Browsing by Author "Hamid ,Afra"

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    Analysis and Control of Non-Classically Damped Structures
    (University of 20 August 1955-Skikda, 2024) Hisham, Suleiman; Hamid ,Afra
    This thesis explores the dynamic analysis of complex civil engineering structures, focusing on accurately modelling their responses to external forces. Solving the equation of motion directly for these systems often demands extreme computational time. Another option is to decouple these systems into modal form by solving the quadratic eigenvalue problem for them. Forced diagonalization or lightly damping assumptions are often used for this purpose. However, this technique has limited applicability for lightly damping scenarios. These challenges need more adaptable solutions. The exact state-space method stands out for its analytical accuracy in decoupling. It addresses the quadratic eigenvalue problem without simplifying the physical phenomenon. However, this method doubles the problem size, increasing computational demands. In response to these limitations, this research advances the field by examining approximation decoupling techniques that maintain the system's physical meaning while minimizing computational efforts. These techniques aim to improve the modelling efficiency of complex civil engineering structures and ensure the clarity of their dynamic behaviour interpretations. Two innovative methods introduced in our published papers are central to the thesis. The first proposed method, "Exploring Decoupling Techniques for Linear Structures with Non-Classical Damping," looks at a system with four degrees of freedom (4-DOF) and shows that it works well in three different damping situations. This method evaluates the efficacy of lightly non-classical damping against Adhikari's method, underscoring the importance of choosing a method based on the damping matrix's characteristics. It also introduces a new subspace technique that merges the advantages of previous methods for enhanced results. The second proposed method, "An Extension to Adhikari Iterative Method," builds upon existing frameworks by incorporating spectral localization and the self-adjoint theorem. This improves stability and precision in identifying complex eigenvalues. This advancement facilitates a novel approach for calculating the frequency response function (FRF), showcasing significant progress in the field. By integrating these methods, this thesis addresses computational and applicability challenges in modelling complex civil engineering structures and paves the way for further developments in structural dynamics analysis.