Publication: Modelado mediante elementos finitos y análisis vibratorio de cristales sónicos
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2015-09
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2015-10-06
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Abstract
Las ondas se propagan de manera omnidireccional cuando entran en un medio continuo. Para algunas aplicaciones tecnológicas puede resultar de utilidad restringir la propagación de una onda dentro de un espacio finito. Los cristales sónicos son estructuras periódicas que poseen propiedades vibratorias diferentes en función de la configuración estructural y material de los componentes que conforman el sistema. Concretamente la capacidad de absorber ondas incidentes, sin importar la dirección de éstas, presentes en estas estructuras se debe a la existencia de bandgaps (rangos de frecuencias que el cristal no es capaz de transmitir).
El objeto de estudio de este Trabajo es el análisis de un cristal sónico tridimensional para localizar los rangos de frecuencias prohibidas presentes en él así como la influencia de la densidad y dimensiones de los elementos que componen la estructura, para poder diseñar futuras estructuras con propiedades que se adapten, de la manera más precisa posible, a las necesidades requeridas.
Para ello, se realiza un análisis analítico de las ecuaciones que rigen el movimiento en la estructura seguido de un análisis paramétrico de dichas ecuaciones para identificar los parámetros influyentes en el movimiento del cristal sónico. Una vez identificados los parámetros, se genera un modelo y se analiza, haciendo uso del Método de los Elementos Finitos, a través código comercial ABAQUS.
Finalmente se presentan los resultados obtenidos, tanto para el análisis principal como para los estudios paramétricos realizados, y un apéndice con las conclusiones generales a las que se ha llegado.
Waves propagate omnidirectional through a continuous medium. For some technological applications could be useful to restrict the propagation of a wave along a finite path. Sonic crystals are periodic structures with different vibrational properties with direct dependence on its elements configuration, both structural and material. In particular, the ability to absorb wave’s energy, no matter in which direction the wave impacts the crystal, of this kind of structures is due to the existence of bandgaps (specific range of frequencies that the crystal cannot transmit). The main objective of this Project is the analysis of a tridimensional sonic crystal in order to locate those bandgaps that the system would have. The influence in bandgaps due to the density and dimension of the elements that form the structure is also evaluated. This knowledge will permit the creation of different sonic crystals which will have an accurate adaptation into a specific request. With that aim, an analytic analysis of the movement equations of the system is made in first place. Later a parametric analysis of those equations is made in order to identify the most influent values that will affect the movement of the whole structure. Once this previous analysis are made, the model is generated and analyzed using the Finite Element Method, by using the computational code ABAQUS.
Waves propagate omnidirectional through a continuous medium. For some technological applications could be useful to restrict the propagation of a wave along a finite path. Sonic crystals are periodic structures with different vibrational properties with direct dependence on its elements configuration, both structural and material. In particular, the ability to absorb wave’s energy, no matter in which direction the wave impacts the crystal, of this kind of structures is due to the existence of bandgaps (specific range of frequencies that the crystal cannot transmit). The main objective of this Project is the analysis of a tridimensional sonic crystal in order to locate those bandgaps that the system would have. The influence in bandgaps due to the density and dimension of the elements that form the structure is also evaluated. This knowledge will permit the creation of different sonic crystals which will have an accurate adaptation into a specific request. With that aim, an analytic analysis of the movement equations of the system is made in first place. Later a parametric analysis of those equations is made in order to identify the most influent values that will affect the movement of the whole structure. Once this previous analysis are made, the model is generated and analyzed using the Finite Element Method, by using the computational code ABAQUS.
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Mecánica de medios continuos, Vibraciones, Ensayo de materiales, Método de los Elementos Finitos, Cristal sónico tridimensional