Damage modelling and detection in beams and plates by analytical and numerical methods

Satpute, Akshay 2024. Damage modelling and detection in beams and plates by analytical and numerical methods. PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

This PhD thesis focuses on developing advanced damage detection methods for beam and plate structures to prevent catastrophic failures, with a particular emphasis on plate structures. The research is grounded in vibrational analysis, specifically leveraging changes in natural frequency as a diagnostic tool. In the initial phase, a rotational spring is used to model a crack in isotropic beam structures. The reduced stiffness of the beam at the location of the crack is incorporated into the dynamic stiffness matrix. The natural frequencies are extracted using the Newton-Raphson method and Wittrick-William algorithm. The obtained results are validated against previous research studies. Additionally, the results are compared with an analytical solution based on a strain energy approach, which is developed as part of this work. To achieve computational efficiency, the strain energy approach is employed for crack location and characterization in beams, using both noise-free and noisecontaminated natural frequencies. For noise-free simulations, vector analysis and gradient-based optimization are utilized to obtain crack parameters, while interval arithmetic methods are applied for crack localization in noise-contaminated simulations. The developed analytical solution for beam structures is further used as a framework to solve the inverse problem. Its use enhances computational efficiency during parameter optimization. Building on the insights gained from the beam studies, a novel method for isotropic plate structures is developed to calculate the degradation in natural frequencies due to the presence of cracks. This method considers changes in rotation and bending moments to calculate the total change in the strain energy of the plate. Using the law of conservation of energy, a formulation is developed to calculate the difference between the intact and cracked plate by integrating changes in strain energy over the crack length. This methodology is validated against prior research for simple crack cases parallel to plate edges. The analytical formulation is further expanded to model arbitrarily oriented cracks, incorporating the twisting effect on the change in strain energy of the cracked plate. To validate this expanded work, a corresponding model is developed using the finite element software ABAQUS. iv The developed analytical solution based on the strain energy approach is further employed as a framework to solve an inverse problem for determining crack parameters. This involves identifying the location and characterization of damage using the first six natural frequencies of the cracked plate. The inverse problem is formulated using the least-squares difference method and solved using gradient-based optimization. The methods presented in this thesis provide promising results in terms of accuracy and computational efficiency. For future work, improvements are highlighted to expand the research for complex geometries, environmental conditions, sensor inaccuracies, and human errors.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Schools > Engineering
Uncontrolled Keywords:	1. Natural frequency. 2. strain energy approach. 3. inverse problem. 4. Rotational spring. 5. least squares method. 6. gradient based optimisation.
Date of First Compliant Deposit:	24 July 2025
Last Modified:	24 Jul 2025 08:34
URI:	https://orca.cardiff.ac.uk/id/eprint/180019

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