Polen - İTÜ Akademik Açık Arşive Hoş Geldiniz

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  Assessment of spectral matching approaches considering near-fault ground motions in nonlinear time history analysis

  (ITU Graduate School, 2026) Orhan, Dilara; Fahjan, Yasin; 501231001; Civil Engineering

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  This thesis investigates the applicability of spectrum matching approaches for near-fault ground motions in nonlinear time-history analysis. Near-fault earthquake records exhibit distinctive characteristics such as strong directivity effects, pronounced velocity pulses, and highly directional energy content. These features may govern structural response and lead to seismic demands that differ significantly from those associated with far-field ground motions. As nonlinear time-history analysis is increasingly adopted in performance-based seismic design, the selection and modification of ground motion records capable of realistically representing near-fault effects has become a critical issue in engineering practice. Spectrum matching is widely used to improve the compatibility of selected ground motion records with code-based or site-specific target spectra and to reduce record-to-record variability in nonlinear analyses. Despite its practical advantages, the application of spectrum matching to near-fault ground motions remains controversial, as the frequency-dependent modifications required to enforce spectral compatibility may alter physically meaningful wave characteristics. In particular, changes in velocity pulse shape, energy concentration, and directional properties may affect the reliability of nonlinear time-history analysis results when near-fault effects dominate structural response. Within this context, this study focuses on evaluating whether commonly used spectrum matching approaches can achieve spectral compatibility while maintaining the essential characteristics of near-fault ground motions. To address this objective, a selected set of near-fault ground motion records is analyzed using both uni-directional and bi-directional spectrum matching approaches. The analyses are conducted within a nonlinear time-history analysis framework using single-degree-of-freedom systems, which allow fundamental response characteristics to be examined in a controlled and interpretable manner. The effects of spectrum matching are evaluated through response spectrum comparisons, time-history analyses of acceleration and velocity records, wavelet-based time–frequency assessment, and the examination of nonlinear response quantities such as deformation and ductility demand. This multi-level evaluation enables the influence of spectrum matching to be assessed not only in terms of spectral agreement, but also with respect to time-domain behavior and resulting structural response. The results demonstrate that spectrum matching is effective in improving agreement with target response spectra; however, this improvement may be accompanied by notable modifications in near-fault ground motion characteristics. The analyses show that strict enforcement of spectral compatibility can lead to partial distortion of velocity pulse features and redistribution of energy content, particularly within specific period ranges that are critical for near-fault response. These effects highlight the limitations of evaluating spectrum matching performance solely based on spectral criteria, especially for pulse-dominated ground motions. A comparative assessment of uni-directional and bi-directional spectrum matching approaches indicates that their performance differs depending on the characteristics of the original records. Bi-directional spectrum matching generally provides improved spectral agreement across both horizontal components and leads to more balanced modifications in the time domain. In many cases, this coordinated treatment results in smoother time-history behavior and reduced artificial oscillations when compared to the uni-directional approach. However, the results also indicate that bi-directional spectrum matching does not fully eliminate distortions in records dominated by strong velocity pulses. For such cases, both matching approaches may compromise certain near-fault features when strict spectral compatibility is enforced, suggesting an inherent trade-off between spectral agreement and physical realism. The findings further demonstrate that reliance on spectral compatibility alone may be insufficient for reliable nonlinear time-history analysis under near-fault conditions. While spectrum matching can improve consistency with target spectra, additional evaluation of time-domain characteristics and near-fault-specific features is necessary to ensure physically meaningful representation of seismic demand. In this regard, the study emphasizes the importance of considering velocity pulse integrity, energy localization, and directional effects alongside conventional spectral measures. Finally, the analytical results are interpreted in relation to existing seismic design code practices, particularly those adopted in ASCE standards and TBDY-2018. The findings suggest that while spectrum matching should not be categorically excluded for near-fault applications, its use requires careful interpretation and, where appropriate, additional guidance to balance spectral compatibility with the preservation of near-fault ground motion characteristics. Overall, this study contributes to a clearer understanding of the conditions under which spectrum matching approaches may be applied more reliably in nonlinear time-history analysis involving near-fault ground motions.

