Topology dynamic optimization of damping plates using GCMOC method based on MO-RAMP

Here, to effectively realize anti-vibration dynamic design of plates, the topological dynamic optimization method of constrained damping plates was studied. The finite element dynamic analysis model of a constrained damping plate was established, and the calculation formula of modal loss factor was derived. Based on the maximization objective of modal loss factor, taking relative densities of damping layer elements as topological variables and the use amount of damping material and structural frequency as control variables, the optimization mathematical model of damping plate was established. The traditional optimization criterion method was improved using the sequential convex programming theory. The improved criterion method GCMOC was used to solve the optimization model and obtain the global optimization solution, and the iterative formula of topology variables facing to GCMOC (global extreme point converged by method of optimization criterion) was derived. Considering the shape of multi-order ramp function has more ideal controllable concave geometric characteristics, a multi-order rational approxination of material properties (MO-RAMP) was proposed to punish the topological variables set in optimization iteration, realize its fast 0 and 1 binarization, and minimize the occurrence of intermediate topological variables in the range of 0.3-0.7. The topological dynamic optimization program facing to constrained damping plate was compiled, and the variable density type topological dynamic optimization for constrained damping plate was realized using GCMOC method based on MO-RAMP. Example analysis showed that when the composite algorithm of MO-RAMP and GCMOC is used in topology iteration of damping plate, the damping element relative density can be quickly pushed to the value close to 0 or 1 to get a clear density cloud of damping element optimization, and be helpful to realizing the optimal configuration; adopting the proposed method can make full use of damping material's viscoelastic energy-dissipating effect under the condition of greatly reducing the amount of damping material, and make the structure obtain better vibration reduction effect on the premise of ensuring basic stability of dynamic characteristics of damping plate. © 2021, Editorial Office of Journal of Vibration and Shock. All right reserved.