Analysis and Control of Non-Classically Damped Structures
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Date
2024
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University of 20 August 1955-Skikda
Abstract
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.