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  Uav quadcopter guidance: Gps-denied 3D mapping and collision avoidance

  (ITU Graduate School, 2026) Aydın, Mehmet Kadri; Caferov, Elbrus M.; 511201189; Aeronautics and Astronautics Engineering

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  İnsansız Hava Araçları (İHA) ve özellikle dört rotorlu platformlar son yıllarda hobi kullanımından endüstri uygulamalarına geniş bir yelpazede yaygınlaşmıştır. Bu araçların sunduğu mekanik basitlik, dikey kalkış ve iniş (VTOL) yeteneği ile yüksek manevra kabiliyeti, tarım, altyapı denetimi, arama-kurtarma ve haritalama gibi alanlarda çığır açan çözümler sunmaktadır. Ancak, mevcut ticari ve askeri İHA sistemleri büyük ölçüde Küresel Konumlandırma Sistemi (GPS) gibi harici GNSS'lere bağımlıdır. Bu bağımlılık, sinyallerin ulaşamadığı veya güvenilmez olduğu ortamlarda büyük kısıtlamalar getirmektedir. Yeraltı maden ocakları, derin tüneller, yıkılmış binaların içi, köprü altları ve Mars ile Ay gibi gelecekteki uzay araştırmalarında hedeflenen lav tüpleri (yanardağ ve lav akışı sebebiyle oluşan tünneller) gibi "GPS bulunmayan" (GPS-denied) ortamlarda, otonom sistemler önemli zorluklar yaşamaktadır. Bu ortamlarda, harici konum referansı olmadan çalışan standart otopilotlar, zamanla atalet sensörlerindeki gürültü birikimi nedeniyle hızla sürüklenmesi (drift) kaza riskine yol açmaktadır. Ayrıca, bu ortamların genellikle dar, karmaşık ve düzensiz yapıları, kaya veya beton blokların radyo sinyallerini zayıflatması, uzaktan manuel kontrolü imkânsız hale getirir. Bu nedenlerle, tam otonom çözümler geliştirmek kaçınılmazdır. Bu tez, GPS sinyallerinin bulunmadığı zorlayıcı ortamlarda, harici seyrüsefer yardımına ihtiyaç duymadan otonom şekilde uçabilen, engellerden kaçınabilen ve ortamın 3 boyutlu haritasını çıkarabilen dört rotorlu bir otopilot sisteminin tasarımı, geliştirilmesi ve doğrulamasını ele almaktadır. Temel amacı, düşük maliyetli donanım sınırlamalarıyla dahi güvenli uçuş sağlayabilen reaktif bir kontrol yapısı geliştirmektir. Bu hedef doğrultusunda, çalışma kapsamında Model Tabanlı Tasarım (Model-Based Design - MBD) metodolojisi benimsenmiş ve yüksek sadakatli bir ortak simülasyon (co-simulation) altyapısı geliştirilmiştir. Sistem mimarisi, uçuş dinamiği ve kontrol algoritmalarının MATLAB/Simulink ortamında çalıştırılmasıyla desteklenirken, RoadRunner 3D oyun motoru kullanılarak gerçekçi çevresel algılama ve fiziksel çarpışma testleri gerçekleştirilmiştir. Bu Döngüde Yazılım (Software-in-the-Loop - SIL) yaklaşımı, karmaşık algoritmaların gerçek donanım kullanmadan, sanal ortamda risk olmadan güvenle test edilmesine imkan sağlamıştır. Dört rotorlu araç, simülasyon ortamında X-konfigürasyonlu rotor yerleşimine sahip, 6 Serbestlik Dereceli (6DOF) katı bir nesne olarak tanımlanmıştır. Hareket denklemleri, her motorun itki ve tork kuvvetlerinin gövde üzerindeki