Abstract
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.
Highlights
The structural complexity of mechanical systems has significantly increased due to the increase of requirements in dynamic performance
If the natural frequency of the satellite structure overlaps with the frequency of excitation coming from the engine of launch vehicle, resonance will happen and high-amplitude vibration transmitting through the satellite structure will cause destruction to the payloads inside
The dynamic structural optimization problem with frequency constraint to be solved is: find the set of design variables that will minimize the objective with local frequency constrained to a required value, which can be formulated as follow
Summary
The structural complexity of mechanical systems has significantly increased due to the increase of requirements in dynamic performance. Li [9] studied the topology optimization with frequency band constraints for resonance avoidance Most of these papers consider a single or multiple frequency constraints in the general structural optimization, which use only the information about the global vibration frequency, such as the first-order lateral and the first-order vertical natural frequency. Mode switching is the main problem in the process of dynamic structure optimization with local frequency constraints. A new method is proposed to solve the structural optimization problem with local frequency constraints. In order to avoid the obstruction of mode switching, the essential idea of the new method is to transform the original structural dynamic optimization problem with local frequency constraints into an approximate static optimization problem with nodal displacements constraints. The method is further applied in satellite structural optimization problem
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