Unsteady shock motion on a NACA0012 aerofoil at low reduced frequencies

Using transonic blowdown windtunnel experiments, the 2D unsteady shock motion on a NACA0012 aerofoil is examined at various frequencies typical for helicopter blades in forward flight. The aerofoil is subjected to freestream velocities oscillating periodically between M = 0.66 and M = 0.77. Unsteady pressure traces and schlieren images are analyzed over a range of low reduced frequencies to provide information on shock location and strength throughout the cycle. Unsteady effects were noticeable even at very low reduced frequencies (down to O(0.01). However, through the range of frequencies investigated, and within experimental error, the unsteady shock location showed no discernible lag compared to the quasi-steady behaviour. On the other hand, significant variations were observed in shock strengths with the upstream running part of the cycle (decreasing Mach number) displaying considerably stronger shocks than during the accelerating part of the cycle. It could be shown that this variation in shock strength is primarily caused by the shock motion modifying the relative shock Mach number. As a result is was possible to use the quasi-steady results to predict the unsteady shock behaviour at the frequencies investigated here (below 0(0.1)).

Unsteady shock motion on a NACA0012 aerofoil at low reduced frequencies

Using transonic blowdown windtunnel experiments, the 2D unsteady shock motion on a NACA0012 aerofoil is examined at various frequencies typical for helicopter blades in forward flight. The aerofoil is subjected to freestream velocities oscillating periodically between M = 0.66 and M = 0.77. Unsteady pressure traces and schlieren images are analyzed over a range of low reduced frequencies to provide information on shock location and strength throughout the cycle. Unsteady effects were noticeable even at very low reduced frequencies (down to O(0.01). However, through the range of frequencies investigated, and within experimental error, the unsteady shock location showed no discernible lag compared to the quasi-steady behaviour. On the other hand, significant variations were observed in shock strengths with the upstream running part of the cycle (decreasing Mach number) displaying considerably stronger shocks than during the accelerating part of the cycle. It could be shown that this variation in shock strength is primarily caused by the shock motion modifying the relative shock Mach number. As a result is was possible to use the quasi-steady results to predict the unsteady shock behaviour at the frequencies investigated here (below 0(0.1)).

Dynamic characterisation and longitudinal strength of swaged joints

Swaging is a cold working process involving plastic deformation of the work piece to change its shape. A swaged joint is a connection between two components whereby a swaging tool induces plastic deformation of the components at their junction to effectively bind them together. This is commonly used when welding or other standard joining techniques are not viable. Swaged joints can be found for example, in nuclear fuel assemblies to connect the edges of thin rectangular plates to a supporting structure or frame. The aim of this work is to find a model to describe the vibrational behaviour of a swaged joint and to estimate its strength in resisting a longitudinally applied load. The finite element method and various experimental rigs were used in order to find relationships between the natural frequencies of the plate, the joint stiffness and the force required to shift the plate against the restraining action of the swage connection. It is found that a swaged joint is dynamically equivalent to a simple support with the rotation elastically restrained and a small stiffness is enough to resist an important load. © 2011 Elsevier Ltd. All rights reserved.

Efficient truncation scheme for modeling deepwater mooring lines

This paper is aimed at enabling the confident use of existing model test facilities for ultra deepwater application without having to compromise on the widely accepted range of scales currently used by the floating production industry. Passive line truncation has traditionally been the preferred method of creating an equivalent numerical model at reduced depth; however, these techniques tend to suffer in capturing accurately line dynamic response and so reproducing peak tensions. In an attempt to improve credibility of model test data the proposed truncation procedure sets up the truncated model, based on line dynamic response rather than quasi-static system stiffness. The upper sections of each line are modeled in detail, capturing the wave action zone and all coupling effects with the vessel. These terminate to an approximate analytical model that aims to simulate the remainder of the line. Stages 1 & 2 are used to derive a water depth truncation ratio. Here vibration decay of transverse elastic waves is assessed and it is found that below a certain length criterion, the transverse vibrational characteristics for each line are inertia driven, hence with respect to these motions the truncated model can assume a linear damper whose coefficient depends on the local line properties and vibration frequency. Stage 3 endeavors to match the individual line stiffness between the full depth and truncated models. In deepwater it is likely that taut polyester moorings will be used which are predominantly straight and have high axial stiffness that provides the principal restoring force to static and low frequency vessel motions. Consequently, it means that the natural frequencies of axial vibrations are above the typical wave frequency range allowing for a quasi-static solution. In cases of exceptionally large wave frequency vessel motions, localized curvature at the chain seabed segment and tangential skin drag on the polyester rope can increase dynamic peak tensions considerably. The focus of this paper is to develop an efficient scheme based on analytic formulation, for replicating these forces at the truncation. The paper will close with an example case study of a single mooring under extreme conditions that replicates exactly the static and dynamic characteristics of the full depth line. Copyright © 2012 by the International Society of Offshore and Polar Engineers (ISOPE).

Status of vibrational structure in Ni62

Measurements consisting of γ-ray excitation functions and angular distributions were performed using the (n,n′γ) reaction on Ni62. The excitation function data allowed us to check the consistency of the placement of transitions in the level scheme. From γ-ray angular distributions, the lifetimes of levels up to ~3.8 MeV in excitation energy were extracted with the Doppler-shift attenuation method. The experimentally deduced values of reduced transition probabilities were compared with the predictions of the quadrupole vibrator model and with large-scale shell model calculations in the fp shell configuration space. Two-phonon states were found to exist with some notable deviation from the predictions of the quadrupole vibrator model, but no evidence for the existence of three-phonon states could be established. Z=28 proton core excitations played a major role in understanding the observed structure. © 2011 American Physical Society.

Vibrations of coupled cylindrical-conical shells

The free vibrational characteristics of coupled conical-cylindrical shells is presented. The equations of motion for the cylindrical shell are solved using a wave approach while the equations of motion for the conical shells are solved using a power series solution. The use of both Donnell-Mushtari and Flügge equations of motion are investigated and their limitations are discussed. Results are presented in terms of natural frequencies for different boundary conditions and the purely torsional mode solution is described. The results from the analytical model presented are compared with those obtained from a finite element model solved with Nastran and other data available in literature.

Modelling the vibration of tyre sidewalls

The dynamical behaviour of the sidewall has an important influence on tyre vibration characteristics. Nonetheless, it remains crudely represented in many existing models. The current work considers a geometrically accurate, two-dimensional, sidewall description, with a view to identifying potential shortcomings in the approximate formulations and identifying the physical characteristics that must be accounted for. First, the mean stress state under pressurisation and centrifugal loading is investigated. Finite-Element calculations show that, while the loaded sidewall shape remains close to a toroid, its in-plane tensions differ appreciably from the associated analytical solution. This is largely due to the inability of the anisotropic sidewall material to sustain significant azimuthal stress. An approximate analysis, based on the meridional tension alone, is therefore developed, and shown to yield accurate predictions. In conjunction with a set of formulae for the 'engineering constants' of the sidewall material, the approximate solutions provide a straightforward and efficient means of determining the base state for the vibration analysis. The latter is implemented via a 'waveguide' discretisation of a variational formulation. Its results show that, while the full geometrical description is necessary for a complete and reliable characterisation of the sidewall's vibrational properties, a one-dimensional approximation will often be satisfactory in practice. Meridional thickness variations only become important at higher frequencies (above 500 Hz for the example considered here), and rotational inertia effects appear to be minor at practical vehicle speeds. © 2013 Elsevier Ltd. All rights reserved.