Travelling and standing envelope solitons in discrete non-linear cyclic structures

International audienceEnvelope solitons are demonstrated to exist in non-linear discrete structures with cyclic symmetry. The analysis is based on the Non-Linear Schrodinger Equation for the weakly non-linear limit, and on numerical simulation of the fully non-linear equations for larger amplitudes. Envelope solitons exist for parameters in which the wave equation is focussing and they have the form of shape-conserving wave packages propagating roughly with group velocity. For the limit of maximum wave number, where the group velocity vanishes, standing wave packages result and can be linked via a bifurcation to the non-localised non-linear normal modes. Numerical applications are carried out on a simple discrete system with cyclic symmetry which can be seen as a reduced model of a bladed disk as found in turbo-machinery

DIC Measurement of the Kinematics of a Friction Damper for Turbine Applications

International audienceHigh cycle fatigue (HCF) caused by large resonant stresses is a common cause for turbine blades failure. Passive damping systems, such as friction dampers are often used by aero-engine manufacturers to reduce the resonant stresses and mitigate the risk of HCF. The presence of friction dampers makes the dynamics of the system highly nonlinear, due to the complex stick-slip and separation phenomena taking place at the contact interface. Due to this nonlinear behaviour, an accurate understanding of the operating deflection shapes is needed for an accurate stress prediction. In this study, digital image correlation (DIC) in combination with a high speed camera is used to provide insights into the kinematics of the damper in a recently developed test rig. The in-phase and out-of-phase first bending modes of the blades were investigated leading to a full field measurement of the global ODS of the blades, and the local motion of the damper against its platforms. A significant change in the blades operational deflection shape could be observed due to the damper, and the sliding and rolling motion of the damper during a vibration cycle was accurately visualised

Comparison of contact parameters measured with two different friction rigs for nonlinear dynamic analysis

The accurate measurement of contact interface parameters is of great importance for nonlinear dynamic response computations since there is a lack of predictive capabilities for such input parameters. Several test rigs have been developed at different institutions, and a series of measurements published, but their reliability remains unknown due to a lack of direct comparisons. To somehow address this issue, a Round-Robin test campaign was performed including the high frequency friction rigs of Imperial College London and Politecnico di Torino. Comparable hysteresis loops were recorded on specimen pairs manufactured from the same batch of raw stainless steel, for a wide range of test conditions, including varying normal loads, sliding distances and nominal areas of contact. Measurements from the two rigs were compared to quantify the level of agreement between the two very different experimental setup, showing a reasonably good matching in the results, but also highlighting some differences. Results also demonstrated that loading conditions can strongly affect the contact parameters, and consequently their effect must be included in future nonlinear dynamic simulations for more reliable predictions

High-resolution projections of ambient heat for major European cities using different heat metrics

Heat stress in cities is projected to strongly increase due to climate change. The associated health risks will be exacerbated by the high population density in cities and the urban heat island effect. However, impacts are still uncertain, which is among other factors due to the existence of multiple metrics for quantifying ambient heat and the typically rather coarse spatial resolution of climate models. Here we investigate projections of ambient heat for 36 major European cities based on a recently produced ensemble of regional climate model simulations for Europe (EURO-CORDEX) at 0.11∘ spatial resolution (∼ 12.5 km). The 0.11∘ EURO-CORDEX ensemble provides the best spatial resolution currently available from an ensemble of climate model projections for the whole of Europe and makes it possible to analyse the risk of temperature extremes and heat waves at the city level. We focus on three temperature-based heat metrics – yearly maximum temperature, number of days with temperatures exceeding 30 ∘C, and Heat Wave Magnitude Index daily (HWMId) – to analyse projections of ambient heat at 3 ∘C warming in Europe compared to 1981–2010 based on climate data from the EURO-CORDEX ensemble. The results show that southern European cities will be particularly affected by high levels of ambient heat, but depending on the considered metric, cities in central, eastern, and northern Europe may also experience substantial increases in ambient heat. In several cities, projections of ambient heat vary considerably across the three heat metrics, indicating that estimates based on a single metric might underestimate the potential for adverse health effects due to heat stress. Nighttime ambient heat, quantified based on daily minimum temperatures, shows similar spatial patterns to daytime conditions, albeit with substantially higher HWMId values. The identified spatial patterns of ambient heat are generally consistent with results from global Earth system models, though with substantial differences for individual cities. Our results emphasise the value of high-resolution climate model simulations for analysing climate extremes at the city level. At the same time, they highlight that improving the predominantly rather simple representations of urban areas in climate models would make their simulations even more valuable for planning adaptation measures in cities. Further, our results stress that using complementary metrics for projections of ambient heat gives important insights into the risk of future heat stress that might otherwise be missed.</p

Analysis of blade-tip casing interaction using harmonic balance method

This paper presents an application of the harmonic balance method for modelling the blade-tip casing interaction. A new nonlinear element has been implemented in the in-house code FORSE in order to take into account the contact with friction that can occur when blade tip touches the abradable coating of the casing. This approach permits to efficiently calculate the frequency response of the blade excited by the contact of the casing. Numerical results presented in this paper agree with other observations proposed in the literature both numerical and experimental

