Active control of the accordion modes of a submerged hull

Active vibration control of a submerged hull is presented. A submarine hull can be idealised as a ring stiffened finite cylinder with applied fluid loading. At low frequencies, rotation of the propeller results in discrete tones at the blade passing frequency and its harmonics. The low frequency axial and radial vibration modes of the submerged body can result in a high level of radiated noise. Global hull modes are difficult to attenuate since passive control techniques such as damping materials are not practical due to size and weight constraints. This work investigates active vibration control of a submarine hull for attenuation of the structural and acoustic responses. Based on a feedforward algorithm at tonal frequencies, active vibration suppression of the axial and radial hull displacements are investigated. The effect of the various control arrangements on the structure-borne radiated noise is examined. Numerical simulations of the control performance are presented.

Mechanical response of carbon fiber composite sandwich panels with pyramidal truss cores

The combination of light carbon fiber reinforced polymer (CFRP) composite materials with structurally efficient sandwich panel designs offers novel opportunities for ultralight structures. Here, pyramidal truss sandwich cores with relative densities ρ̄ in the range 1-10% have been manufactured from carbon fiber reinforced polymer laminates by employing a snap-fitting method. The measured quasi-static shear strength varied between 0.8 and 7.5 MPa. Two failure modes were observed: (i) Euler buckling of the struts and (ii) delamination failure of the laminates. Micro-buckling failure of the struts was not observed in the experiments reported here while Euler buckling and delamination failures occurred for the low (ρ̄≤1%) and high (ρ̄>1%) relative density cores, respectively. Analytical models for the collapse of the composite cores by these failure modes are presented. Good agreement between the measurements and predictions based on the Euler buckling and delamination failure of the struts is observed while the micro-buckling analysis over-predicts the measurements. The CFRP pyramidal cores investigated here have a similar mechanical performance to CFRP honeycombs. Thus, for a range of multi-functional applications that require an "open-celled" architecture (e.g. so that cooling fluid can pass through a sandwich core), the CFRP pyramidal cores offer an attractive alternative to honeycombs. © 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.

Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach

We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat-release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We also find that its effect is maximized when it is placed at the downstream end of the tube. This feedback mechanism could be supplied, for example, by an adiabatic mesh. We illustrate the base-state sensitivity by calculating the effects of small variations in the damping factor, the heat-release time-delay coefficient, the heat-release parameter, and the hot-wire location. The successful application of sensitivity analysis to thermo-acoustics opens up new possibilities for the passive control of thermo-acoustic oscillations by providing gradient information that can be combined with constrained optimization algorithms in order to reduce linear growth rates. © Cambridge University Press 2013.

High-order DES and zonal LES of a labyrinth seal

Hybrid numerical large eddy simulation (NLES) and detached eddy simulation (DES) methods are assessed on a labyrinth seal geometry. A high sixth order discretization scheme is used and is validated using a test case of a two dimensional vortex. The hybrid approach adopts a new blending function and along with DES is initially validated using a simple cavity flow. The NLES method is also validated outside of RANS zones. It is found that there is very little resolved turbulence in the cavity for the DES simulation. For the labyrinth seal calculations the DES approach is problematic giving virtually no resolved turbulence content. It is seen that over the tooth tips the extent of the LES region is small and is likely to be a strong contributor to excessive flow damping in these regions. On the other hand the zonal Hamilton-Jacobi approach did not suffer from this trait. In both cases the meshes used are considered to be hybrid RANS-LES adequate. Fortunately (or perhaps unfortunately) the DES profiles are in agreement with the time mean experimental measurements. It is concluded that for an inexperienced CFD practitioner this could have wider implications particularly if transient results such as unsteady loading are desired. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc.