etkilerini hesap edecek şekilde tasarlanmıştır. Gerçek dünya koşullarını yansıtmak amacıyla, sensör modelleri idealize edilmemiştir; aksine, düşük maliyetli yaygın donanımların (örneğin MPU-9250 atalet ölçüm birimi ve Raspberry Pi işlemci kapasitesi) özelliklerine uygun gürültü ve hata modelleri eklenmiştir. Kontrol sisteminde, aracın yönelimini (yatış, yunuslama, sapma) yüksek frekansla stabilize eden iç döngü ile hız ve konumu yöneten dış döngüden oluşan, Kademeli PID (Oransal-İntegral-Türev) denetleyici kullanılmıştır. GPS yokluğunda konum belirsizliğini yönetmek için, yüksek frekanslı (100 Hz) ancak gürültülü ivmeölçer ve jiroskop verilerini, simüle edilen Lidar sensöründen gelen düşük frekanslı konum güncellemeleriyle (sensör füzyonu) birleştiren Genişletilmiş Kalman Filtresi (EKF) tasarlanmıştır. Bu filtre, aracın konum ve hız tahminini sağlar. Tezin en önemli teknik katkısı, 'Yol Noktası Düzeltici' (Waypoint Fixer) adını taşıyan, özgün ve düşük maliyetli bir reaktif güdüm algoritmasının geliştirilmesidir. Geleneksel yol planlama algoritmaları, A* veya RRT (Hızla Keşfeden Rastgele Ağaçlar) gibi, bilinmeyen bir ortamda küresel haritalar oluşturarak bu harita üzerinde sürekli optimal yolun yeniden hesaplanmasını gerektirir. Bu, küçük İHA'lar için yüksek hesaplama yükü anlamına gelir. Geliştirilen 'Yol Noktası Düzeltici' algoritması ise, küresel haritalar yerine, yerel ve anlık sensör verisine dayanan 'Güvenlik Küresi' (Safety Sphere) mantığını kullanır. Algoritma, aracın takip etmesi gereken rotayı temsil eden ve 3x3 matris yapısında tutulan bir 'İleriye Bakış Tamponu'nu (Look-Ahead Buffer) sürekli analiz eder. Her hedef yol noktası için, sanal bir güvenlik küresi (örneğin 4 metre yarıçapında) tanımlar. Eğer yerleşik Lidar sensöründen gelen nokta bulutu verisi, bu küre içinde herhangi bir engel tespit ederse, algoritma anlık olarak bir 'itme vektörü' hesaplar. Bu vektör, engelin merkezinden yol noktasına doğru yönlendirilmiş birim vektördür ve hedef yol noktasını, engelden belirlenen güvenlik mesafesi kadar uzaklaştırır, yani güvenlik küresinin sınırına taşır. Bu süreç, tünel duvarları veya mağara engelleri etrafında sanal bir itici alan oluşturarak, aracın karmaşık yapılı ortamlarda bile duvarlara çarpmadan, tünelin ortasında güvenli bir koridor kalmasını sağlar. Geliştirilen sistemin performansı, üç farklı simülasyon senaryosu kullanılarak detaylı şekilde doğrulanmıştır. İlk senaryo (Senaryo A), 100 metre uzunluğundaki düz bir tüneli kapsar ve sistemin temel stabilliğini sınamak üzere tasarlanmıştır. Bu senaryoda araç, herhangi bir sapma göstermeden tünel boyunca güvenli biçimde ilerlemiş ve PID katsayılarının yanı sıra temel uçuş dinamiğinin doğruluğu doğrulanmıştır. İkinci senaryo (Senaryo B), sistemin geometrik karmaşıklığa karşı tepkisini değerlendirmek amacıyla tasarlanmış; daralan geçitler, sarkıtlar ve keskin virajlar içeren 100 metrelik "Kıvrımlı