In this work, the time varying stresses in a Howden axial flow fan are obtained by finite element analyses. Dynamic substructuring is used to obtain accurate values of the stresses in the threads of the blade shaft, the component which connects the blade with the hub. Three different global models are used to compare the influence of neglecting the fan shaft and the stiffness influence of the centrifugal force. The relative displacements, which are obtained from the global models, have been used as boundary condition in the detailed models. The detailed models are used to obtain the Von Mises stresses in the root of the threads of the blade shaft. Finally the results of the three global models are compared with experimental measured data provided by Howden. The experimental data results in the highest Von Mises stresses. The model with the fan shaft and the stiffness influence of the centrifugal force gives values for the Von Mises stresses which are approximately twenty percent lower. The model without the fan shaft results in the lowest stresses which are approximately forty percent lower than the stresses obtained using the measured data.

Tires serve as important components of wheeled vehicles and their analytical modeling has drawn the attention of many researches in the past decades. A high-resolution finite element (FE) tire model contains detailed structural and material characteristics of a tire that exhibit degrees-of-freedom (DoF) in the order of 10⁵ or greater. However, such high-resolution models in their full detail are not practically applicable in multibody dynamic analysis of vehicles and a reduction in their order becomes necessary. In this research different formulations to construct condensed FE tire models suitable for multibody simulations are developed and their characteristics are discussed. In addition, two new and novel forms of substructuring are presented that aim at isolating the contact region of a tire without the need for keeping the boundary DoF which otherwise remain in the reduced system in the standard substructuring procedures. The new substructuring methods provide a great tool in constructing condensed FE tire models with much less total number of DoF compared to cases where a standard substructuring is used. In order to increase the computational efficiency of the condensed FE tire models even further, the possibility of model condensation in the contact region is studied. This research also addresses the applicability of available friction models into the condensed FE tire models. Different formulations of a condensed tire model presented in this research are used to construct several computational models. These models are utilized to simulate certain scenarios and the results are discussed.

Perforated tubes in mufflers are generally modeled by the transfer impedance approach since modeling the actual geometry of the perforated tubes with holes is very expensive due to the enormity of the boundary elements required. With the development of the substructuring technique which greatly reduces the number of elements required detailed modeling of the perforated tubes has become possible. In this thesis mufflers with perforated tubes are analyzed by modeling the actual geometry and locations of holes on the perforated tubes. The Direct-mixed-body boundary element method with substructuring is used to model the mufflers. Mufflers of various geometry containing perforated tubes with holes of different sizes and porosity are tested. The results obtained from the analyses are compared with the empirical formula results and experimental results. A preliminary investigation on the detailed modeling of flow-through catalytic converters is also conducted.

Successful race teams rely heavily on track testing to search for the ideal suspension setup. As more restrictions are placed on the amount of on-track testing by major racing sanctioning bodies, such as NASCAR, teams have increased their attention to alternate testing methods to augment their track data and better understand the dynamics of their racecars. One popular alternate to track testing is 8-post dynamic shaker rig testing. Eight-post rig testing gives the team a better understanding of the vehicle's dynamics before they arrive at the race track, allowing them to use their limited track testing time more efficiently. While 8-post rig testing certainly is an attractive option, an extensive test matrix is often required to find the best suspension setups. To take full advantage of 8-post rig tests, more efficient experimental methods are needed. Since investigating shock absorber selection is often the most time-consuming task, this study focuses on developing more efficient methods to select the best shock absorber setups. This study develops a novel method that applies dynamic substructuring and system identification to generate a mathematical model that predicts the results of future tests as both command inputs and components are changed. This method is used to predict the results of 8-post rig tests as actuator commands and shock absorber forces are varied. The resulting model can then be coupled with shock absorber models to simulate how the vehicle response changes with shock absorber selection. This model can then be applied to experimental design. First, a physically-motivated nonlinear dynamic shock absorber model is developed, suitable for quickly fitting experimental data and implementing in simulation studies. Next, a system identification method to identify a vehicle model using experimental data is developed. The vehicle model is then used to predict response trends as shock absorber selection is varied. Comparison of simulation and experimental results show that this model can be used to predict the response levels for 8-post rig tests and aid in streamlining 8-post rig testing experimental designs. / Ph. D.

