Analytical investigation of squeeze film dampers

Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Starting from linear Reynolds equation which governs the fluid behavior coupled with structure domain which is modeled by Kirchhoff plate equation, the effects of nondimensional parameters on the damped natural frequencies are presented using boundary characteristic orthogonal functions. For this purpose, the nondimensional coupled partial differential equations are obtained using Rayleigh-Ritz method and the weak formulation, are solved using polynomial and sinusoidal boundary characteristic orthogonal functions for structure and fluid domain respectively. In order to implement present approach to the complex geometries, a two dimensional isoparametric coupled finite element is developed based on Reissner-Mindlin plate theory and linearized Reynolds equation. The coupling between fluid and structure is handled by considering the pressure forces and structural surface velocities on the boundaries. The effects of the driving parameters on the frequency response functions are investigated. As the next logical step, an analytical method for solution of squeeze film damping based upon Green’s function to the nonlinear Reynolds equation considering elastic plate is studied. This allows calculating modal damping and stiffness force rapidly for various boundary conditions. The nonlinear Reynolds equation is divided into multiple linear non-homogeneous Helmholtz equations, which then can be solvable using the presented approach. Approximate mode shapes of a rectangular elastic plate are used, enabling calculation of damping ratio and frequency shift as well as complex resistant pressure. Moreover, the theoretical results are correlated and compared with experimental results both in the literature and in-house experimental procedures including comparison against viscoelastic dampers.

Effect of mesh distortion on the accuracy of high order vorticity-velocity CFD approaches

The numerical solution of the incompressible Navier-Stokes equations offers an alternative to experimental analysis of fluid-structure interaction (FSI). We would save a lot of time and effort and help cut back on costs, if we are able to accurately model systems by these numerical solutions. These advantages are even more obvious when considering huge structures like bridges, high rise buildings or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the Kinematic Laplacian Equation (KLE) to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ordinary differential equations (ODE) time integration schemes, allowing us to tackle each problem as a separate module. The current algortihm for the KLE uses an unstructured quadrilateral mesh, formed by dividing each triangle of an unstructured triangular mesh into three quadrilaterals for spatial discretization. This research deals with determining a suitable measure of mesh quality based on the physics of the problems being tackled. This is followed by exploring methods to improve the quality of quadrilateral elements obtained from the triangles and thereby improving the overall mesh quality. A series of numerical experiments were designed and conducted for this purpose and the results obtained were tested on different geometries with varying degrees of mesh density.

Differential GPS as a monitoring tool on Volcano Santa Ana (Illamatepec) and the Coatepeque Caldera, El Salvador

We used differential GPS measurements from a 13 station GPS network spanning the Santa Ana Volcano and Coatepeque Caldera to characterize the inter-eruptive activity and tectonic movements near these two active and potentially hazardous features. Caldera-forming events occurred from 70-40 ka and at Santa Ana/Izalco volcanoes eruptive activity occurred as recently as 2005. Twelve differential stations were surveyed for 1 to 2 hours on a monthly basis from February through September 2009 and tied to a centrally located continuous GPS station, which serves as the reference site for this volcanic network. Repeatabilities of the averages from 20-minute sessions taken over 20 hours or longer range from 2-11 mm in the horizontal (north and east) components of the inter-station baselines, suggesting a lower detection limit for the horizontal components of any short-term tectonic or volcanic deformation. Repeatabilities of the vertical baseline component range from 12-34 mm. Analysis of the precipitable water vapor in the troposphere suggests that tropospheric decorrelation as a function of baseline lengths and variable site elevations are the most likely sources of vertical error. Differential motions of the 12 sites relative to the continuous reference site reveal inflation from February through July at several sites surrounding the caldera with vertical displacements that range from 61 mm to 139 mm followed by a lower magnitude deflation event on 1.8-7.4 km-long baselines. Uplift rates for the inflationary period reach 300 mm/yr with 1σ uncertainties of +/- 26 – 119 mm. Only one other station outside the caldera exhibits a similar deformation trend, suggesting a localized source. The results suggest that the use of differential GPS measurements from short duration occupations over short baselines can be a useful monitoring tool at sub-tropical volcanoes and calderas.

Energy and conductance state modeling of power electronic converters for DC microgrids

This document will demonstrate the methodology used to create an energy and conductance based model for power electronic converters. The work is intended to be a replacement for voltage and current based models which have limited applicability to the network nodal equations. Using conductance-based modeling allows direct application of load differential equations to the bus admittance matrix (Y-bus) with a unified approach. When applied directly to the Y-bus, the system becomes much easier to simulate since the state variables do not need to be transformed. The proposed transformation applies to loads, sources, and energy storage systems and is useful for DC microgrids. Transformed state models of a complete microgrid are compared to experimental results and show the models accurately reflect the system dynamic behavior.