Research On Topology Optimization Of Viscoelastic Damping Structure Based On Variable Density Method

Viscoelastic material is widely used in engineering structures as vibration damping because of its perfect energy loss characteristics.The final performance of the damping structure is mainly determined by two parts.From the design and practice perspective,it is necessary to consider the comprehensive effect of key factors such as damping structure type,material laying strategy,and material volume usage.From the perspective of theoretical calculations,how to deal with the computational difficulty derived from the non-convex objective function in the optimization design is a challenge.In views of the above problems,a series of study on the structural topology optimization problems of viscoelastic material damping structures are launched.The main works are described as follows:(1)The concept of displacement continuity is introduced to deduce the constitutive relation and energy relationship of the constrained damping structure.The finite element model is established based on the modal strain energy method for the constrained damping structure,moreover,the reliability of the finite element model is proved by the classical example.The modal loss factor is used as the damping performance index to measure the effect of damping.The influence of material thickness,laying position and volume usage on the modal loss factor is analyzed,the results show that the thickness ratio of each layer of the damping structure is an important factor affecting its damping performance.The satisfied damping performance can be obtained by reasonable material placement position and material volume configuration.(2)The weighted sum of the reciprocal of the multi-mode loss factor is set as the objective function,the sensitivity expression of which in relation to the design variable is derived.Furthermore,the optimization model of damping structure topology is built by the variable density method.The sequential convex programming ideas is introduced to improve the conventional optimization criterion method,which makes the non-convex objective function becomes strictly convex.The improved optimization criterion method eliminates the adverse effect of negative sensitivity on iterative calculations and enables the algorithm to obtain the global optimal solution.The concept of negative sensitivity proportion and volume convergence is proposed and the damping optimization of free-damping structure and constrained dampingstructure.The results show that the improved optimization criteria method ensures all units are involved in optimization and includes less cells with intermediate density values,the optimization efficiency is improved in comparison with conventional optimization criterion method.(3)The sensitivity expressions of classical density penalty functions such as SIMP and RAMP are derived.Based on the improved optimization criterion method,combined with SIMP and RAMP and.The feasibility of the improved optimization criterion method with classical penalty function for vibration reduction optimization is verified by damping optimization of the first three single-mode of the constrained damping structure.To make up for the shortcomings of SIMP and RAMP,a new interpolation function that can selectively punish the cell density range is constructed by Logistic function.Finally,the effects on the first three-order multi-mode composite damping of damped structure with three different penalty functions are analyzed and compared separately.