Free vibration analysis of an Air Compressor Blade by using Euler Bernoulli and Timoshenko Beam theory

Abstract

Compressor blades in gas turbines are highly susceptible to resonant vibrations caused by aerodynamic and mechanical loads, which can lead to fatigue failure. Accurate prediction of their natural frequencies is crucial to ensure safe and efficient operation. This study investigates the free vibration characteristics of a compressor blade with a NACA 6412 airfoil cross-section using both analytical and numerical methods. The blade was modeled as a cantilever beam, and natural frequencies were calculated using Euler-Bernoulli and Timoshenko beam theories. While the Euler-Bernoulli theory neglects shear deformation and rotary inertia, the Timoshenko theory includes both, making it more suitable for thicker or moderately short blades. Material and geometric properties of the blade were incorporated to compute the first three modal frequencies. To validate the analytical results, a 3D finite element model of the blade was developed in ANSYS, and modal analysis was performed under fixed-root conditions. The comparison revealed that both beam theories closely matched the FEM result for the first natural frequency. However, at higher modes, Timoshenko theory demonstrated greater accuracy than Euler-Bernoulli by accounting for shear and rotary effects.