Transmission problem for waves with frictional damping April 22, 2007

In this paper we consider the transmission problem, in one space dimension, for linear dissipative waves with frictional damping. We study the wave propagation in a medium with a component with attrition and another simply elastic. We show that for this type of material, the dissipation produced by the frictional part is strong enough to produce exponential decay of the solution, no matter how small is its size. ©2007 Texas State University.

A transmission problem for the Timoshenko system

In this work we study a transmission problem for the model of beams developed by S.P. Timoshenko [10]. We consider the case of mixed material, that is, a part of the beam has friction and the other is purely elastic. We show that for this type of material, the dissipation produced by the frictional part is strong enough to produce exponential decay of the solution, no matter how small is its size. We use the method of energy to prove exponential decay for the solution.

The study and measurements of the behaviour and characteristics of electromagnetic relays

The thesis presents a theoretical and practical study of the dynamic behaviour of electromagnetic relays. After discussing the problem of solving the dynamicc equations analytically and presenting a historical survey of the earlier works in the relay and its dynamics, the simulation of a relay on the analogue computer is discussed. It is shown that the simulation may be used to obtain specific solutions to the dynamic equations. The computer analysis provides the dynamic characteristics for design purposes and may be used in the study of bouncing, rebound oscillations and stability of the armature motion. An approximate analytical solution to the two dynamic equations is given based on the assumption that the dynamic variation of the pull with the position of the armature is linear. The assumption is supported by the Computer-aided analysis and experimental results. The solution is intended to provide a basis for a rational design. A rigorous method of analysing the dynamic performance by using Ahlberg's theory is also presented. This method may be justified to be the extension of Ahlberg's theory by taking the mass and frictional damping forces into account. While calculating the armature motion mathematically, Ahlberg considers the equilibrium of two kinds of forces, namely pull and load, and disregards the mass and friction forces, whereas the present method deals with the equilibrium of all four kinds of forces. It is shown how this can be utilised to calculate the dynamic characteristics for a specific design. The utility of this method also extends to the study of stability, contact bounce and armature rebound. The magnetic circuit and other related topics which are essential to the study of relay dynamics are discussed and some necessary experimental results are given.

Application of fibre assemblies as damping elements in the automotive industry

This investigation aims to characterise the damping properties of the nonwoven materials with potential applications in automotive and aerospace industry. Nonwovens are a popular choice for many applications due to their relatively low manufacturing cost and unique properties. It is known that nonwovens are efficient energy dispersers for certain applications such as acoustic damping and ballistic impact. It is anticipated that these energy absorption properties could eventually be used to provide damping for mechanical vibrations. However the behaviour of nonwovens under dynamic load and vibration has not been investigated before. Therefore we intend to highlight these aspects of the behaviour of the nonwovens through this research. In order to obtain an insight to the energy absorption properties of the nonwoven fabrics, a range of tests has been performed. Forced vibration of the cantilever beam is used to explore damping over a range of resonance modes and input amplitudes. The tests are conducted on aramid, glass fibre and polyester fabrics with a range of area densities and various coatings. The tests clarified the general dynamic behaviour of the fabrics tested and the possible response in more real application condition as well. The energy absorption in both thickness and plane of the fabric is tested. The effects of the area density on the results are identified. The main absorption mechanism is known to be the friction. The frictional properties are improved by using a smaller fibre denier and increasing fibre length, this is a result of increasing contact surface between fibres. It is expected the increased friction result in improving damping. The results indicate different mechanism of damping for fiber glass fabrics compared to the aramid fabrics. The frequency of maximum efficiency of damping is identified for the fabrics tested. These can be used to recommend potential applications.

A simplified Fermi Accelerator Model under quadratic frictional force

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)