths of 12% of the natural frequencies. The modal energies and the Coordinate Modal Energy Assurance Criterion (COMEAC) are used to train the two frequency-response-function-neural-networks. The averages of the two sets of trained-networks (COMAC and COMEAC as well as modal properties and modal energies) form two committees of networks. The COMEAC and the COMAC are found to be better identification data than using modal properties and modal energies directly. The committee approach is observed to give lower standard deviations than the individual methods. The main advantage of the Bayesian formulation is that it gives identities of damage and their respective confidence intervals.

Sound radiation from point-excited structures: Comparison of plate and sphere

Acoustic radiation from a structure can be expressed in terms of modal radiation and modal coefficients. This paper investigates the contributions of these two modal properties to radiation excited by a point force. Sound radiation from two basic structures is considered: a baffled rectangular plate and a closed spherical shell. The plate behaviour is familiar, and governed by the relation between the natural frequency of a mode and its coincidence frequency. For a closed spherical shell, there are either zero or two critical frequencies, depending on the radius and thickness. When there are two the shell radiates well both above and below the two frequencies, and poorly in the frequency range between them. © 2012 Elsevier Ltd. All rights reserved.

Linear quadratic game and non-cooperative predictive methods for potential application to modelling driver-AFS interactive steering control

This paper is concerned with the modelling of strategic interactions between the human driver and the vehicle active front steering (AFS) controller in a path-following task where the two controllers hold different target paths. The work is aimed at extending the use of mathematical models in representing driver steering behaviour in complicated driving situations. Two game theoretic approaches, namely linear quadratic game and non-cooperative model predictive control (non-cooperative MPC), are used for developing the driver-AFS interactive steering control model. For each approach, the open-loop Nash steering control solution is derived; the influences of the path-following weights, preview and control horizons, driver time delay and arm neuromuscular system (NMS) dynamics are investigated, and the CPU time consumed is recorded. It is found that the two approaches give identical time histories as well as control gains, while the non-cooperative MPC method uses much less CPU time. Specifically, it is observed that the introduction of weight on the integral of vehicle lateral displacement error helps to eliminate the steady-state path-following error; the increase in preview horizon and NMS natural frequency and the decline in time delay and NMS damping ratio improve the path-following accuracy. © 2013 Copyright Taylor and Francis Group, LLC.

Fluid-structure interaction simulations of a tension-cone inflatable aerodynamic decelerator

A series of fluid-structure interaction simulations of an aerodynamic tension-cone supersonic decelerator prototype intended for large mass payload deployment in planetary explorations are discussed. The fluid-structure interaction computations combine large deformation analysis of thin shells with large-eddy simulation of compressible turbulent flows using a loosely coupled approach to enable quantification of the dynamics of the vehicle. The simulation results are compared with experiments carried out at the NASA Glenn Research Center. Reasonably good agreement between the simulations and the experiment is observed throughout a deflation cycle. The simulations help to illuminate the details of the dynamic progressive buckling of the tension-cone decelerator that ultimately results in the collapse of the structure as the inflation pressure is decreased. Furthermore, the tension-cone decelerator exhibits a transient oscillatory behavior under impulsive loading that ultimately dies out. The frequency of these oscillations was determined to be related to the acoustic time scale in the compressed subsonic region between the bow shock and the structure. As shown, when the natural frequency of the structure and the frequency of the compressed subsonic region approximately match, the decelerator exhibits relatively large nonaxisymetric oscillations. The observed response appears to be a fluid-structure interaction resonance resulting from an acoustic chamber (pistonlike) mode exciting the structure. Copyright © 2013 by Christopher Porter, R. Mark Rennie, Eric J. Jumper.

Interaction between heavy vehicles and roads

This paper discusses road damage caused by heavy commercial vehicles. Chapter 1 presents some important terminology and a brief historical review of road construction and vehicle-road interaction, from ancient times to the present day. The main types of vehicle-generated road damage, and the methods that are used by pavement engineers to analyze them are discussed in Chapter 2. Attention is also given to the main features of the response of road surfaces to vehicle loads and mathematical models that have been developed to predict road response. Chapter 3 reviews the effects on road damage of vehicle features which can be studied without consideration of vehicle dynamics. These include gross vehicle weight, axle and tire configurations, tire contact conditions and static load sharing in axle group suspensions. The dynamic tire forces generated by heavy vehicles are examined in Chapter 4. The discussion includes their simulation and measurement, their principal characteristics, the effects of tires and suspension design on dynamic forces, and the potential benefits of using advanced suspensions for minimizing dynamic tire forces. Chapter 5 discusses methods for estimating the effects of dynamic tire forces on road damage. The two main approaches are either to examine the statistics of the forces themselves; or to calculate the response of a pavement model to the forces, and to calculate the resulting wear using a material damage model. The issues involved in assessing vehicles for 'road friendliness' are discussed in Chapter 6. Possible assessment methods include measuring strains in an instrumented pavement traversed by the vehicle, measuring dynamic tire forces, or measuring vehicle parameters such as the 'natural frequency' and 'damping ratio'. Each of these measurements involves different assumptions and analysis methods for converting the results into some measure of road damage. Chapter 7 includes a summary of the main conclusions of the paper and recommendations for tire and suspension design, road design and construction, and for vehicle regulations.

Lock-in and quasiperiodicity in a forced hydrodynamically self-excited jet

The ability of hydrodynamically self-excited jets to lock into strong external forcing is well known. Their dynamics before lock-in and the specific bifurcations through which they lock in, however, are less well known. In this experimental study, we acoustically force a low-density jet around its natural global frequency. We examine its response leading up to lock-in and compare this to that of a forced van der Pol oscillator. We find that, when forced at increasing amplitudes, the jet undergoes a sequence of two nonlinear transitions: (i) from periodicity to T{double-struck}2 quasiperiodicity via a torus-birth bifurcation; and then (ii) from T{double-struck}2 quasiperiodicity to 1:1 lock-in via either a saddle-node bifurcation with frequency pulling, if the forcing and natural frequencies are close together, or a torus-death bifurcation without frequency pulling, but with a gradual suppression of the natural mode, if the two frequencies are far apart. We also find that the jet locks in most readily when forced close to its natural frequency, but that the details contain two asymmetries: the jet (i) locks in more readily and (ii) oscillates more strongly when it is forced below its natural frequency than when it is forced above it. Except for the second asymmetry, all of these transitions, bifurcations and dynamics are accurately reproduced by the forced van der Pol oscillator. This shows that this complex (infinite-dimensional) forced self-excited jet can be modelled reasonably well as a simple (three-dimensional) forced self-excited oscillator. This result adds to the growing evidence that open self-excited flows behave essentially like low-dimensional nonlinear dynamical systems. It also strengthens the universality of such flows, raising the possibility that more of them, including some industrially relevant flames, can be similarly modelled. © 2013 Cambridge University Press.