In this work, the feasibility to perform substructuring technique with experimental data is demonstrated. This investigation examines two structures with different additional mass‑loads, i.e. transmission simulators (TSs). The two structures are a single blade and the hub together with two blades from an Ampair 600 wind turbine. Simulation data from finite element models of the TSs are numerically decoupled from each of the two structures. The resulting two structures are coupled to each other. The calculations are made exclusively in the frequency domain. A comparison between the predicted behavior from this assembled structure and measurements on the full hub with all three blades is carried out. The result is discouraging for the implemented method. It shows major problems, even though the measurements were performed in a laboratory environment.

This research focuses on implementing and improving a parallel solution framework for the linear static analysis of large structural models on PC clusters. The framework consists of two separate programs where the first one is responsible from preparing data for the parallel solution that involves partitioning, workload balancing, and equation numbering. The second program is a fully parallel nite element program that utilizes substructure based solution approach with direct solvers. The first step of data preparation is partitioning the structure into substructures. After creating the initial substructures, the estimated imbalance of the substructures is adjusted by iteratively transferring nodes from the slower substructures to the faster ones. Once the final substructures are created, the solution phase is initiated. Each processor assembles its substructure&#039 / s stiffness matrix and condenses it to the interfaces. The interface equations are then solved in parallel with a block-cyclic dense matrix solver. After computing the interface unknowns, each processor calculates the internal displacements and element stresses or forces. Comparative tests were done to demonstrate the performance of the solution framework.

The field of modal testing and analysis is currently facing a surge of interest in error modelling. Several errors which occur during testing campaigns are modelled analytically or numerically and propagated to various system coupling and interface reduction routines effectively. This study aims to propagate human errors, like position measurement errors and orientation measurement errors, and random noise-based errors in the measured Frequency Response Functions(FRFs) to the interface reduction algorithm called Virtual Point Transformation(VPT) and later to a substructure coupling method called Frequency-Based Substructuring(FBS). These methods form the cornerstone for Transfer Path Analsysis (TPA). Furthermore, common sources of error like sensor mass loading effect and sensor misalignment have also been investigated. Lastly, a new method to calculate the sensor positions and orientations after a measurement has been devised based on rigid body properties of the system and from the applied force characteristics. The error propagation was performed using a computationally efficient, moment method of the first order and later validated using Monte-Carlo simulations. The results show that the orientation measurement error is the most significant followed by FRF error and position measurement error. The mass loading effect is compensated using the Structural Modification Using Response Functions (SMURF) method and the sensor misalignment is corrected using coordinate transformation. The sensor positions and orientations are accurately estimated from rigid body properties and applied force characteristics; individually using matrix algebra and simultaneously using an optimization-based non-linear least squares solver. / För närvarande ser vi ett ökat intresse för felmodellering inom området modal provning och analys. Flera fel som uppstår under testserier modelleras analytiskt eller numeriskt och propageras effektivt till olika systemkopplings- och gränssnittsreduktionsrutiner. Denna studie syftar till att hantera mänskliga fel, som positionsmätningsfel och orienteringsmätfel, och slumpmässiga brusbaserade fel i de uppmätta frekvensresponsfunktionerna (FRF) till den gränssnittsreduktionsalgoritm, som kallas ”Virtual Point Transformation” (VPT), och senare till en substrukturskopplingsmetod, som kallas FBS (Frequency-Based Substructuring). Dessa metoder utgör hörnstenen för ”Transfer Path Analsysis” (TPA). Dessutom har vanliga felkällor som sensormassbelastningseffekter och felorientering av sensorer undersökts. Slutligen har en ny metod för att beräkna sensorns positioner och riktningar, efter att mätning gjorts, baserat på systemets stelkroppsegenskaper och de applicerade krafterna. Felpropageringen estimerades med en beräkningseffektiv, momentmetod av första ordningen och validerades senare med Monte-Carlo-simuleringar. Resultaten visar att orienteringsmätfelet är den mest signifikanta felkällan följt av FRF-fel och positionsmätningsfel. Massbelastningseffekten kompenseras med hjälp av ”Structural Modification Using Response Functions” (SMURF) -metoden och sensorjusteringen korrigeras med hjälp av koordinatomvandling. Sensorpositionerna och positioner och orientering beräknas exakt från stelkroppsegenskaperna och de applicerade krafterna; individuellt med matrisalgebra och samtidigt med en optimeringsbaserad icke-linjär minsta kvadratlösare.