An efficient model for the dynamic behaviour of a single pile in viscoelastic soil

This paper presents a novel, three-dimensional, single-pile model, formulated in the wavenumber domain and adapted to account for boundary conditions using the superposition of loading cases. The pile is modelled as a column in axial vibration, and a Euler-Bernoulli beam in lateral vibration. The surrounding soil is treated as a viscoelastic continuum. The response of the pile is presented in terms of the stiffness and damping coefficients, and also the magnitude and phase of the pile-head frequency-response function. Comparison with existing models shows that excellent agreement is observed between this model, a boundary-element formulation, and an elastic-continuum-type formulation. This three-dimensional model has an accuracy equivalent to a 3D boundary-element model, and a runtime similar to a 2D plane-strain analytical model. Analysis of the response of the single pile illustrates a difference in axial and lateral vibration behaviour; the displacement along the pile is relatively invariant under axial loads, but in lateral vibration the pile exhibits localised deformations. This implies that a plane-strain assumption is valid for axial loadings and only at higher frequencies for lateral loadings. © 2013 Elsevier Ltd.

When will a flame describing function approach to thermoacoustics work well?

In any thermoacoustic analysis, it is important not only to predict linear frequencies and growth rates, but also the amplitude and frequencies of any limit cycles. The Flame Describing Function (FDF) approach is a quasi-linear analysis which allows the prediction of both the linear and nonlinear behaviour of a thermoacoustic system. This means that one can predict linear growth rates and frequencies, and also the amplitudes and frequencies of any limit cycles. The FDF achieves this by assuming that the acoustics are linear and that the flame, which is the only nonlinear element in the thermoacoustic system, can be adequately described by considering only its response at the frequency at which it is forced. Therefore any harmonics generated by the flame's nonlinear response are not considered. This implies that these nonlinear harmonics are small or that they are sufficiently filtered out by the linear dynamics of the system (the low-pass filter assumption). In this paper, a flame model with a simple saturation nonlinearity is coupled to simple duct acoustics, and the success of the FDF in predicting limit cycles is studied over a range of flame positions and acoustic damping parameters. Although these two parameters affect only the linear acoustics and not the nonlinear flame dynamics, they determine the validity of the low-pass filter assumption made in applying the flame describing function approach. Their importance is highlighted by studying the level of success of an FDF-based analysis as they are varied. This is achieved by comparing the FDF's prediction of limit-cycle amplitudes to the amplitudes seen in time domain simulations.

Optimisation of passive and semi-active heavy vehicle suspensions

An investigation into the potential for reducing road damage by optimising the design of heavy vehicle suspensions is described. In the first part of the paper two simple mathematical models are used to study the optimisation of conventional passive suspensions. Simple modifications are made to the steel spring suspension of a tandem axle trailer and it is found experimentally that RMS dynamic tyre forces can be reduced by 15% and theoretical road damage by 5.2%. A mathematical model of an air-sprung articulated vehicle is validated, and its suspension is optimised according to the simple models. This vehicle generates about 9% less damage than the leaf-sprung vehicle in the unmodified state and it is predicted that, for the operating conditions examined, the road damage caused by this vehicle can be reduced by a further 5.4%. Finally, it is shown experimentally that computer-controlled semi-active dampers have the potential to reduce road damage by a further 5-6%, compared to an air suspension with optimum passive damping. © Copyright 1994 Society of Automotive Engineers, Inc.

