Local Modal Frequency Improvement with Optimal Stiffener by Constraints Transformation Method

Local modal vibration could adversely affect the dynamical environment, which should be considered in the structural design. For the mode switching phenomena, the traditional structural optimization method for problems with specific order of modal frequency constraints could not be directly applied to solve problems with local frequency constraints. In the present work, a novel approximation technique without mode tracking is proposed. According to the structural character, three reasonable assumptions, unchanged mass matrix, accordant modal shape, and reversible stiffness matrix, have been used to transform the optimization problem with local frequency constraints into a problem with nodal displacement constraints in the local area. The static load case is created with the modal shape equilibrium forces, then the displacement constrained optimization is relatively easily solved to obtain the optimal design, which satisfies the local frequency constraints as well. A numerical example is used to verify the feasibility of the proposed approximation method. Then, the method is further applied in a satellite structure optimization problem.