A unified friction description and its application to the simulation of frictional instability using the finite element method

This article first summarizes some available experimental results on the frictional behaviour of contact interfaces, and briefly recalls typical frictional experiments and relationships, which are applicable for rock mechanics, and then a unified description is obtained to describe the entire frictional behaviour. It is formulated based on the experimental results and applied with a stick and slip decomposition algorithm to describe the stick-slip instability phenomena, which can describe the effects observed in rock experiments without using the so-called state variable, thus avoiding related numerical difficulties. This has been implemented to our finite element code, which uses the node-to-point contact element strategy proposed by the authors to handle the frictional contact between multiple finite-deformation bodies with stick and finite frictional slip, and applied here to simulate the frictional behaviour of rocks to show its usefulness and efficiency.

Damping in zinc-based alloys

The damping behaviour of the cold chamber pressure-die-casting alloy: M3, ZA8, ZA27, ZM11, Cosmal, Supercosmal and newly developed ZA27H1 and ZA27H2 was investigated at room temperature and elevated temperatures of up to 90 degrees C. The damping properties of the alloys were established at all temperatures. Formulas were established to predict damping properties of each alloy at any given temperature. The prediction formulae were found to be very accurate. All of the experimental alloys were heterogenous with varying microstructure and grain size; this was the major contribution and dominated the damping properties of the alloys. Super cosmal and ZA27 possessed the highest tensile strength but ZA27H1, ZA27H2 and ZM11 showed the highest damping properties. The relationship between microstructure and damping capacity of all alloys was also examined using back-scattered electron on the SEM. Further more detailed examinations of the microstructures of alloys ZM11, Cosmal and Supercosmal were carried out on the transmission electron microscope in order to establish the phases present in all alloys. These helped to obtain the mechanism of damping in the experimental alloys. The main damping mechanism in most of the experimental alloys was due to grain-boundary-sliding. Micro structural examinations also revealed the absence of -phase in the Cosmal and Supercosmal. This was thought to be due to a change in solid solubility of the alloys, which could have been caused by the addition of Si.

Anomalies in stiffness and damping of a 2D discrete viscoelastic system due to negative stiffness components

The recent development of using negative stiffness inclusions to achieve extreme overall stiffness and mechanical damping of composite materials reveals a new avenue for constructing high performance materials. One of the negative stiffness sources can be obtained from phase transforming materials in the vicinity of their phase transition, as suggested by the Landau theory. To understand the underlying mechanism from a microscopic viewpoint, we theoretically analyze a 2D, nested triangular lattice cell with pre-chosen elements containing negative stiffness to demonstrate anomalies in overall stiffness and damping. Combining with current knowledge from continuum models, based on the composite theory, such as the Voigt, Reuss, and Hashin-Shtrikman model, we further explore the stability of the system with Lyapunov's indirect stability theorem. The evolution of the microstructure in terms of the discrete system is discussed. A potential application of the results presented here is to develop special thin films with unusual in-plane mechanical properties. © 2006 Elsevier B.V. All rights reserved.

Oscillation Theorems for Perturbed Second Order Nonlinear Differential Equations with Damping

Some oscillation criteria for solutions of a general perturbed second order ordinary differential equation with damping (r(t)x′ (t))′ + h(t)f (x)x′ (t) + ψ(t, x) = H(t, x(t), x′ (t)) with alternating coefficients are given. The results obtained improve and extend some existing results in the literature.

Analysis and improvement of performance in LCL filter-based PWM rectifier/inverter application using hybrid damping approach

A hybrid passive-active damping solution with improved system stability margin and enhanced dynamic performance is proposed for high power grid interactive converters. In grid connected active rectifier/inverter application, line side LCL filter improves the high frequency attenuation and makes the converter compatible with the stringent grid power quality regulations. Passive damping though offers a simple and reliable solution but it reduces overall converter efficiency. Active damping solutions do not increase the system losses but can guarantee the stable operation up to a certain speed of dynamic response which is limited by the maximum bandwidth of the current controller. This paper examines this limit and introduces a concept of hybrid passive-active damping solution with improved stability margin and high dynamic performance for line side LCL filter based active rectifier/inverter applications. A detailed design, analysis of the hybrid approach and trade-off between system losses and dynamic performance in grid connected applications are reported. Simulation and experimental results from a 10 kVA prototype demonstrate the effectiveness of the proposed solution. An analytical study on system stability and dynamic response with the variations of various controller and passive filter parameters is presented.

Oscillation Criteria for Nonlinear Differential Equations of Second Order with Damping Term

2000 Mathematics Subject Classification: 34C10, 34C15.

Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term

2000 Mathematics Subject Classification: 34C10, 34C15.

Distributed Power balance and damping control for high power multiport LCL DC hub

This project is funded by European Research Council in FP7; grant no 259328, 2010 and EPSRC grant no EP/K006428/1, 2013.