Research Projects

The governing differential equation of a rotating beam subjected to an aerodynamic force requires a numerical approach, typically using Euler-Bernoulli beam theory and modal analysis. This problem requires a thorough understanding of structural dynamics, helicopter dynamics, and finite element methods. The problem can be solved in forward flight and hover conditions, with the Timoshenko beam theory and Rayleigh beam theory not explored in literature. The aerodynamic force includes complex terms like forward velocity, induced velocity, rotor angular velocity, and angle of attack. The use of finite difference in time is crucial for solving this problem. The governing differential equation of free vibration is a centrifugal force, requiring numerical solutions. Stability analysis can be performed for both forward flight and hover conditions using Floquet theory, with variations in advance ratio and lock number. The response can be calculated for uniform and linear inflow modes, considering control angle variations. The literature does not provide a complete process for this differential equation, but solutions can be explored and combinations can be considered. The finite element method in space offers alternatives, such as stiff or string basis functions. Coupled equations obtained during solutions are challenging to solve. The selection of shape function in time is crucial for periodic conditions.