A Modal Reduction Scheme for the Free Vibration of Strings with Inertially Loaded Boundary

• Autor(a) principal: Jales, Pedro Menescal
• Data de Publicação: 2023
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: eng
• Título da fonte: Repositório Institucional da UFRN
• Texto Completo: https://repositorio.ufrn.br/handle/123456789/55908
• topic: modal reduction; modal analysis; strings; orthogonality; modal participation

In structural engineering, it is essential to minimize computational costs when simulating systems governed by differential equations. Modal reduction techniques are widely employed to achieve this objective without compromising accuracy. These techniques involve excluding higher-order modes that have negligible influence on the system's response. This study proposes a modal reduction scheme designed for the free vibration analysis of a string with fixed-inertially loaded boundaries. Modified orthogonality relationships, considering the boundary conditions, are derived to determine the modal shapes. Through the modal expansion, the original partial differential equation of motion is transformed into a set of independent ordinary differential equations solvable for the modal coordinates. The methodology estimates modal participation factors by analyzing the energy distribution among modal coordinates. The proposed scheme significantly reduces computational expenses by disregarding less significant modes and accuracy of the reduced model is evaluated using absolute and root mean square error expressions. The effectiveness of the modal reduction scheme is demonstrated through three illustrative examples: validating the methodology by exciting a single mode, releasing a linearly stretched string, and plucking the string at its midpoint. This modal reduction approach provides a practical solution for maintaining accuracy while significantly reducing computational costs in simulating the system dynamic behavior.