Mağara" ortamını kapsar. Bu durumda, Lidar sensörünün yüksek hızda (10 Hz) güncelleme yaptığı ideal donanım koşulu simüle edilmiştir. Sonuçlar, "Yol Noktası Düzeltici" algoritmasının, değişen tünel geometrisine hızlı adaptasyon sağlayarak yol noktalarını duvarlardan başarıyla uzaklaştırdığını göstermiştir. Araç, mağara boyunca hiçbir engele 3 metreden fazla yaklaşmamış ve çarpışmasız bir şekilde uçuşunu tamamlamıştır. Üçüncü ve en kritik senaryo (Senaryo C), sistemin donanım kısıtlamaları ve sensör gecikmelerine dayanıklılığını test ediliştir. Aynı ortam olan "Kıvrımlı Mağara" kullanılmış, ancak Lidar konum güncelleme hızı 0.75 Hz'e (her 1.5 saniyede bir) düşürülmüştür. Bu, işlemcinin (örneğin Raspberry Pi 4) yoğun nokta bulutu verisiyle başa çıkmakta zorlanması nedeniyle oluşan gecikmeyi temsil etmiştir. Bu senaryoda, Lidar güncellemeleri arasındaki 1.5 saniyelik boşlukta EKF tahmini gerçek konumdan sapmaya başlamıştır. Ancak, en kritik özellik burada ortaya çıkmıştır: Algoritma, küresel konum yerine, aracın gövde eksenine göre yerel sensör verisi (Lidar taraması) kullanarak, küresel konum tahmini yanlış olsa bile, duvar ile araç arasındaki bağıl mesafeyi doğru tespit ettiği için aracı duvardan uzak tutmuştur. Sonuç olarak, konum tahminindeki sapmalara rağmen araç, kazaya uğramadan parkuru tamamladı. Bu, GPS olmayan ortamlarda hayatta kalma (güvenlik) mekanizmasının, hassas küresel haritalamadan bağımsız olabileceğini ve düşük maliyetli donanımlarla dahi yerel reaktif döngülerin uçuş güvenliğini sağlayabileceğini kanıtlamıştır. Çalışmanın diğer bir sonucu ise 3 boyutlu haritalama performansıdır. Senaryo B'de (hızlı sensörler) oluşturulan harita, yüksek doğruluk ve pürüzsüz yüzey sağlamaktadır. Ancak, Senaryo C'de (gecikmeli sensörler) oluşturulan haritada, EKF sapmaları nedeniyle "katman kayması" olarak adlandırılan geometrik bozulmalar ortaya çıkmıştır. Nokta bulutu verileri, offline teknikler kullanılarak post-processing ile düzeltilmiştir. Bu analiz, düşük maliyetli donanımlarla gerçek zamanlı güvenli uçuşun mümkün olduğunu, ancak yüksek hassasiyetli haritalama için uçuş sonrası veri işlemenin şart olduğunu göstermiştir. Sonuç olarak, bu tez çalışmasıyla geliştirilmiş olan otonom otopilot sistemi ve "Yol Noktası Düzeltici" algoritması, GPS sinyallerinin alınamadığı zorlu ortamlarda İHA'ların güvenli görev yapmasını sağlayan, hesaplama açısından verimli ve donanım gecikmelerine dirençli bir çözüm sunar. Simülasyonlar, bu yöntemin tünel, mağara gibi kapalı alanlarda arama-kurtarma, maden denetimi ve bilimsel keşif görevlerinde kullanılabileceğini göstermektedir. Gelecek çalışmalar arasında, sistemin gerçek donanımlar (NVIDIA Jetson veya Raspberry Pi) üzerine taşınması, nokta bulutu verilerinin otomatik olarak katı hacimsel modellere (Octomap) dönüştürülmesi ve çıkmaz sokakları aşmak için küresel bir yol planlayıcıyla hibrit hale getirilmesi yer almaktadır.

