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.

Friction-induced vibration: Model development and comparison with large-scale experimental tests

This paper presents a comparison between theoretical predictions and experimental results from a pin-on-disc test rig exploring friction-induced vibration. The model is based on a linear stability analysis of two systems coupled by sliding contact at a single point. Predictions are compared with a large volume of measured squeal initiations that have been post-processed to extract growth rates and frequencies at the onset of squeal. Initial tests reveal the importance of including both finite contact stiffness and a velocity-dependent dynamic model for friction, giving predictions that accounted for nearly all major clusters of squeal initiations from 0 to 5 kHz. However, a large number of initiations occurred at disc mode frequencies that were not predicted with the same parameters. These frequencies proved remarkably difficult to destabilise, requiring an implausibly high coefficient of friction. An attempt has been made to estimate the dynamic friction behaviour directly from the squeal initiation data, revealing complex-valued frequency-dependent parameters for a new model of linearised dynamic friction. These new parameters readily destabilised the disc modes and provided a consistent model that could account for virtually all initiations from 0 to 15 kHz. The results suggest that instability thresholds for a wide range of squeal-type behaviour can be predicted, but they highlight the central importance of a correct understanding and accurate description of dynamic friction at the sliding interface. © 2013 Elsevier Ltd. All rights reserved.

Transient response of structures with uncertain properties to nonlinear shock loading

A method is presented to predict the transient response of a structure at the driving point following an impact or a shock loading. The displacement and the contact force are calculated solving the discrete convolution between the impulse response and the contact force itself, expressed in terms of a nonlinear Hertzian contact stiffness. Application of random point process theory allows the calculation of the impulse response function from knowledge of the modal density and the geometric characteristics of the structure only. The theory is applied to a wide range of structures and results are experimentally verified for the case of a rigid object hitting a beam, a plate, a thin and a thick cylinder and for the impact between two cylinders. The modal density of the flexural modes for a thick slender cylinder is derived analytically. Good agreement is found between experimental, simulated and published results, showing the reliability of the method for a wide range of situations including impacts and pyroshock applications. © 2013 Elsevier Ltd. All rights reserved.

Sound radiation from point-driven shell structures

A numerical study is presented showing the structural response and sound radiation from a range of thin shell structures excited by a point force: a baffled flat plate, a sphere, a family of spheroids and a family of closed circular cylinders. All the structures have the same material properties, thickness and total surface area so the asymptotic modal density is the same. Dramatic differences are shown in the total radiated sound power for the different shells. It was already known that the flat plate and the sphere behave very differently. These results show that the cylinders and, particularly, the spheroids show patterns that are not intermediate between the two but instead display new features: in certain frequency ranges the radiated sound power can be at least an order of magnitude greater than either the plate or the sphere. © 2013 Elsevier Ltd.

Digital elevation models and GIS for watershed modelling and flood prediction-A case study of Accra Ghana

Geographical Information Systems (GIS) and Digital Elevation Models (DEM) can be used to perform many geospatial and hydrological modelling including drainage and watershed delineation, flood prediction and physical development studies of urban and rural settlements. This paper explores the use of contour data and planimetric features extracted from topographic maps to derive digital elevation models (DEMs) for watershed delineation and flood impact analysis (for emergency preparedness) of part of Accra, Ghana in a GIS environment. In the study two categories of DEMs were developed with 5 m contour and planimetric topographic data; bare earth DEM and built environment DEM. These derived DEMs were used as terrain inputs for performing spatial analysis and obtaining derivative products. The generated DEMs were used to delineate drainage patterns and watershed of the study area using ArcGIS desktop and its ArcHydro extension tool from Environmental Systems Research Institute (ESRI). A vector-based approach was used to derive inundation areas at various flood levels. The DEM of built-up areas was used as inputs for determining properties which will be inundated in a flood event and subsequently generating flood inundation maps. The resulting inundation maps show that about 80% areas which have perennially experienced extensive flooding in the city falls within the predicted flood extent. This approach can therefore provide a simplified means of predicting the extent of inundation during flood events for emergency action especially in less developed economies where sophisticated technologies and expertise are hard to come by. © 2009 Springer Netherlands.

Digital Elevation Models and GIS for watershed modelling and flood prediction - A case study of Accra Ghana

Geographical Information Systems (GIS) and Digital Elevation Models (DEM) can be used to perform many geospatial and hydrological modelling including drainage and watershed delineation, flood prediction and physical development studies of urban and rural settlements. This paper explores the use of contour data and planimetric features extracted from topographic maps to derive digital elevation models (DEMs) for watershed delineation and flood impact analysis (for emergency preparedness) of part of Accra, Ghana in a GIS environment. In the study two categories of DEMs were developed with 5 m contour and planimetric topographic data; bare earth DEM and built environment DEM. These derived DEMs were used as terrain inputs for performing spatial analysis and obtaining derivative products. The generated DEMs were used to delineate drainage patterns and watershed of the study area using ArcGIS desktop and its ArcHydro extension tool from Environmental Systems Research Institute (ESRI). A vector-based approach was used to derive inundation areas at various flood levels. The DEM of built-up areas was used as inputs for determining properties which will be inundated in a flood event and subsequently generating flood inundation maps. The resulting inundation maps show that about 80% areas which have perennially experienced extensive flooding in the city falls within the predicted flood extent. This approach can therefore provide a simplified means of predicting the extent of inundation during flood events for emergency action especially in less developed economies where sophisticated technologies and expertise are hard to come by. © Springer Science + Business Media B.V. 2009.