Purpose <p>This study aims to develop a complete dynamic model of a rotating cantilever beam and analyze its vibration behavior.</p> Methods <p>The finite element method (FEM) is applied using beam elements with six degrees of freedom per node to capture both translational and rotational motions. The equations of dynamics are solved in the time domain using the implicit Newmark method. The structural damping is represented by a Rayleigh proportional damping model with a single calibrated coefficient to match available exprimental data.</p> Results <p>Numerical results indicate that increasing the proportional damping coefficient decreases the higher-order natural frequencies and reduces the amplitudes of their corresponding resonance peaks. The centrifugal effect increases the first three natural frequencies but slightly decreases the fourth without causing instability. The damping and centrifugal effects on the fundamental bending mode shapes are also obtained. The gyroscopic effect generates coupled extension and torsion vibrations when the beam is subjected to a sinusoidal bending force.</p> Conclusion <p>It is important to include the centrifugal, gyroscopic, and damping effects in predicting the three-dimensional vibration behavior of rotating beams.</p>

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Three-dimensional Linear Vibration of a Rotating Cantilever Beam with an Adjusted Proportional Damping Model

  • Hedi Hamdi

摘要

Purpose

This study aims to develop a complete dynamic model of a rotating cantilever beam and analyze its vibration behavior.

Methods

The finite element method (FEM) is applied using beam elements with six degrees of freedom per node to capture both translational and rotational motions. The equations of dynamics are solved in the time domain using the implicit Newmark method. The structural damping is represented by a Rayleigh proportional damping model with a single calibrated coefficient to match available exprimental data.

Results

Numerical results indicate that increasing the proportional damping coefficient decreases the higher-order natural frequencies and reduces the amplitudes of their corresponding resonance peaks. The centrifugal effect increases the first three natural frequencies but slightly decreases the fourth without causing instability. The damping and centrifugal effects on the fundamental bending mode shapes are also obtained. The gyroscopic effect generates coupled extension and torsion vibrations when the beam is subjected to a sinusoidal bending force.

Conclusion

It is important to include the centrifugal, gyroscopic, and damping effects in predicting the three-dimensional vibration behavior of rotating beams.