Noise and vibration transmitted through the tire and suspension system are strong indicators of overall vehicle ride quality. Often, during the tire design process, target specifications are used to achieve the desired ride performance. To validate the design, subjective evaluations are performed by expert drivers. These evaluations are usually done on a test track and are both quite expensive and time consuming due to the several experimental sets of tires that must be manufactured, installed, and then tested on the target vehicle. In order to evaluate the performance, expert drivers tune themselves to the frequency response of the tire/vehicle combination. Provided the right models exist, this evaluation can also be achieved in a laboratory. The research presented here is a method which utilizes the principles of frequency based substructuring (FBS) to separate or combine frequency response data for the tire and suspension. This method allows for the possibility of combining high fidelity tire models with analytical or experimental suspension data in order to obtain an overall response of the combined system without requiring an experimental setup or comprehensive simulations. Though high fidelity models are not combined with experimental data in the present work, these coupling/decoupling techniques are applied independently to several quarter car models of varying complexity and to experimental data. These models range from a simplified spring-mass model to a generalized 3D model including rotation. Further, decoupling techniques were applied to simulations of a rigid ring tire model, which allows for inclusion of nonlinearities present in the tire subsystem and provides meaningful information for a loaded tire. By reducing the need for time consuming simulations and experiments, this research has the potential to significantly reduce the time and cost associated with tire design for ride performance. In order to validate the process experimentally, a small-scale quarter car test rig was developed. This novel setup was specifically designed for the challenges associated with the testing necessary to apply FBS techniques to the tire and suspension systems. The small-scale quarter car system was then used to validate both the models and the testing processes unique to this application. By validating the coupling/decoupling process for the first time on the tire/vehicle system with experimental data, this research can potentially improve the current process of tire design for ride performance. / Ph. D. / Noise and vibration transmitted through the tire and suspension system of a vehicle strongly influence the comfort of passengers. Often, during the tire design process, target specifications are used to achieve the desired vibrational characteristics. Subjective evaluations are then performed by expert drivers in order to validate the tire design. These evaluations are usually done on a test track and are both quite expensive and time consuming due to the several experimental sets of tires that must be manufactured, installed, then tested on the target vehicle. The research presented here utilizes techniques from the field of Dynamic Substructuring which allow frequency data for the tire and suspension systems to be separated or combined. This method allows for the possibility of combining high fidelity tire models with analytical or experimental suspension data in order to obtain an overall response of the combined system without requiring an experimental setup or comprehensive simulations. Several analytical tire and suspension models were developed for this work and the process of separating/combining the frequency data was performed. Then, a small scale test system was developed and used to establish experimental procedures to collect the data necessary to carry out the Dynamic Substructuring techniques. Finally, the process was validated by repeating the process of separating/combing the frequency properties of the experimental data.

