Decoupled three-dimensional finite element computation of thermoelastic damping using Zener's approximation

We consider three dimensional finite element computations of thermoelastic damping ratios of arbitrary bodies using Zener's approach. In our small-damping formulation, unlike existing fully coupled formulations, the calculation is split into three smaller parts. Of these, the first sub-calculation involves routine undamped modal analysis using ANSYS. The second sub-calculation takes the mode shape, and solves on the same mesh a periodic heat conduction problem. Finally, the damping coefficient is a volume integral, evaluated elementwise. In the only other decoupled three dimensional computation of thermoelastic damping reported in the literature, the heat conduction problem is solved much less efficiently, using a modal expansion. We provide numerical examples using some beam-like geometries, for which Zener's and similar formulas are valid. Among these we examine tapered beams, including the limiting case of a sharp tip. The latter's higher-mode damping ratios dramatically exceed those of a comparable uniform beam.

Automatic identification of modal damping from Floquet analysis

A practical method is proposed to identify the mode associated with the frequency part of the eigenvalue of the Floquet transition matrix (FTM). From the FTM eigenvector, which contains the states and their derivatives, the ratio of the derivative and the state corresponding to the largest component is computed. The method exploits the fact that the imaginary part of this (complex) ratio closely approximates the frequency of the mode. It also lends itself well to automation and has been tested over a large number of FTMs of order as high as 250.

Analysis of shear bands in slow granular flows using a frictional Cosserat model

The slow flow of granular materials is often marked by the existence of narrow shear layers, adjacent to large regions that suffer little or no deformation. This behaviour, in the regime where shear stress is generated primarily by the frictional interactions between grains, has so far eluded theoretical description. In this paper, we present a rigid-plastic frictional Cosserat model that captures thin shear layers by incorporating a microscopic length scale. We treat the granular medium as a Cosserat continuum, which allows the existence of localised couple stresses and, therefore, the possibility of an asymmetric stress tensor. In addition, the local rotation is an independent field variable and is not necessarily equal to the vorticity. The angular momentum balance, which is implicitly satisfied for a classical continuum, must now be solved in conjunction with the linear momentum balances. We extend the critical state model, used in soil plasticity, for a Cosserat continuum and obtain predictions for flow in plane and cylindrical Couette devices. The velocity profile predicted by our model is in qualitative agreement with available experimental data. In addition, our model can predict scaling laws for the shear layer thickness as a function of the Couette gap, which must be verified in future experiments. Most significantly, our model can determine the velocity field in viscometric flows, which classical plasticity-based model cannot.

A note on the damping and oscillations of a fluid drop moving in another fluid

The oscillations of a drop moving in another fluid medium have been studied at low values of Reynolds number and Weber number by taking into consideration the shape of the drop and the viscosities of the two phases in addition to the interfacial tension. The deformation of the drop modifies the Lamb's expression for frequency by including a correction term while the viscous effects split the frequency into a pair of frequencies—one lower and the other higher than Lamb's. The lower frequency mode has ample experimental support while the higher frequency mode has also been observed. The two modes almost merge with Lamb's frequency for the asymptotic cases of a drop in free space or a bubble in a dense viscous fluid but the splitting becomes large when the two fluids have similar properties. Instead of oscillations, aperiodic damping modes are found to occur in drops with sizes smaller than a critical size ($\sim\hat{\rho}\hat{\nu}^2/T $). With the help of these calculations, many of the available experimental results are analyzed and discussed.

Defining the ‘modified Griffin plot’ in vortex-induced vibration: revealing the effect of Reynolds number using controlled damping

In the present work, we study the transverse vortex-induced vibrations of an elastically mounted rigid cylinder in a fluid flow. We employ a technique to accurately control the structural damping, enabling the system to take on both negative and positive damping. This permits a systematic study of the effects of system mass and damping on the peak vibration response. Previous experiments over the last 30 years indicate a large scatter in peak-amplitude data ($A^*$) versus the product of mass–damping ($\alpha$), in the so-called ‘Griffin plot’. A principal result in the present work is the discovery that the data collapse very well if one takes into account the effect of Reynolds number ($\mbox{\textit{Re}}$), as an extra parameter in a modified Griffin plot. Peak amplitudes corresponding to zero damping ($A^*_{{\alpha}{=}0}$), for a compilation of experiments over a wide range of $\mbox{\textit{Re}}\,{=}\,500-33000$, are very well represented by the functional form $A^*_{\alpha{=}0} \,{=}\, f(\mbox{\textit{Re}}) \,{=}\, \log(0.41\,\mbox{\textit{Re}}^{0.36}$). For a given $\mbox{\textit{Re}}$, the amplitude $A^*$ appears to be proportional to a function of mass–damping, $A^*\propto g(\alpha)$, which is a similar function over all $\mbox{\textit{Re}}$. A good best-fit for a wide range of mass–damping and Reynolds number is thus given by the following simple expression, where $A^*\,{=}\, g(\alpha)\,f(\mbox{\textit{Re}})$: \[ A^* \,{=}\,(1 - 1.12\,\alpha + 0.30\,\alpha^2)\,\log (0.41\,\mbox{\textit{Re}}^{0.36}). \] In essence, by using a renormalized parameter, which we define as the ‘modified amplitude’, $A^*_M\,{=}\,A^*/A^*_{\alpha{=}0}$, the previously scattered data collapse very well onto a single curve, $g(\alpha)$, on what we refer to as the ‘modified Griffin plot’. There has also been much debate over the last three decades concerning the validity of using the product of mass and damping (such as $\alpha$) in these problems. Our results indicate that the combined mass–damping parameter ($\alpha$) does indeed collapse peak-amplitude data well, at a given $\mbox{\textit{Re}}$, independent of the precise mass and damping values, for mass ratios down to $m^*\,{=}\,1$.

