Dynamic Modeling and Analysis of Centrifugally Stiffened Proportionally Damped Timoshenko Beam

To study the effect of proportional damping on the dynamic response of centrifugally stiffened Timoshenko beam.

A novel method has been successfully developed to model and analyze the forced damped response of centrifugally stiffened Timoshenko beam. The method uses a single beam element with six physical nodal coordinates. The transverse displacement and rotation of the beam are described using a mixture of polynomial and enriching trigonometric shape functions. The damping matrix is incorporated into the equations of motion (EOM) according to Rayleigh assumption. The damped EOM are expressed in state space form.

The dynamic characteristics for the rotating forced damped vibration of Timoshenko beam are analyzed by assuming modal damping ratios for the first two modes and then finding the constants for the proportional damping. The EOM are integrated numerically to evaluate the system’s dynamic time response under various rotating speeds, external loading conditions, and modal damping ratios. Notably, the study goes a step further, providing a comprehensive exploration of the frequency response function (FRF) across a spectrum of parameter changes. The validity and efficiency of the developed method are demonstrated through numerical examples across various cases.

Proportional damping is pivotal for controlling vibrations, stability, and energy dissipation in rotating beams, shaping their response characteristics. It affects the damping ratio, natural frequency, and amplitude of the beam’s response. Higher damping ratios lead to quicker vibration decay, lower natural frequencies, and diminished amplitudes.