Na engenharia, existem diversas técnicas de análise estrutural que conduzem à obtenção de esforços e deslocamentos com considerável grau de eficácia e acurácia e, dentre estas, há a técnica de SUBESTRUTURAÇÃO. Esta técnica consiste na divisão e análise de um modelo estrutural completo, através da divisão de seu domínio em SUBESTRUTURAS, permitindo uma considerável eficiência nos cálculos e na avaliação de modelos estruturais combinados com a análise hierárquica de estruturas. Neste trabalho, seguindo-se a metodologia de pesquisa, que envolveu revisão bibliográfica e desenvolvimento de modelos computacionais, apresentaram-se as principais técnicas de subestruturas - seção 1, definições e formulação teórica dos principais métodos - desenvolvidos por Przemienieck (1963), Rosen e Rubinstein (1968), Rubinstein (1970) e El-Sayed e Hsiung (1990) - e a conceituação da análise hierárquica de estruturas com as respectivas aplicações combinadas com técnica de subestruturação para análise de fissuras em estruturas aeronáuticas, proposta de Starnes e Britt (1991) e aplicada por Potyondy (1993) - seção 2. Nesse contexto, na seção 3 se propôs a metodologia hierárquica para análise de estruturas típicas da construção civil, utilizando técnicas de subestruturação. Apresentaram-se instrumentos úteis à respectiva aplicação, dentre os quais se destaca a proposta de metodologia simplificada de análise hierárquica. Algumas precauções a serem adotadas na aplicação da metodologia também foram apresentadas. Na seção 4, desenvolveram-se cinco estudos de caso aplicando-se as metodologias, instrumentos e precauções desenvolvidos na seção 3, destacando-se a eficácia das metodologias. Conclui-se a pesquisa na seção 5 sendo que, na seção 6, indicam-se novas linhas de pesquisas a serem desenvolvidas sobre a metodologia proposta na pesquisa. / In engineering, there are several structural analysis techniques leading to obtain displacements and efforts with a considerable degree of efficacy and accuracy, and, among these, there is the SUBSTRUCTURING technique. This method consists in the division and analysis of a complete structural model, by subdividing his field in SUBSTRUCTURES, allowing a considerable efficiency in calculations and evaluation of structural models combined with hierarchical structures analysis. In this work, following the methodology research, which involved a literature review and computational models development, the key techniques of substructures were presented - section 1, as well as main methods definitions and theoretical formulation - developed by Przemienieck (1963), Rosen and Rubinstein (1968), Rubinstein (1970) and El-Sayed and Hsiung (1990) - and structural hierarchical analysis concept with their applications combined with aircraft structures cracks substructuring technical analysis, proposed by Starnes and Britt (1991), and implemented by Potyondy (1993) - Section 2. In this context, a civil construction typical structures analysis methodology was proposed in section 3. Besides, many useful tools for their implementation were presented, among which stands out the simplified hierarchy analysis methodology proposal. Some precautions in the methodology applying were also presented. In section 4, five case studies were developed, applying the methodology, tools and precautions explained in section 3, especially the methodologies effectiveness. The research is concluded in section 5, and new research lines, to be undertaken on the methodology proposed, were outpointed in section 6.

Esta dissertação tem como objetivo principal o estudo das técnicas de cancelamento de massa, bem como suas aplicações em análise modal experimental. Estas técnicas são utilizadas na redução de determinados erros nos dados de resposta em frequência da estrutura sob estudo. Estes erros são por sua vez causados por fontes adicionais de inércia, tais como acelerômetros e transdutores de força, que são frequentemente utilizados nos ensaios para o levantamento das características dinâmicas da estrutura. As técnicas de cancelamento de massa estudadas neste trabalho são desenvolvidas a partir de uma modelagem das relações de entrada e saída no domínio da frequência, utilizando-se para tanto as Funções de Resposta em Frequência (FRF), bem como conceitos de subestruturação. Os modelos analíticos utilizados no problema de cancelamento de massa são também aplicados na geração de FRFs desconhecidas para a estrutura sob estudo, a partir de um subconjunto de FRFs medidas com massas adicionais acopladas à estrutura. Os métodos estudados são aplicados a dados obtidos através de simulações numéricas em sistemas discretos, bem como a dados experimentais provenientes de ensaios em estruturas simples. Resultados satisfatórios foram obtidos tanto a partir das simulações numéricas quanto na análise experimental para o problema de cancelamento de massa. Na obtenção de FRFs desconhecidas, verificou-se que os modelos teóricos conduzem a resultados satisfatórios em determinadas situações, e que o ruído encontrado em dados experimentais representa um fator detrimental na utilização das técnicas de cancelamento de massa para o propósito de gerar-se FRF desconhecidas a partir de FRF efetivamente medidas na estrutura sob estudo. / The goal of this dissertation is to develop a study on mass cancellation techniques and their applications in experimental modal analysis. These techniques are commonly employed in the reduction of experimental errors on the structure\'s measured frequency response data. Such errors are in turn caused by extra masses such as accelerometer and force transducers, that are utilized on the measurement of the system\'s Frequency Response Functions (FRF). The mass cancellation techniques studied here are developed through frequency domain input and output relationships as well as substructuring concepts. The analytical models employed in the mass cancellation problem are also applied in obtaining unknown FRF from a subset of measured FRF that are measured with extra masses attached to the structure. The methods studied are applied to numerically simulated data from discrete systems, as well as to experimental data coming from modal tests performed on simple structures. Reasonably good results are obtained in either the numerical and experimental analysis for the mass cancellation problem. In obtaining unknown FRF data, it was verified that the models generated reasonable results in some circumstances, and that experimental noise is a major source of error in using these mass cancellation techniques for the purpose of obtaining unmeasured data from a subset of measured FRF.