Synchronizing and Damping Torques Analysis of Nonlinear Voltage Regulators

This paper makes an attempt to assess the benefits of replacing a conventional generator excitation system (AVR + PSS) with a nonlinear voltage regulator using the concepts of synchronizing and damping torque components in a single machine infinite bus (SMIB) system. In recent years, there has been considerable interest in designing nonlinear excitation controllers, which are expected to give better dynamic performance over a wider range of system and operating conditions. The performance of these controllers is often justified by simulation studies on few test cases which may not adequately represent the diverse operating conditions of a typical power system. The performance of two such nonlinear controllers which are designed based on feedback linearization and include automatic voltage regulation with good dynamic performance have been analyzed using an SMIB model. Linearizing the nonlinear control laws along with the SMIB system equations, a Heffron Phillip's type of a model has been derived. Concepts of synchronizing and damping torque components have been used to show that such controllers can impair the small signal stability under certain operating conditions. This paper shows the possibility of negative damping contribution due to nonlinear voltage regulators and gives a new insight on understanding the physical impact of complex nonlinear control laws on power system dynamics.

Damping and synchronising torques contributed by a voltage regulator to a synchronous generator: a quantitative assessment

In the paper, the total damping and synchronising torques, which determine the dynamic stability of a synchronous generator in a power system, have been traced to their origin. The positive and negative components released or consumed by the voltage regulator, and by the various windings of the machine, have been isolated, with the object of making a quantitative assessment of the effects of various gains and time constants on the dynamic stability of a synchronous machine under different operating conditions. The analysis is based on the properties of quadratic invariance in tensor calculus. An alternative solution by network analysis has also been provided to establish the validity of the tensor approach.

Fuzzy logic based TCSC supplementary controller for damping of inter area oscillations in power system

This paper describes an application of a FACTS supplementary controller for damping of inter area oscillations in power systems. A fuzzy logic controller is designed to regulate a thyristor controlled series capacitor (TCSC) in a multimachine environment to produce additional damping in the system. Simultaneous application of the excitation controller and proposed controller is also investigated. Simulation studies have been done with different types of disturbances and the results are shown to be consistent with the expected performance of the supplementary controller.

Neural network based power system damping controller for SVC

The development of a neural network based power system damping controller (PSDC) for a static VAr compensator (SVC), designed to enhance the damping characteristics of a power system network representing a part of the Electricity Generating Authority of Thailand (EGAT) system is presented. The proposed stabilising controller scheme of the SVC consists of a neuro-identifier and a neuro-controller which have been developed based on a functional link network (FLN) model. A recursive online training algorithm has been utilised to train the two networks. The simulation results have been obtained under various operating conditions and disturbance cases to show that the proposed stabilising controller can provide a better damping to the low frequency oscillations, as compared to the conventional controllers. The effectiveness of the proposed stabilising controller has also been compared with a conventional power system stabiliser provided in the generator excitation system

Neural network based power system damping controller for SVC

The development of a neural network based power system damping controller (PSDC) for a static Var compensator (SVC), designed to enhance the damping characteristics of a power system network representing a part of the Electricity Generating Authority of Thailand (EGAT) system is presented. The proposed stabilising controller scheme of the SVC consists of a neuro-identifier and a neuro-controller which have been developed based on a functional link network (FLN) model. A recursive online training algorithm has been utilised to train the two networks. The simulation results have been obtained under various operating conditions and disturbance cases to show that the proposed stabilising controller can provide a better damping to the low frequency oscillations, as compared to the conventional controllers. The effectiveness of the proposed stabilising controller has also been compared with a conventional power system stabiliser provided in the generator excitation system.