Ultrasonic monitoring of friction contacts during shear vibration cycles

Complex high-value jointed structures such as aero-engines are carefully designed and optimized to prevent failure and maximise their life. In the design process, physically-based numerical models are employed to predict the nonlinear dynamic response of the structure. However, the reliability of these models is limited due to the lack of accurate validation data from metallic contact interfaces subjected to high-frequency vibration cycles. In this study, ultrasonic shear waves are used to characterise metallic contact interfaces during vibration cycles, hence providing new validation data for an understanding of the state of the friction contact. Supported by numerical simulations of wave propagation within the material, a novel experimental method is developed to simultaneously acquire ultrasonic measurements and friction hysteresis loops within the same test on a high-frequency friction rig. Large variability in the ultrasound reflection/transmission is observed within each hysteresis loop and is associated with stick/slip transitions. The measurement results reveal that the ultrasound technique can be used to detect stick and slip states in contact interfaces subjected to high-frequency shear vibration. This is the first observation of this type and paves the way towards real-time monitoring of vibrating contact interfaces in jointed structures, leading to a new physical understanding of the contact states and new validation data needed for improved nonlinear dynamic analyses

Nonlinear dynamics of turbine bladed disk with friction dampers: Experiment and simulation

Accurately predicting the nonlinear dynamic response of aero-engine components is critical, as excessive vibration amplitudes can considerably reduce the operational lifespan. This paper compares experimental and numerical nonlinear dynamic responses of an industrial aero-engine, specifically focusing on the first stage turbine bladed disk with under-platform dampers (UPDs). The friction forces between UPDs and blades result in a strongly nonlinear dynamic response, influenced by stick, slip and separation contact states at the interfaces. These contact states, and the resulting global dynamic responses, are predicted with an advanced industrial modelling approach for nonlinear dynamics. The predictions are compared, updated and validated against measurement data from an operational engine test. Results highlight the importance to validate models against industrial data and show that realistic contact pressure distributions are required for increased prediction reliability. The novelty of this work includes (1) the use of unique industrial experimental data from a fully operational aero-engine, (2) the observation, at the end of engine testing, of real contact conditions in blade/UPD interfaces, (3) detailed modelling of these contact conditions with high-fidelity finite element representations in nonlinear dynamic solvers. Based on this unique industrial validation work, guidelines are proposed to improve the state-of-the-art modelling of nonlinear dynamics in structures with friction contacts

Solitons in non-linear cyclic system

In this paper we consider the case of a non-linear structure with cyclic symmetry which can be seen as approximation for bladed disk type structures. Using the multiple scale method, we show that soliton solutions are possible within such structure. The theoretical developments are illustrated with numerical simulations on a simple system with cubic non-linearities

A theoretical approach to assess soil moisture–climate coupling across CMIP5 and GLACE-CMIP5 experiments

Terrestrial climate is influenced by various land–atmosphere interactions that involve numerous land surface state variables. In several regions on Earth, soil moisture plays an important role for climate via its control on the partitioning of net radiation into sensible and latent heat fluxes; consequently, soil moisture also impacts on temperature and precipitation. The Global Land–Atmosphere Coupling Experiment–Coupled Model Intercomparison Project phase 5 (GLACE-CMIP5) aims to quantify the impact of soil moisture on these important climate variables and to trace the individual coupling mechanisms. GLACE-CMIP5 provides experiments with different soil moisture prescriptions that can be used to isolate the effect of soil moisture on climate. Using a theoretical framework that relies on the distinct relation of soil moisture with evaporative fraction (the ratio of latent heat flux over net radiation) in different soil moisture regimes, the climate impact of the soil moisture prescriptions in the GLACE-CMIP5 experiments can be emulated and quantified. The framework-based estimation of the soil moisture effect on the evaporative fraction agrees very well with estimations obtained directly from the GLACE-CMIP5 experiments (pattern correlation of 0.85). Moreover, the soil moisture effect on the daily maximum temperature is well captured in regions where soil moisture exerts a strong control on latent heat fluxes. The theoretical approach is further applied to quantify the soil moisture contribution to the projected change of the temperature on the hottest day of the year, confirming recent estimations by other studies. Finally, GLACE-style soil moisture prescriptions are emulated in an extended set of CMIP5 models. The results indicate consistency between the soil moisture–climate coupling strength estimated with the GLACE-CMIP5 and the CMIP5 models. Although the theoretical approach is only designed to capture the local soil moisture–climate coupling strength, it can also help to distinguish non-local from local soil moisture–atmosphere feedbacks where sensitivity experiments (such as GLACE-CMIP5) are available. Overall, the theoretical framework-based approach presented here constitutes a simple and powerful tool to quantify local soil moisture–climate coupling in both the GLACE-CMIP5 and CMIP5 models that can be applied in the absence of dedicated sensitivity experiments.</p

The impact of fretting wear on structural dynamics: Experiment and simulation

This paper investigates the effects of fretting wear on frictional contacts. A high frequency friction rig is used to measure the evolution of hysteresis loops, friction coefficient and tangential contact stiffness over time. This evolution of the contact parameters is linked to significant changes in natural frequencies and damping of the rig. Hysteresis loops are replicated by using a Bouc-Wen modified formulation, which includes wear to simulate the evolution of contact parameters and to model the evolving dynamic behaviour of the rig. A comparison of the measured and predicted dynamic behaviour demonstrates the feasibility of the proposed approach and highlights the need to consider wear to accurately capture the dynamic response of a system with frictional joints over its lifetime