Isogeometric shape optimization method for vibration of variable section blade

Abstract

An accurate and efficient shape optimization model is a practical approach to improving the vibration characteristics of blades. This paper proposes an isogeometric shape optimization method that uses control point coordinates as optimal design variables for the rotating variable-section blade model. The local modification feature of NURBS curves allows for the adjustment of blade profiles without the need to change the number and quality of parameter elements. Integrating the centrifugal force step-by-step solution method and three-dimensional elasticity theory, while accounting for centrifugal shear stress and omitting deformation assumptions, a vibration solving model of the rotating variable section blades is firstly established to determine the objective function for blade optimization. By comparing with the numerical data from the finite element method (FEM) and modal experiments, the accuracy and effectiveness of the current vibration modelling method are validated. Using the Campbell diagram, a safe operational range is determined to avoid resonance at certain rotational speeds. This constraint is then applied to find the optimal lightweight shape for the blade. Finally, the effects of different rotational speeds, constraints, and design variable variation ranges on the shape optimization results are investigated. The method can perform extensive analysis automatically by changing the geometric design parameters, which greatly improves the efficiency of blade optimization design and provides a new idea for blade optimization design.