Multimode radiation from an unflanged, semi-infinite circular duct with uniform flow.

Multimode sound radiation from an unflanged, semi-infinite, rigid-walled circular duct with uniform subsonic mean flow everywhere is investigated theoretically. The multimode directivity depends on the amplitude and directivity function of each individual cut-on mode. The amplitude of each mode is expressed as a function of cut-on ratio for a uniform distribution of incoherent monopoles, a uniform distribution of incoherent axial dipoles, and for equal power per mode. The directivity function of each mode is obtained by applying a Lorentz transformation to the zero-flow directivity function, which is given by a Wiener-Hopf solution. This exact numerical result is compared to an analytic solution, valid in the high-frequency limit, for multimode directivity with uniform flow. The high-frequency asymptotic solution is derived assuming total transmission of power at the open end of the duct, and gives the multimode directivity function with flow in the forward arc for a general family of mode amplitude distribution functions. At high frequencies the agreement between the exact and asymptotic solutions is shown to be excellent.

Models for acoustic propagation through turbofan exhaust flows-lined ducts

Turbomachinery noise radiating into the rearward arc is an important problem. This noise is scattered by the trailing edges of the nacelle and the jet exhaust, and interacts with the shear layers between the external flow, bypass stream and jet, en route to the far field. In the past a range of relevant model problems involving semi-infinite cylinders have been solved. However, one limitation of these previous solutions is that they do not allow for the jet nozzle protruding a finite distance beyond the end of the nacelle (or in certain configurations being buried a finite distance upstream). With this in mind, we have used the matrix Wiener-Hopf technique to allow precisely this finite nacelle-jet nozzle separation to be included. We have previously reported results for the case of hard-walled ducts, which requires factorisation of a 2 × 2 matrix. In this paper we extend this work by allowing one of the duct walls, in this case the outer wall of the jet pipe, to be acoustically lined. This results in the need to factorise a 3 × 3 matrix, which is completed by use of a combination of pole-removal and Pad́e approximant techniques. Sample results are presented, investigating in particular the effects of exit plane stagger and liner impedance. Here we take the mean flow to be zero, but extension to nonzero Mach numbers in the core and bypass flow has also been completed. Copyright © 2009 by Nigel Peake & Ben Veitch.

The direct field boundary impedance of two-dimensional periodic structures with application to high frequency vibration prediction.

Large sections of many types of engineering construction can be considered to constitute a two-dimensional periodic structure, with examples ranging from an orthogonally stiffened shell to a honeycomb sandwich panel. In this paper, a method is presented for computing the boundary (or edge) impedance of a semi-infinite two-dimensional periodic structure, a quantity which is referred to as the direct field boundary impedance matrix. This terminology arises from the fact that none of the waves generated at the boundary (the direct field) are reflected back to the boundary in a semi-infinite system. The direct field impedance matrix can be used to calculate elastic wave transmission coefficients, and also to calculate the coupling loss factors (CLFs), which are required by the statistical energy analysis (SEA) approach to predicting high frequency vibration levels in built-up systems. The calculation of the relevant CLFs enables a two-dimensional periodic region of a structure to be modeled very efficiently as a single subsystem within SEA, and also within related methods, such as a recently developed hybrid approach, which couples the finite element method with SEA. The analysis is illustrated by various numerical examples involving stiffened plate structures.

A model for the erosive wear of rubber at oblique impact angles

A model has been developed to predict the erosive wear behaviour of elastomers under conditions of glancing impact by small hard particles. Previous work has shown the erosive wear mechanism of elastomers under these conditions to be similar in nature to that of abrasive wear by a sharp blade. The model presented here was developed from the model of Southern and Thomas for sliding abrasion, by combining their treatment of the growth of surface cracks with a model for particle impact in which the force - displacement relationship for an idealized flat-ended punch on a semi-infinite elastic solid was assumed. In this way an expression for the erosive wear rate was developed, and compared with experimental measurements of wear rate for natural rubber, styrene - butadiene rubber and a highly crosslinked polybutadiene rubber. Good qualitative agreement was found between the predictions of the model and the experimental measurements. The variation of erosion rate with impact velocity, impact angle, particle size, elastic modulus of the material, coefficient of friction and fatigue properties were all well accounted for. Quantitative agreement was less good, and the effects of erosive particle shape could not be accounted for. The reasons for these discrepancies are discussed. © 1992 IOP Publishing Ltd.

Feedback control and the arrow of time

The purpose of this paper is to highlight the central role that the time asymmetry of stability plays in feedback control. We show that this provides a new perspective on the use of doubly-infinite or semi-infinite time axes for signal spaces in control theory. We then focus on the implication of this time asymmetry in modeling uncertainty, regulation and robust control. We point out that modeling uncertainty and the ease of control depend critically on the direction of time. We finally discuss the relationship of this control-based time arrow with the well-known arrows of time in physics. © 2008 IEEE.

