The Influence of Structural Modeshape Variability on Limit Cycle Oscillation Behaviour

Modal analysis is a popular approach used in structural dynamic and aeroelastic problems due to its efficiency. The response of a structure is compo
sed of the sum of orthogonal eigenvectors or modeshapes and corresponding modal frequencies. This paper investigates the importance of modeshapes on the aeroelastic response of the Goland wing subject to structural uncertainties. The wing undergoes limit cycle oscillations (LCO) as a result of the inclusion of polynomial stiffness nonlinearities. The LCO computations are performed using a Harmonic Balance approach for speed, the modal properties of the system are extracted from MSC NASTRAN. Variability in both the wing’s structure and the store centre of gravity location is investigated in two cases:- supercritical and subcritical type LCOs. Results show that the LCO behaviour is only sensitive to change in modeshapes when the nature of the modes are changing significantly.

Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

Universal behaviour of shock precursors in the presence of efficient cosmic ray acceleration

The self-consistent interaction between energetic particles and self-generated hydromagnetic waves in a cosmic ray pressure dominated plasma is considered. Using a three-dimensional hybrid magnetohydrodynamics (MHD)-kinetic code, which utilizes a spherical harmonic expansion of the Vlasov-Fokker-Planck equation, high-resolution simulations of the magnetic field growth including feedback on the cosmic rays are carried out. It is found that for shocks with high cosmic ray acceleration efficiency, the magnetic fields become highly disorganized, resulting in near isotropic diffusion, independent of the initial orientation of the ambient magnetic field. The possibility of sub-Bohm diffusion is demonstrated for parallel shocks, while the diffusion coefficient approaches the Bohm limit from below for oblique shocks. This universal behaviour suggests that Bohm diffusion in the root-mean-squared field inferred from observation may provide a realistic estimate for the maximum energy acceleration time-scale in young supernova remnants. Although disordered, the magnetic field is not self-similar suggesting a non-uniform energy-dependent behaviour of the energetic particle transport in the precursor. Possible indirect radiative signatures of cosmic ray driven magnetic field amplification are discussed.

Biomechanics of Vertebroplasty: Effect of Cement Viscosity on Mechanical Behaviour

Vertebroplasty is a minimally invasive surgical procedure, which requires efficacious percutaneous cement delivery via a cannulated needle to restore the strength and stiffness in osteoporotic vertebral bodies. Cement viscosity is understood to influence the injectability, cohesion and cement retention within the vertebral body. Altering the liquid to powder ratio modifies the viscosity of bone cement; however, the cement viscosity-response association between cement fill and augmentation of strength and stiffness is unknown. The aim of this study was to determine the relationship between viscosity, cement fill and the potential augmentation of strength and stiffness in an open pore foam structure that was representative of osteoporotic cancellous bone using an in vitro prophylactic vertebroplasty model. The results showed a strong linear correlation between compressive strength and stiffness augmentation with percentage cement fill, the extent of which was strongly dependent on the cement viscosity. Significant forces were required to ensure maximum delivery of the high viscosity cement using a proprietary screw-driven cement delivery technology. These forces could potentially exceed the normal human physical limit. Similar trends were observed when comparing the results from this study and previously reported cadaveric and animal based in vitro models.

Analysis of Transonic Limit Cycle Oscillations under Uncertainty

For the computation of limit cycle oscillations (LCO) at transonic speeds, CFD is required to capture the nonlinear flow features present. The Harmonic Balance method provides an effective means for the computation of LCOs and this paper exploits its efficiency to investigate the impact of variability (both structural a nd aerodynamic) on the aeroelastic behaviour of a 2 dof aerofoil. A Harmonic Balance inviscid CFD solver is coupled with the structural equations and is validated against time marching analyses. Polynomial chaos expansions are employed for the stochastic investiga tion as a faster alternative to Monte Carlo analysis. Adaptive sampling is employed when discontinuities are present. Uncertainties in aerodynamic parameters are looked at first followed by the inclusion of structural variability. Results show the nonlinear effect of Mach number and it’s interaction with the structural parameters on supercritical LCOs. The bifurcation boundaries are well captured by the polynomial chaos.

Investigation of Limit Cycle Oscillations Using Aeroelastic-Harmonic Balance Method

This work investigates limit cycle oscillations in the transonic regime. A novel approach to predict Limit Cycle Oscillations using high fidelity analysis is exploited to accelerate calculations. The method used is an Aeroeasltic Harmonic Balance approach, which has been proven to be efficient and able to predict periodic phenomena. The behaviour of limit cycle oscillations is analysed using uncertainty quantification tools based on polynomial chaos expansions. To improve the efficiency of the sampling process for the polynomial-chaos expansions an adaptive sampling procedure is used. These methods are exercised using two problems: a pitch/plunge aerofoil and a delta-wing. Results indicate that Mach n. variability is determinant to the amplitude of the LCO for the 2D test case, whereas for the wing case analysed here, variability in the Mach n. has an almost negligible influence in amplitude variation and the LCO frequency variability has an almost linear relation with Mach number. Further test cases are required to understand the generality of these results.

The role of societal norms in portion size related behaviour in Denmark and on the Island of Ireland

Purpose:
Social norms influence eating behavior, but little is known about their role in portion size-related behavior. This study
explored the role of social eating norms in Denmark (DK) and the Island of Ireland (IOI) in relation to portion size-related
behavior.

Methods:
In a survey DK (n=1063) and IOI (n=1012) respondents rated social eating norms (11 items) and portion size-related behavior
(3 items) on a 7-point scale (1=strongly disagree to 7=strongly agree). The 3 items relate to: 1) anticipating how
much will be eaten at the beginning of a meal, 2) clearing the plate, and 3) clearing the plate even when full. Sociodemographics
and eating attitudes (e.g. cognitive restraint) were measured as background variables

Results:
Two social eating factors were identified: The ‘limit intake’ norm (6 items) and the ‘plate cleaning’ norm (3 items). The
DK participants reported stronger ‘limit intake’ norms and weaker ‘plate cleaning’ norms than IOI. In both countries
females reported stronger ‘limit intake’ norms while males reported stronger ‘plate cleaning’ norms. In DK, age was
positively correlated with both social eating norm factors. The ‘limit intake’ norm had stronger association with anticipating
how much will be eaten at the beginning of a meal, but the ‘plate cleaning’ norm had stronger association with
clearing the plate. Only the ‘plate cleaning’ norm was associated with clearing the plate even when full.

Conclusions:
The social eating norms vary significantly between countries and genders. The ‘limit intake’ and ‘plate cleaning’ norms
play a role in consumers’ reported portion size-related behavior.