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  Hybrid mssa-geostatistical approach to spatio-temporal interpolation of meteorological variables: The case of the Meric-Ergene Basin

  (ITU Graduate School, 2026) Ünal, Emel; Koçak, Kasım; 511111004; Meteorological Engineering

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  This thesis examines the critical challenge of obtaining accurate and continuous climate records, which are essential for hydrological modeling, disaster management, and sustainable water resource planning in regions such as the Meriç-Ergene Basin. The primary issue arises from the inherent difficulties of meteorological observation, including sparse monitoring networks and the complex spatio-temporal characteristics of variables such as daily maximum and minimum temperatures and total daily precipitation. Traditional interpolation methods are limited because they treat simultaneous measurements independently and do not account for natural temporal evolution, long-term trends, or seasonal fluctuations within climate data. This research develops and evaluates a robust hybrid statistical framework for spatio-temporal interpolation of point meteorological measurements. The primary methodological innovation integrates the time-series analysis capabilities of Multivariate Singular Spectrum Analysis (MSSA) with the spatial estimation strengths of geostatistical techniques, including Inverse Distance Weighting (IDW), Radial Basis Function (RBF), and Kriging. The approach is systematic: MSSA is first applied to decompose multivariate time-series data from 20 stations in the Meriç-Ergene Basin, extracting dominant temporal patterns such as nonlinear trends and periodicities. Subsequently, the spatial distribution of the resulting eigenvectors is modeled using the selected geostatistical methods. This process enables reconstruction of underlying signals through Reconstructed Components (RCs), which are then used to generate synthetic time series and accurately fill missing data at locations without measurement stations, such as test station 18096 in Lalapaşa. The efficacy of this combined approach is rigorously evaluated using performance metrics, including Root Mean Square Error (RMSE), to demonstrate a more robust spatio-temporal predictive model compared to existing methods. Additionally, Cluster Analysis (CA) is employed to identify homogeneous climatic regions within the basin, supporting network design and regionalization. The research produced three principal conclusions regarding the performance of the hybrid model: Efficacy of the Hybrid Model: The integration of MSSA's temporal pattern extraction with geostatistical methods for spatial modeling demonstrates a powerful, data-adaptive alternative to static interpolation. This framework effectively reconstructs the continuous spatio-temporal field of the meteorological variables. Model performance varies according to the type of meteorological variable: Continuous Variables (Temperature): For daily maximum and minimum temperatures, the hybrid approach achieved high success, with spatial interpolation rates exceeding 90% using only two nearby stations. Notably, the Root Mean Square Error (RMSE) for temperature decreased as the MSSA sliding window size (M) was varied, confirming the effectiveness of temporal decomposition for continuous data. Discontinuous Variables (Precipitation): Precipitation, characterized by its intermittent and non-continuous structure, presented greater challenges. Reliable spatial representation required a denser monitoring network, with six to seven nearby stations necessary to maintain high logical success. Unlike temperature, the RMSE for precipitation increased with variations in M, indicating greater difficulty in modeling its complex temporal structure. Framework, by isolating and filtering stochastic noise to reconstruct dominant signals, failed to accurately capture extreme meteorological values (both peaks and troughs). This constraint inherently limits the model's direct applicability in specific high-stakes fields, such as flood and drought risk assessment, where the fidelity of extreme-event simulation is a paramount requirement. In summary, the thesis validates the hybrid MSSA-Geostatistical framework as a viable method for enhancing the integrity of basin-level climate records. It also provides data-driven recommendations for optimal parameter selection and monitoring network density, tailored to the distinct spatio-temporal behavior of continuous and discontinuous meteorological variables.

