Research On Dynamic Topology Optimization Of Thin Wall Structure With Constrained Layer Damping Treatment

Thin wall structure can undertake a considerable load with a small weight cost and has good heat dissipation performance, so it is widely used in aerospace and automobile industries. Lightweight becomes an important part in product design with the modern industrial requirements of energy conservation and environmental protection, and when vibration and noise of thin-wall structure become increasingly outstanding. The constrained layer damping(CLD) structure can effectively supress the broadband vibration and noise. In the traditional design of vibration reduction, CLD material covered on the surface of the whole structure effectively suppress structural vibration and noise, and improve the quality of the additional structure at the same time. This dissertation analyzes the finite element modeling and distribution characteristic of the thin-wall plates with CLD treatments, and uses topology optimization method to seek the optimal layout of CLD material. A new method is proposed to improve the utilization rate of CLD material and the ability to suppress vibration. The features obtained in this dissertation are mainly as follows:According to the constitutive relation of elastic and visco-elastic materials, the finite element model of CLD plate is builded with energy method. The validity of finite element model is verified by the example. It is analyzed that the consumption and distribution of CLD material affects the vibration characteristics of the cantilever plate. The necessity of optimizing the layout of CLD material is illustrated.The maximum of modal loss factor is considered as the objective function in the topology optimization model. The sensitivity of the objective function to design variables is deduced by using the modal strain energy method. Mesh-independent filter method is used to remove checkerboards. The rules of the delete and add element are set and topology optimization process based on Bi-directional Evolutionary Structural Optimization(BESO) method is established. The BESO is proposed to search the optimal layout of CLD material of the cantilever plate with CLD treatments. The results are compared with those from the Evolutionary Structural Optimization(ESO) method. It is demonstrated clearly that the proposed BESO method can achieve a better layout of CLD material than that of ESO method. The effectiveness of the proposed BESO method is thus identified.The mass matrix and stiffness matrix of CLD plate are reassembled based on SIMP interpolation model. The topology optimization model is established with minimizing the reciprocal of modal loss factor as objective function. The mode-tracking method is used to avoid altering modal order. The sensitivity of the objective function to design variables is deduced and mesh-independent filter method is used to remove checkerboards. The optimization procedure is complied based on the SIMP interpolation model and MMA. With the cantilever plate and two short side fixed plate as the examples, the layout of CLD material is optimized to verify the applicability and effectiveness of the proposed optimization method.A topology optimization method is proposed to minimize the resonant response of plates with CLD treatment under specified broadband harmonic excitations. The topology optimization problem is formulated and the square of displacement resonant response in frequency domain at the specified point is considered as the objective function. The derivative of modal damp ratio, which will give rise to error in sensitivity analysis and produce a deviation from the optimal layout of constrained layer damping treatment in structures, is not considered in the conventional sensitivity analysis method. An improved sensitivity analysis method considering the derivative of modal damp ratio is developed to improve the computational accuracy of the sensitivity. The evolutionary structural optimization(ESO) method is used to search the optimal layout of CLD material on plates. The layout of CLD material of the cantilever and four edges fixed plate with CLD treatment is optimized by the proposed topology optimization method. The results show that the optimal layout of CLD treatment on the plate from the proposed topology optimization using the conventional sensitivity analysis or the improved sensitivity analysis can both reduce the displacement resonant response. However, the optimization method using the improved sensitivity analysis can produce a higher modal damping ratio than that using the conventional sensitivity analysis and develop a smaller displacement resonant response. It is seen that the improved sensitivity analysis method considering the derivative of modal damp ratio is more effective.A topology optimization method is proposed to design the optimal layout of CLD material in structures subjected to harmonic excitations or brand harmonic excitations. The minimization of vibration displacement amplitude at specified one or several points in structures are selected as the design objective. The complex mode superposition method is used to solve the kinetic equation of CLD structure. The characteristics and the applicable scope of the direct method and the adjoint method are analyzed and the adjoint method is determined to calculate the sensitivity of the dynamic optimization model through the case analysis. The MMA is used to search the optimal layout of CLD material on plates and the optimization procedure with minimization of vibration displacement amplitude as the design objective is complied. The validation of the method is carried out by numerical cases.Finally, the experimental validation is carried out for the optimal layout of CLD plates. The validity and effectiveness of the proposed topology optimization method is verified.