Aiming at effective implementation of anti-vibration dynamic design of engineering structural plates, the topological dynamic optimization method of damping plates was studied. A dynamical finite element method for constrained damping plates was built with which a formula for calculation the modal loss factors of the plates could be derived. Based on the objective of maximizing modal loss factor, an optimization mathematical model for the damping plates was presented, which took the relative density of damping layer elements as topological variables, and the amount of damping materials and structural frequency as optimal control. Using the theory of sequential convex programming, and by improving the traditional optimization criterion method, an optimal method called GCMOC was proposed to solve the optimization model, so as to obtain a global solution of topology dynamics optimization problem, and an iteration formula of topological variables for GCMOC was achieved. Considering that the shape of multi-order RAMP function had ideal controllable concave geometric feature, a multi-order RAMP material interpolation(MO-RAMP) model was introduced into the optimization iteration, so as to punish topological variables effectively and realize its 0 and 1 binarization quickly, and minimize the occurrence of intermediate topological variable values of 0.3 ~ 0.7 as well. A topological dynamic optimization program for the plates was developed, and the variable density vibration reduction topology dynamic optimization process of GCMOC method based on MO-RAMP was implemented. The results showed that GCMOC combined with MO-RAMP can push the damping element density to the value close to 0 or 1 quickly. It obtained clear optimized density cloud for the damping layer, which was very conducive to the process realization. It exerted its viscoelastic energy dissipation effect under the condition of greatly reducing damping materials. It can keep the dynamic characteristics of the plate basically stable, and made it get better vibration reduction effect.
Key words
constrained damping plates /
topology dynamic optimization /
multi-order RAMP /
GCMOC optimization method /
vibration reduction characteristics
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Footnotes
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