Publicación: Estudio del efecto de la esbeltez en el comportamiento dinámico de una viga rotatoria fisurada
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2022
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['Universidad Nacional de Educación a Distancia (España)', 'Universidad Politécnica de Madrid. Departamento de Ingeniería Mecánica']
Resumen
En este trabajo se presenta un estudio del efecto de algunos de los parámetros característicos de una viga rotatoria fisurada en las dos primeras frecuencias de vibración. Se ha partido de un modelo matemático de una viga rotatoria fisurada. El problema dinámico se resuelve mediante el método de integración de Frobenius. Los parámetros que se incluyen en el modelo son: el radio del buje, la esbeltez de la viga, la profundidad y posición de la fisura y la velocidad de giro. De estos parámetros, se han estudiado en detalle: la esbeltez y la velocidad de giro. Se concluye que un incremento en la velocidad de giro produce incrementos en las frecuencias y que aumentos de la esbeltez producen una disminución la frecuencia. Se han presentado, además, las frecuencias adimensionalizadas. Por un lado, se adimensionalizan con la frecuencia de la viga intacta no rotatoria y por otro, con la de la viga intacta rotatoria. Se ha visto cómo a diferencia de lo que ocurre con las frecuencias dimensionales, las adimensionales sufren un incremento con la esbeltez que se debe exclusivamente al efecto combinado del incremento (mayor) de la esbeltez con el decremento (menor) de la frecuencia. Si la adimensionalización se hace con la viga no rotatoria, las frecuencias adimensionales tienen un valor superior a la unidad, como consecuencia de la rigidización por la fuerza centrífuga y que es tanto mayor cuanto mayor es la velocidad. En el caso de la adimensionalización con la frecuencia de la viga intacta rotatoria, los valores siempre están por debajo de la unidad al eliminar con la adimensionalización el efecto rigidizador de la fuerza centrífuga.
This paper presents a study of the effect of some of the characteristic parameters of a cracked rotating beam on the first two vibration frequencies. A mathematical model of a cracked rotating beam has been used as a starting point. The dynamic problem is solved using the Frobenius integration method. The parameters included in the model are: the radius of the hub, the slenderness of the beam, the relative depth and position of the crack and the rotational speed. Two of them have been analysed in this work: the slenderness and the rotational speed. It is concluded that the increase of the rotational speed produces increases in the frequencies and that the increase of the slenderness produces a decrease in the frequency. The dimensionless frequencies have also been presented. On the one hand, they have been nondimensionalized with the frequency of the non-rotating intact beam and, on the other hand, with that of the rotating intact beam. It has been shown that, unlike the dimensional frequencies, the dimensionless frequencies undergo an increase with slenderness due to the combined effect of the (higher) increase in slenderness with the (lower) decrease in frequency. The dimensionless frequencies, with that of the non-rotating beam, have a value greater than unity, as a consequence of the stiffness due to the centrifugal force, which is greater the higher the velocity. The dimensionless frequencies, with the intact beam in rotation are always less than unity, since the stiffness effect of the centrifugal force is eliminated in the nondimensioning.
This paper presents a study of the effect of some of the characteristic parameters of a cracked rotating beam on the first two vibration frequencies. A mathematical model of a cracked rotating beam has been used as a starting point. The dynamic problem is solved using the Frobenius integration method. The parameters included in the model are: the radius of the hub, the slenderness of the beam, the relative depth and position of the crack and the rotational speed. Two of them have been analysed in this work: the slenderness and the rotational speed. It is concluded that the increase of the rotational speed produces increases in the frequencies and that the increase of the slenderness produces a decrease in the frequency. The dimensionless frequencies have also been presented. On the one hand, they have been nondimensionalized with the frequency of the non-rotating intact beam and, on the other hand, with that of the rotating intact beam. It has been shown that, unlike the dimensional frequencies, the dimensionless frequencies undergo an increase with slenderness due to the combined effect of the (higher) increase in slenderness with the (lower) decrease in frequency. The dimensionless frequencies, with that of the non-rotating beam, have a value greater than unity, as a consequence of the stiffness due to the centrifugal force, which is greater the higher the velocity. The dimensionless frequencies, with the intact beam in rotation are always less than unity, since the stiffness effect of the centrifugal force is eliminated in the nondimensioning.
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Palabras clave
frecuencias naturales, vigas rotatorias fisuradas, vigas Euler-Bernoulli, palas rotatorias fisuradas
Citación
Centro
E.T.S. de Ingenieros Industriales
Departamento
Mecánica