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

Viscoelastic damping technology is widely used in many fields,such as industrial production,transportation and so on,because it can effectively improve the system damping of the whole structure and suppress the vibration and noise of the structure in a wide frequency band.The most direct method in use is to lay the damping material on the surface of the controlled structure completely,but this method wastes too much damping material,and the damping effect is general.At present,in order to improve the damping effect,the rational distribution of damping materials has been discussed,which can not only reduce the overall weight of the overall laying damping,but also obtain better damping effect.Therefore,it is an urgent problem to lay viscoelastic damping layer on the surface of the structure and arrange it reasonably in the field of vibration and noise control.In this paper,the topology optimization method of constrained damping layer is investigated.The main contents are as follows:(1)The complex constant modulus model is selected to represent the constitutive relation of viscoelastic damping materials.Through the change of geometric displacement of each layer,the expression of energy of each layer is obtained,and the finite element dynamic model is established.The modeling method is verified by a classical example.The influence of different damping materials on the inherent characteristics of the model structure is analyzed by using the example model.The results show that the reasonable layout of the laying length and position of the damping material can not only effectively improve the utilization rate of the material,but also give full play to the damping characteristics of the damping material.(2)The mathematical model of topology optimization of damping layer with modal loss factor constrained by the actual amount of damping material is established.According to the strain energy of each layer mode,the sensitivity analysis of the variables is derived.Helmholtz PDE filtering technology and projection technology are introduced to suppress the grid and gray-scale unit data instability.MMA algorithm is used to solve the problem.The free damping plate and the constrained damping plate were taken as the research objects,and the layout of the damping material was optimized based on the SIMP method to obtain a clear and smooth topological configuration.Compared with the existing research,the superiority and practicability of the optimization method were demonstrated.(3)Aiming at the problem of optimizing the layout of damping materials for cylindrical shell structures,a dynamic finite element model of constrained damping cylindrical shells was established.The applicability of SIMP and RAMP models in variable density method to different structures is discussed.The cylindrical shell is designed based on the RAMP method,the Lagrange function is constructed,and the Lagrange multiplier is solved by the dichotomy method.The two examples of the constrained damping layer of the short cylindrical shell and the long cylindrical shell are verified,and the corresponding topological configurations are obtained.Compared with the existing research,the correctness and effectiveness of the optimization method are proved.(4)According to the optimal design of constrained damping plate,the topology optimal layout of constrained damping cantilever beam is studied,and the experimental design of constrained damping layer structure of cantilever beam is carried out.The frequency response results of finite element calculation and experimental measurement are obtained respectively,and the comparison data shows the accuracy and application value of the optimization layout.Secondly,the optimization method of constrained damping cylindrical shell is applied to the damping and vibration reduction design of submarine hull surface structure.The change of mode loss factor of the third order hull is studied under the condition of reducing 50% material consumption.The layout of damping material of the hull is obtained,the frequency response of acceleration response point is analyzed,the effectiveness of topology optimization technology is proved,and the vibration reduction effect of submarine structure is improved.