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Journal of applied research and technology
versão On-line ISSN 2448-6736versão impressa ISSN 1665-6423
J. appl. res. technol vol.8 no.2 Ciudad de México Ago. 2010
Vibration Analysis Of a SelfExcited Elastic Beam
M. A. BarrónMeza
Departamento de Materiales Universidad Autónoma Metropolitana Azcapotzalco Av. San Pablo 180, Col. ReynosaTamaulipas C.P. 02200, México, D.F., MÉXICO. Email: bmma@correo.azc.uam.mx
ABSTRACT
The vibration behavior and the energy exchange among the normal modes of a clampedfree selfexcited elastic beam are analyzed in this work. To model this kind of beam, the damping term of a van der Pol oscillator is directly added to the equation of a linear elastic beam, yielding a single nonlinear partial differential equation. To solve this equation, a spectral method is employed. Three vibration modes are considered in the analysis, and the values of the selfexciting constant are varied in order to cover from linear to nonlinear vibration behavior. Multiple frequencies of the nonlinear beam are determined through the power spectral density of the beam freeend time series. Given that this relatively simple model mimics at least in a qualitative way some key issues of the fluidstructure problem, it could be potentially useful for fatigue studies and vibration analysis of rotating blades in turbomachinery.
Keywords: Beam vibration, fluidstructure problem, modal interaction, selfexcited beam, spectral method, turbine blade vibration, van der Pol oscillator.
RESUMEN
En este trabajo se analizan el comportamiento bajo vibración y el intercambio de energía entre los modos normales de una barra elástica autoexcitada con un extremo fijo y el otro libre. Para modelar esta clase de barra se le agrega directamente el término de amortiguamiento de un oscilador van der Pol a la ecuación de una barra elástica lineal, obteniéndose una sola ecuación diferencial parcial. Para resolver esta ecuación se usa el método espectral. En el análisis se consideran tres modos de vibración, y los valores de la constante de autoexcitación se varían a modo de cubrir un comportamiento a la vibración desde lineal hasta no lineal. Las múltiples frecuencias de la barra no lineal se determinan mediante el espectro de potencias de las series de tiempo del extremo libre. Dado que este modelo relativamente simple reproduce, al menos cualitativamente, algunos aspectos clave del problema fluidoestructura, puede ser potencialmente útil para estudios de fatiga y análisis de la vibración de álabes rotatorios en turbomaquinaria.
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