Topology optimization for removing internal resonances of a rotating thin plate
Jialiang Sun
Abstract: Internal resonance allows energy to transfer between eigenmodes and sometimes results in undesirable phenomena. Topology optimization has the ability to control the eigenfrequencies of a structure and is therefore possible to remove the internal resonances. In this study, topology optimization is studied for removing internal resonances of a rotating rectangular thin plate. First of all, an accurate dynamic model is established for the rotating thin plate by considering the Coriolis force. The thin plate element of the absolute nodal coordinate formulation (ANCF) is used to discretize the rotating thin plate and establish the dynamic equation. When the dynamic equation is transformed from the absolute frame to the rotating frame for modal analysis, the Coriolis force term shows up and is analytically derived. Then, an explicit and efficient topology optimization method, i.e., the method of moving morphable components (MMC) is employed to optimize the rotating thin plate. In order to remove the internal resonances, the detuning parameters are defined so that removing the internal resonances is equivalent to maximizing the minimum absolute detuning parameter. The corresponding max-min optimization problem can be dealt with via a bound formulation. Finally, three numerical examples are presented to validate the dynamic model and the topology optimization methodology. Two objectives are considered for optimization, i.e., removing the internal resonances of the rotating thin plate at different specific angular speeds and removing the most common 1:1 or 1:2 internal resonances of the rotating thin plate during a certain range of angular speeds.
Keywords: Topology optimization, Internal resonance, Rotating rectangular thin plate, Absolute nodal coordinate formulation, Moving morphable components
Optimized results for removing 1:1 or 1:2 internal resonances of the rotating thin plate at all angular speeds. (a) Removing 1:1 internal resonance; (b) removing 1:2 internal resonance
原文链接：https://www.sciencedirect.com/science/article/pii/S0022460X20302522?dgcid=author
