The Topological Dynamic Optimization Study On Constrained Damped Plates For Vibration Suppression

In vibration control for engineering structures, when the damping material is placed on the structure surface, it increases structural damping, inhibit the peak vibration, reduce the radiated noise effectively. But in order to implement the structure lightweight design, the introduction of damping mass is restricted. While reducing the dosage of viscoelastic damping materials, damping structure suppression optimization design is realized. The vibration reduction optimization of constrained damping structure is studied, the research could show in the following aspects:(1) A model of the modal loss factor maximum as the objective function is established. Evolutionary structural optimization method is used to optimize the constrained damping plate model. The simulations show that compared with the non-optimized method, evolutionary structural optimization is more advantageous to realize the viscoelastic material optimization layout and modal frequency variation is stable. Harmonic response analysis is carried out on the damping structure to verify that the topology optimization method is effective, The modal loss factor density index is introduced to evaluate damping plate damping topological optimization performance.(2)The dynamic equation of constrained damping plate is deduced by principle of virtual work, modal loss factor mathematical calculation formula is deduced based on the energy dissipation. A modal that maximize the modal loss factor and minimum modal frequency changes as the objective function is built. Evolutionary structural optimization is introduced to solve the topological optimization mathematical model.The simulations show that multi-objective of the evolutionary structural optimization can significantly improve the vibration reduction effectiveness of the damping material, guarantee the stability of frequency characteristics of the damping plate and greatly reduce the dosage of damping materials. The harmonic response analysis is carried out on the damping plate to verify the effectiveness of the optimization results.(3)On the basis of Hamilton variational principle, the constrained damping plate dynamic differential equation is derived. The mathematical model is Built. structural modal damping ratio formula is derived, the sensitivity equation in frequencyconstraints is introduced. After optimization, structural modal damping ratio is increased, the modal frequency is varied stability, and according to the element number deleting damping materials of optimization methods, the damping ratio can show a trend of decline, and the structure of frequency is increased dramatically. For single order modal optimization, specific order response peak are decreased, and for the structure of compound multimodal optimization, the composite vibration damping structure effect is better. when maximizing structure composite modal damping ratio.(4)The topological optimization mathematical model is set up. the model is solved by adding evolutionary structural optimization(AESO) algorithm. A numerical example shows that based on AESO method for damping structure, damping materials are mainly placed on the maximum mode strain locations of the structure. The checkerboard phenomenon is avoided. After AESO for the structure, the first order damping ratio is increased by 83.6%, while after evolutionary structural optimization(ESO)for the structure,the number is 72.13%. To verify topology optimization result,harmonic response analysis is carried out on the damping structure, the result shows that by the AESO optimization, structure vibration suppression effect is better.(5) Based on the deformation displacement relationship of damping structure,structure vibration differential equation is deduced. The damping element adding and deleting criterion is presented. After ESO for damping structure, the increase of first and third order damping ratio is 54.51% and 36.21%, while after Bi-directional Evolutionary Structural Optimization(BESO)for damping structure, the increase number is 76.69% and 58.36%. harmonic response analysis is carried out on the damping structure, the simulation show that using BESO method, response amplitude is lower and vibration suppression effect is better.