Minimum Weight Optimal Design of Truss Structure with Frequency Response Function Constraint

Abstract

The dynamic sizing optimization problem of a truss structure is studied for its weight minimization with a constraint of the frequency response function (FRF) over a certain frequency bandwidth. First, a discrete representation of the FRF is proposed such that the integral FRF variation within the frequency range can be indicated effectively and efficiently by means of the dynamic responses at several specified characteristic frequency points. As a consequence of this approximation, the continuous FRF constraint is well represented through a few discrete constraints at those characteristic frequencies. Then, an evolutionary optimization procedure is developed based on the FRF sensitivity analysis. In the optimization procedure, the FRF amplitude is reduced while the resonance peaks (eigenfrequencies) within the frequency range of interest are essentially kept. The minimum weight design of a structure is obtained indirectly from a preliminary design by a lesser increase of the weight together with a significant reduction of the structural FRF. Finally, the proposed optimization method is verified through two typical examples, and the obtained results show that the present optimal design approach on an FRF constraint is superior to the natural frequency constraint for overall attenuation of the structural dynamic responses in a wide frequency range.