High frequency multimode radiation from ducts with flow

Multimode sound radiation from hard-walled semi-infinite ducts with uniform subsonic flow is investigated theoretically. An analytic expression, valid in the high frequency limit, is derived for the multimode directivity function in the forward arc for a general family of mode distribution functions. The multimode directivity depends on the amplitude and directivity function of each individual mode. The amplitude of each mode is expressed as a function of cut-off ratio for a uniform distribution of incoherent monopoles, a uniform distribution of incoherent axial dipoles and for equal power per mode. The modes' directivity functions are obtained analytically by applying a Lorentz transformation to the zero flow solution. The analytic formula for the multimode directivity with flow is derived assuming total transmission of power at the open-end of the duct. This formula is compared to the exact numerical result for an unflanged duct, computed utilizing a Wiener-Hopf solution. The agreement is shown to be excellent. Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Aerodynamic noise from a poroelastic trailing edge with implications for the silent flight of owls

The interaction of a turbulent eddy with a semi-infinite, poroelastic edge is examined with respect to the effects of both elasticity and porosity on the efficiency of scattered aerodynamic noise. The scattering problem is solved using the Wiener-Hopf technique for constant plate properties to identify their scaling dependence on the resulting aerodynamic noise, including the dependence on flight velocity, where special attention is paid to the limiting cases of rigid, porous and elastic, impermeable plate conditions. Results from these analyses attempt to address how trailing edge noise may be mitigated by porosity and seek to deepen the understanding of how owls hunt in acoustic stealth. © 2012 by Justin W. Jaworski and Nigel Peake. Published by the American Institute of Aeronautics and Astronautics, Inc.

Parametric guidance for turbulent noise reduction from poroelastic trailing edges and owls

The interaction of a turbulent eddy with a semi-infinite, poroelastic edge is examined with respect to the effects of both elasticity and porosity on the efficiency of aerodynamic noise generation. The edge is modelled as a thin plate poroelastic plate, which is known to admit fifth-, sixth-, and seventh-power noise dependences on a characteristic velocity U of the turbulent eddy. The associated acoustic scattering problem is solved using the Wiener-Hopf technique for the case of constant plate properties. For the special cases of porous-rigid and impermeable-elastic plate conditions, asymptotic analysis of the Wiener- Hopf kernel function furnishes the parameter groups and their ranges where U5, U6, and U7 behaviours are expected to occur. Results from this analysis attempt to help guide the search for passive edge treatments to reduce trailing-edge noise that are inspired by the wing features of silently flying owls. Furthermore, the appropriateness of the present model to the owl noise problem is discussed with respect to the acoustic frequencies of interest, wing chord-lengths, and foraging behaviour across a representative set of owl species.

Models for acoustic propagation through turbofan exhaust flows

Turbomachinery noise radiating into the rearward arc is an important problem. This noise is scattered by the trailing edges of the nacelle and the jet exhaust, and interacts with the shear layers between the external flow, bypass stream and jet, en route to the far field. In the past a range of relevant model problems involving semi-infinite cylinders have been solved. However, one limitation of previous solutions is that they do not allow for the jet nozzle to protrude a finite distance beyond the end of the nacelle (or in certain configurations being buried a finite distance upstream). In this paper we use the matrix Wiener-Hopf technique, which will allow precisely the finite nacelle-jet nozzle separation to be included. The crucial step in our work is to factorise a certain matrix as a product of terms analytic and invertible in the upper/lower halves of the complex plane. The way we do this matrix factorisation is quite different in the buried and protruding nozzle cases. In the buried case our solution method is the so-called pole-removal technique. In the technically more demanding protruding case, however, we must first use Pade approximants to generate a uniformly-valid, meromorphic representation of a certain function, before the same pole-removal method can be applied. Sample results are presented, investigating in particular the effects of exit plane stagger. © 2007 by B Veitch and N Peake.

An analytical model for guided wave inspection optimization for prismatic structures of any cross section.

This paper presents an analytical modeling technique for the simulation of long-range ultrasonic guided waves in structures. The model may be used to predict the displacement field in a prismatic structure arising from any excitation arrangement and may therefore be used as a tool to design new inspection systems. It is computationally efficient and relatively simple to implement, yet gives accuracy similar to finite element analysis and semi-analytical finite element analysis methods. The model has many potential applications; one example is the optimization of part-circumferential arrays where access to the full circumference of the pipe is restricted. The model has been successfully validated by comparison with finite element solutions. Experimental validation has also been carried out using an array of piezoelectric transducer elements to measure the displacement field arising from a single transducer element in an 88.9-mm-diameter pipe. Good agreement has been obtained between the two models and the experimental data.