An analytic model for vibration of turbomachinery rotor blades

An analytic model for the vibration response of turbomachinery rotor blades that includes the effects of variations in blade thickness, curvature of the blade edges, and variations in the curvature of the blade middle surface in two dimensions is developed. Mathematical fits to both surfaces of the blade are generated in terms of polynomial equations with constant coefficients. The polynomial equations for the blade surfaces are then used in shell equations, based on Love's thin shell assumptions, to generate differential equations governing the vibration motion of the blade. The coefficients in the blade-fitting polynomials act as parameters in the equations of motion for the blade, so that equations for a new blade can be developed easily by changing the coefficients in the governing equations to those generated for the new blade. An approximate method of solution for the resonant response of a sample blade is presented.