Topology Optimization Of Added Damping Layer Thin Plate Structure For Vibration Reduction Under Non-stationary Random Excitation

The random vibration problems of structures,especially in the fields of aerospace,ships and automobiles,have been studied by many scholars for a long time.Most of the actual engineering structures are inevitably subjected to various random loads during the service period,such as wind,wave and mechanical noise.Adding damping layer on the surface of structures can effectively suppress the structural vibration.In the traditional design of vibration reduction,the whole structure surface is covered by damping layer.This method can effectively suppress the structural vibration in some extent,but it increases the additional mass of the structure simultaneously and cannot reduce the vibration to the maximum extent.In order to make full use of material efficiency and achieve the best vibration reduction effect,it is very important to find the optimal layout of damping material layer.In recent years,the explicit time-domain method has demonstrated high accuracy and high efficiency in the non-stationary random vibration analysis of large scale structures,and showed good practicability in the sensitivity analysis.The main purpose of this dissertation is dedicated to seek optimal layout of added damping layer in the thin-plate structure under non-stationary random excitation.Based on the establishment of rational finite element model,topology optimization for thin-plate structure with additional damping layer is proposed by introducing dynamic topology optimization technology and the explicit time-domain method.This method provides a new idea for improving the utilization rate of damping materials and the ability to suppress vibration.The detail research contents of this dissertation are mainly as follow:Firstly,according to elasticity plate and shell theory,the finite element model of free layer damping(FLD)thin-plate structure with 5 degrees of freedom per node and constrained layer damping(CLD)thin-plate structure with 7 degrees of freedom per node are established.The rationality of finite element model is verified by numerical example.Furthermore,the effect of the consumption and distribution of added damping material to the variance amplitude of the stochastic dynamic response.The necessity of optimizing the layout of added damping material is illustrated.Secondly,a topological optimization model is established,which takes minimizing the maximum variance of the displacement response at a specific position in the free layer damping thin-plate structure as the objective function.It is considered that the structure is subjected to non-stationary random excitation and elements in the design domain are interpolated on the basis of SIMP method.The stochastic dynamic response variance and its sensitivity are calculated by the explicit time-domain method(ETDM).Then an optimization program is coded to solve optimization model based on GCMMA algorithm.The effectiveness of the proposed optimization method is verified through numerical examples.Finally,a topological optimization model is established,which takes minimizing the maximum variance of the displacement response at a specific position in the constrained layer damping thin-plate structure as the objective function.In order to solve the optimization model,we use the same method as the free layer damping thin-plate structure.Besides,damping matrix of the constrained layer damping thin-plate structure is also constructed by modal damping matrix superposition.The expressions of the sensitivities of the objective function in the two cases without considering and considering the modal damping ratio sensitivity are derived respectively.The numerical examples are given to compare the diversity of sensitivity and topology optimization results between the two cases.