Interactive lecture notes for structural dynamic analysis in frequency domain = Apuntes de clase interactivos para el análisis de la dinámica estructural en el dominio de la frecuencia

Ivan M. Díaz, Carlos M.C. Renedo, José M. Soria, Jorge F. García-Samartín, Jaime H. García-Palacios


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Dynamic and experimental analysis of structures are two of the most abstract and complex disciplines in structural engineering, because of its awkward mathematical and physical background and due to the multidisciplinary knowledge needed to go over the whole analysis (from the acquisition of measures up to the final interpretation of results). In particular, Fourier analysis (frequency domain analysis) in discrete time, which is routinely used in the dynamic analysis, is not usually well-understood and even is not well computed in discrete time. Frequently, students lose motivation trying to decrypt difficult mathematical developments, which do not let them to interpret properly complex concepts which are extremely important for current analysis in discrete time such as: Fourier transforms, aliasing, leakage, filtering, windowing, etc. For this reason, the authors has implemented a new teaching tools based on the numerical experiments and interactive learning that transform the learning experience into a more pleasant process than in the pass. In this way, recently-developed tools as “MATLAB Live Editor” allows professors to create interactive lecture notes, which students can easily follow, modify and simultaneously run during classes, developing its own intuitive interpretation of the knowledge. This tool is been successfully employing to teach dynamic analysis of structures in frequency domain with excellent feedback from the students.


El análisis experimental y dinámico de estructuras son dos de las disciplinas más complejas y abstractas de la ingeniería estructural debido a la complejidad de los fundamentos que se manejan y al conocimiento multidisciplinar necesario para llevar a cabo el proceso completo de análisis (desde la toma de datos hasta la interpretación final de los resultados). En particular, el análisis de Fourier (análisis en el dominio de la frecuencia), el cual se usa continuamente en el análisis dinámico, no siempre se entiende adecuadamente e incluso no se aplica correctamente en el dominio discreto. Con frecuencia los estudiantes pierden la motivación intentando comprender los desarrollos matemáticos asociados, lo que no les permite interpretar adecuadamente conceptos más complejos y a la vez importantes como: la transformada de Fourier, “aliasing”, “leakage”, filtrado, ventanas de ponderación, etc. Por ello, los autores han implementado una nueva herramienta basada en la experimentación numérica y en el aprendizaje interactivo, haciendo del mismo un proceso más llevadero que en el pasado. Así, herramientas recientes como “MATLAB live Editor” permiten que los profesores creen clases interactivas que los estudiantes pueden de forma sencilla, seguir, modificar y ejecutar durante las clases, desarrollando un conocimiento más intuitivo del problema. Los autores están empleando esta herramienta exitosamente en el análisis dinámico de estructuras en el dominio de la frecuencia con muy buenos comentarios por parte de los estudiantes.

Palabras clave

Learning based on experiments; Active learning technologies; Interactive lecture notes; Dynamic analysis of structures; Fourier analysis; Aprendizaje basado en experimentos; Tecnologías activas de aprendizaje; Material docente interactivo; Análisis dinámico de estructuras; Análisis de Fourier


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