The soft impact response of composite laminate beams

The quasi-static and dynamic responses of laminated beams of equal areal mass, made from monolithic CFRP and Ultra high molecular weight Polyethylene (UHMWPE), have been measured. The end-clamped beams were impacted at mid-span by metal foam projectiles to simulate localised blast loading. The effect of clamping geometry on the response was investigated by comparing the response of beams bolted into the supports with the response of beams whose ends were wrapped around the supports. The effect of laminate shear strength upon the static and dynamic responses was investigated by testing two grades of each of the CFRP and UHMWPE beams: (i) CFRP beams with a cured matrix and uncured matrix, and (ii) UHMWPE laminates with matrices of two different shear strengths. Quasi-static stretch-bend tests indicated that the load carrying capacity of the UHWMPE beams exceeds that of the CFRP beams, increases with diminishing shear strength of matrix, and increases when the ends are wrapped rather than through-bolted. The dynamic deformation mode of the beams is qualitatively different from that observed in the quasi-static stretch-bend tests. In the dynamic case, travelling hinges emanate from the impact location and propagate towards the supports; the beams finally fail by tensile fibre fracture at the supports. The UHMWPE beams outperform the CFRP beams in terms of a lower mid-span deflection for a given impulse, and a higher failure impulse. Also, the maximum attainable impulse increases with decreasing shear strength for both the UHMWPE and CFRP beams. The ranking of the beams for load carrying capacity in the quasi-static stretch-bend tests is identical to that for failure impulse in the impact tests. Thus, the static tests can be used to gauge the relative dynamic performances of the beams. © 2013 Elsevier Ltd. All rights reserved.

The effect of shear strength on the ballistic response of laminated composite plates

The ballistic performance of clamped circular carbon fibre reinforced polymer (CFRP) and Ultra High Molecular Weight Polyethylene (UHMWPE) fibre composite plates of equal areal mass and 0/90 lay-up were measured and compared with that of monolithic 304 stainless steel plates. The effect of matrix shear strength upon the dynamic response was explored by testing: (i) CFRP plates with both a cured and uncured matrix and (ii) UHMWPE laminates with identical fibres but with two matrices of different shear strength. The response of these plates when subjected to mid-span, normal impact by a steel ball was measured via a dynamic high speed shadow moiré technique. Travelling hinges emanate from the impact location and travel towards the supports. The anisotropic nature of the composite plate results in the hinges travelling fastest along the fibre directions and this results in square-shaped moiré fringes in the 0/90 plates. Projectile penetration of the UHMWPE and the uncured CFRP plates occurs in a progressive manner, such that the number of failed plies increases with increasing velocity. The cured CFRP plate, of high matrix shear strength, fails by cone-crack formation at low velocities, and at higher velocities by a combination of cone-crack formation and communition of plies beneath the projectile. On an equal areal mass basis, the low shear strength UHMWPE plate has the highest ballistic limit followed by the high matrix shear strength UHMWPE plate, the uncured CFRP, the steel plate and finally the cured CFRP plate. We demonstrate that the high shear strength UHMWPE plate exhibits Cunniff-type ballistic limit scaling. However, the observed Cunniff velocity is significantly lower than that estimated from the laminate properties. The data presented here reveals that the Cunniff velocity is limited in its ability to characterise the ballistic performance of fibre composite plates as this velocity is independent of the shear properties of the composites: the ballistic limit of fibre composite plates increases with decreasing matrix shear strength for both CFRP and UHMWPE plates. © 2013 Elsevier Masson SAS. All rights reserved.

Nonlinear phenomena in thermoacoustic systems with premixed flames

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies, amplitudes and stability of limit cycles. Limit cycles in thermoacoustic systems are reached when the energy input from driving processes and energy losses from damping processes balance each other over a cycle of the oscillation. In this paper an integral relation for the rate of change of energy of a thermoacoustic system is derived. This relation is analogous to the well-known Rayleigh criterion in thermoacoustics, but can be used to calculate the amplitudes of limit cycles, as well as their stability. The relation is applied to a thermoacoustic system of a ducted slot-stabilized 2-D premixed flame. The flame is modelled using a nonlinear kinematic model based on the G-equation, while the acoustics of planar waves in the tube are governed by linearised momentum and energy equations. Using open-loop forced simulations, the flame describing function (FDF) is calculated. The gain and phase information from the FDF is used with the integral relation to construct a cyclic integral rate of change of energy (CIRCE) diagram that indicates the amplitude and stability of limit cycles. This diagram is also used to identify the types of bifurcation the system exhibits and to find the minimum amplitude of excitation needed to reach a stable limit cycle from another linearly stable state, for single- mode thermoacoustic systems. Furthermore, this diagram shows precisely how the choice of velocity model and the amplitudedependence of the gain and the phase of the FDF influence the nonlinear dynamics of the system. Time domain simulations of the coupled thermoacoustic system are performed with a Galerkin discretization for acoustic pressure and velocity. Limit cycle calculations using a single mode, as well as twenty modes, are compared against predictions from the CIRCE diagram. For the single mode system, the time domain calculations agree well with the frequency domain predictions. The heat release rate is highly nonlinear but, because there is only a single acoustic mode, this does not affect the limit cycle amplitude. For the twenty-mode system, however, the higher harmonics of the heat release rate and acoustic velocity interact resulting in a larger limit cycle amplitude. Multimode simulations show that in some situations the contribution from higher harmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Copyright © 2012 by ASME.

