The adaptive growth method is a topology optimization design method for stiffened thin-walled structures based on the formation mechanism of natural branching systems. Aiming at the problem that the existing adaptive growth method has local modes in the topology optimization design of structural natural frequency， a polynomial material interpolation model is proposed. To improve the convergence of the algorithm， the genetic characteristics based on bionics are introduced into the sensitivity information processing， and the sensitivity filtering technique is used to solve numerical instability problems. The stiffeners layout optimization is carried out for the typical plate and shell structure examples of the simple supported and clamped. The design results show that the proposed method can obtain a clear stiffeners layout. The influence of simple-supported constraint and clamped-supported constraint on the topology optimization of structural natural frequency is further analyzed. The results show that although the first-order vibration modes of the structure are the same under the two constraint ways， the stiffener layout is different due to the difference in the degree of freedom of the constraint points. The natural vibration performance of the optimized design results under the two constraint ways is analyzed. It is found that the natural frequency of the stiffened structure obtained under the clamped-supported constraint way is about 7% higher than that under the simple-supported constraint way. Therefore， in practical engineering applications， when the structural boundary constraints are not clear， the clamped supported can be selected as the constraint way of the design model.