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  Synthesis and characterization of new liquid crystalline polyurethane copolymer

  (ITU Graduate School, 2026) Hız, Sermin; Gürsel, Yeşim; 515021019; Polymer Science and Technology

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  Polyurethanes (PU) are polymers synthesized by the reaction of polyols with isocyanates, producing materials that range from soft and flexible to highly rigid depending on their chemical structure. Their physical properties, such as heat resistance, hardness, and flexibility, are strongly influenced by the type of monomers used, while the (-NH-CO-O-) bonds in their backbone provide chemical stability and mechanical strength. Therefore, polyurethanes have a wide range of applications, extending from coatings and elastomers to foams and high‑performance engineering materials Liquid crystal (LC) compounds exhibit an intermediate state of matter, combining the fluidity of liquids with the long-range molecular order of crystalline solids. This unique dual nature allows LC materials to form highly ordered structures while maintaining mobility, making them attractive for advanced functional applications. When incorporated into polymer backbones, LC monomers can significantly enhance thermal, mechanical, and morphological properties. The incorporation of mesogenic groups into polymer structures is intended to improve molecular order and introduce liquid crystalline behavior, while long alkyl chains are often employed to lower the glass transition temperature (Tg), enhancing flexibility and processability. These chains act as flexible spacers, reducing steric hindrance and improving molecular packing, which facilitates the alignment of mesogenic units. By promoting this alignment, long alkyl chains contribute to the formation of ordered phases and help maintain their stability over a broader temperature range This structural design concept combines the flexibility provided by alkyl segments with the orientation of liquid crystalline groups to produce polymers with improved thermal and morphological characteristics. In this study, a side-chain liquid crystal polyurethane copolymer was synthesised. For this purpose, two different monomers, M1-diol (0.5 mmol, octadecyl-2,2-bis(hydroxymethyl)propionate) and M2-diol (0.5 mmol, 8-(4-cyanobiphenyl-4′-oxy) octyl-2,2-bis(hydroxymethyl)propionate) with HMDI (1 mmol, hexamethylene diisocyanate) in the presence of dibutyltin dilaurate as the catalyst. This study was designed based on our research group's previous work on PU synthesis using M2-diol [1].The aim of the thesis is to investigate the effect of incorporating long alkyl chains into the polyurethane structure on its liquid crystalline properties. The reference study [1].reported that the polyurethane showed mesophase formation during both heating and cooling; however, the liquid crystalline phase transitions were not clearly identified. The transition from the liquid crystalline phase to the isotropic state could not be detected by POM because the material began to decompose before reaching the isotropic phase. Additionally, the DSC thermograms did not display thermal transitions that could support the POM observations. The DSC thermograms obtained in this study show distinct thermal transitions for the polyurethane copolymer. The melting of the crystalline domains and the subsequent transition from the liquid crystalline phase to the isotropic state are clearly observed. These results are supported by POM images, which display a well defined nematic texture within a narrow temperature interval and a direct transition to the isotropic phase. Upon cooling, both the isotropic to mesophase transition and crystallization are detected, and POM confirms the presence of a stable nematic mesophase over a wide range. The results, supported by characterization studies, confirmed that these long alkyl chains reduced crystallization and improved the liquid crystalline behavior in the polyurethane copolymer. The chemical structure characterization was carried out using FTIR and HNMR spectroscopy, while the thermal properties were examined by differential scanning calorimetry (DSC), and the identification of liquid crystal mesophase structures and transition temperatures were performed using polarized optical microscopy (POM) and DSC, respectively.