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.

Precracked reinforced concrete t-beams repaired in shear with prestressed carbon fiber-reinforced polymer straps

The results of an experimental and numerical investigation involving unstrengthened reinforced concrete (RC) T-beams and precracked RC T-beams strengthened in shear with prestressed carbon fiber-reinforced polymer (CFRP) straps are presented and discussed. The results provide insights into the influence of load history and beam depth on the structural behavior of both unstrengthened and strengthened beams. The strengthened beams exhibited capacity enhancements of 21.6 to 46% compared to the equivalent unstrengthened beams, demonstrating the potential effectiveness of the prestressed CFRP strap system. Nonlinear finite element (FE) predictions, which incorporated the load history, reproduced the observed experimental behavior but either underestimated or overestimated the post-cracking stiffness of the beams and strap strain at higher load levels. These limitations were attributed to the concrete shear models used in the FE analyses.

Parametrically excited MEMS vibration energy harvesters with design approaches to overcome the initiation threshold amplitude

Resonant-based vibration harvesters have conventionally relied upon accessing the fundamental mode of directly excited resonance to maximize the conversion efficiency of mechanical-to-electrical power transduction. This paper explores the use of parametric resonance, which unlike the former, the resonant-induced amplitude growth, is not limited by linear damping and wherein can potentially offer higher and broader nonlinear peaks. A numerical model has been constructed to demonstrate the potential improvements over the convention. Despite the promising potential, a damping-dependent initiation threshold amplitude has to be attained prior to accessing this alternative resonant phenomenon. Design approaches have been explored to passively reduce this initiation threshold. Furthermore, three representative MEMS designs were fabricated with both 25 and 10 μm thick device silicon. The devices include electrostatic cantilever-based harvesters, with and without the additional design modification to overcome initiation threshold amplitude. The optimum performance was recorded for the 25 μm thick threshold-aided MEMS prototype with device volume ∼0.147 mm3. When driven at 4.2 ms -2, this prototype demonstrated a peak power output of 10.7 nW at the fundamental mode of resonance and 156 nW at the principal parametric resonance, as well as a 23-fold decrease in initiation threshold over the purely parametric prototype. An approximate doubling of the half-power bandwidth was also observed for the parametrically excited scenario. © 2013 IOP Publishing Ltd.

A general mass law for broadband energy harvesting

It is well known that the power absorbed by a linear oscillator when excited by white noise base acceleration depends only on the mass of the oscillator and the spectral density of the base motion. This places an upper bound on the energy that can be harvested from a linear oscillator under broadband excitation, regardless of the stiffness of the system or the damping factor. It is shown here that the same result applies to any multi-degree-of-freedom nonlinear system that is subjected to white noise base acceleration: for a given spectral density of base motion the total power absorbed is proportional to the total mass of the system. The only restriction to this result is that the internal forces are assumed to be a function of the instantaneous value of the state vector. The result is derived analytically by several different approaches, and numerical results are presented for an example two-degree-of-freedom-system with various combinations of linear and nonlinear damping and stiffness. © 2013 The Author.