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  Rotor dynamics analysis overhung rotor-bearing configuration

  (ITU Graduate School, 2026) Kurul, Kayhan; Şen, Osman Taha; 503221405; Mechanical Engineering

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  Rotating machinery is extensively use in everyday life and plays a crucial role in modern engineering. Broad class of rotating machines with overhung-configuration. It plays a critical role in many engineering applications such as wind turbines, aircraft engines, fan, and various rotating machinery Among various structural arrangements, the overhung configuration-where a heavy disc or impeller is mounted outside the bearing planes-is particularly prominent due to its practical advantages in casing design and suction side accessibility. However, this cantilevered mass distribution introduces significant rotordynamic challenges, including pronounced gyroscopic effects and complex modal sensitivities. In the early stages of engine development, rapid design iterations are essential for optimization. Yet, traditional high-calculation load simulations and experimental validations are often too computationally expensive or time-consuming for conceptual phases. This thesis addresses this gap by developing a verified, numerically efficient MATLAB-based tool specifically designed to evaluate the parametric sensitivities of overhung rotor-bearing systems. The framework of the study is established by identifying the fundamental components of rotating machinery-rotors, bearings, and stators-and defining their interactions within a standardized coordinate system. To simplify the complex nature of rotor vibrations, the study first evaluates the system through a single-degree-of-freedom undamped model, progressing toward the classical Jeffcott rotor model on isotropic supports. This progression allows for a rigorous derivation of unbalance forces and moments, which are the primary drivers of dynamic excitation. A central focus is placed on gyroscopic effects; the model explicitly accounts for gyroscopic moments that arise due to the coupled tilting and spinning of the rotor. By analyzing the response of a rigid rotor on flexible supports, the research establishes the criteria for constructing Campbell Diagrams, which are used to visualize the splitting of natural frequencies and identify critical speed intersections. The research begins by establishing a rigorous mathematical framework based on Finite Element Method (FEM) principles. To ensure modeling of the flexible shaft, Timoshenko beam theory was implemented. Unlike simpler models, this approach accounts for shear deformation and rotary inertia, which are critical for the short, rigid shafts typically found in turbomachinery. The theoretical foundation of this framework is rooted in the energy-based formulations of Lagrange's Equations. This approach allows the system's dynamic behavior to be established by defining the kinetic and potential energy states. For the rotating components, the kinetic energy formulation incorporates both translational and rotational inertia, capturing the tilting motion of the discs through transverse and polar moments of inertia. Furthermore, the potential energy of the flexible shaft is derived by accounting for both bending and transverse shear strain energy. This energy-based derivation ensures that all internal coupling effects-such as the interaction between shaft deflection and gyroscopic moments-are inherently preserved. The discretization process involves an eight-degree-of-freedom framework that focuses on lateral vibrations, ensuring that the model captures the essential bending modes without unnecessary computational overhead. To translate these continuous energy expressions into a discrete numerical system, cubic and linear shape functions are employed, ensuring continuity of the shaft's curvature across the entire assembly. The global equations of motion were constructed to include the speed-dependent gyroscopic matrices of both the flexible shaft and the rigid discs. This ensures that the "stiffening" effect caused by the rotation of overhung masses is accurately represented, as these forces significantly shift the system's natural frequencies at high operational speeds.The resulting skew-symmetric gyroscopic matrix, which is dependent on the rotational velocity, enables the model to accurately differentiate between forward and backward precession modes, a distinction essential for constructing Campbell diagrams. An important section of this work is the verification and validation phase, which serves to bridge the gap between theoretical modeling and industrial applicability. The developed tool was first benchmarked against DYROBES, a widely recognized commercial software used in the aerospace industry. The comparison of critical speed predictions yielded a maximum discrepancy of only 0.26 percent, confirming that the numerical assembly of the mass and stiffness matrices was executed with near-perfect precision. Following this, the model was tested against experimental data. While a 10.02 percent deviation was observed in this phase, a critical analysis revealed that the discrepancy stemmed from incomplete physical parameterization in the reference study. The most significant contribution of this thesis is the systematic investigation of the design space through a dual-modeling approach. By analyzing both "Double Overhung" and "Single Overhung" systems, it has been observed that the axial positioning of the bearings plays a pivotal role in system dynamics. The study identifies the axial position of the second bearing as a global sensitivity multiplier. Moving the second bearing closer to the overhung disc results in dramatic increases in the first critical speed; this enhancement represents a ten-fold increase in the double overhung system and more than a two-fold increase (approximately 132 percent ) in the single overhung system. Global stiffness matrix (K) analyses confirm that this shift creates a "near-clamped" boundary condition for the primary degrees of freedom of the disc. In contrast, the behavior of the second critical speed exhibits a fundamental divergence between configurations. While the second critical speed decreases by approximately 14 percent in the double overhung system as the bearing approaches the disc, it increases by 56 percent in the single overhung system due to the reduced bearing span enhancing "pivotal mode" stiffness. Dynamic load analysis reveals that these frequency gains impose a severe mechanical load penalty. Investigation into shaft thickness provides critical insights into stiffness saturation and mode shape transitions in both configurations. While the increase in the area moment of inertia (I ∝ D4) leads to a four-fold increase in the first critical speed for the double overhung system, the single overhung model exhibits a sharp 47 percent initial increase before reaching a plateau where frequency stabilizes. This saturation occurs as the midspan becomes sufficiently rigid, forcing deflection entirely into the overhung section. Dynamic load analysis further shows that increasing shaft diameter results in an 18-fold load increase in the double overhung model, whereas loads stabilize in the single overhung model after a specific thickness threshold. By incorporating torque transmission requirements, the study defines an "optimal diameter range" that simultaneously satisfies structural stress limits and rotordynamic margins. The research also addresses the impact of bearing rigidity, revealing that the system rapidly transitions into a shaft-dominant regime. Despite a 34-fold increase in bearing stiffness in the double overhung system, the first critical speed rises by only 6 percent, proving that natural frequencies are dominated by the shaft's bending characteristics rather than support stiffness. This is explained by the short bearing span relative to total shaft length, where the first bearing provides a dominant constraint that renders second bearing variations secondary. Consequently, dynamic loads follow a stable trend governed by modal mass rather than support rigidity. Furthermore, the concept of dynamic isolation is defined through the analysis of disc geometry. Unique to the double overhung configuration, increasing the second disc diameter allows for the "tuning" of the first critical speed (reducing it by approximately 30 percent) without affecting the stability of the second mode. The second critical speed remains constant across all scenarios, confirming that the second disc is positioned at a nodal point for this mode. Dynamic load analysis indicates that increased diametral inertia enhances the gyroscopic stiffening effect, reducing bearing loads by more than 50 percent. In conclusion, this research proves that rotordynamic design is an achievement of compromised balance. The validated tool developed in this study offers a robust and fast alternative to traditional software, enabling engineers to achieve optimized designs that balance critical speed margins, shaft weight, torque capacity, and bearing loads.

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