Dynamic Optimization Method Research On Vibration Of Constrained Damping Plate

Mechanical structural vibration is a key factor to cause decline in the quality and efficiency of work machine, it is also the main root to cause structural noise, sometimes it would even bring major problems such as structural vibration fatigue. And bring heavy losses to people’s production and life. Aims to lay a foundation for the technical design of dynamics vibration of engineering structures plate. this paper focused on the research of dynamics vibration optimization method for constrained damping plate, and main contents are as follows:(1) In view of adverse consequences caused by vibration of the various types of structure, proposed some commonly used vibration optimization method, focusing on interpretation of the topology optimization methods. Briefly introduces the concept of topology optimization methods, as well as common used variable density method and evolutionary structural optimization methods. The mathematical model of variable density method and the iterative solution model is given, Analysis some commonly used topology optimization method, such as Lagrangian multiplier method、 Sequential linear programming and genetic algorithm, and introduces the advantages and effectiveness of these types of algorithms.(2)Studying the damping characteristics and dynamic model of viscoelastic damping material, given out the oscillation equation of constraint damping plate. Derived the model of finite element method to solve the numerical and modal damping ratio computational of constrained damping plate. Expound Krylov condensation theory, and effectively apply this theory to the dynamics calculate of the constrained damping structure.(3) Based on variable density topology optimization method achieve the dynamic optimized of constrained damping plate damping characteristics. Established the optimization model of constrained damping structure and derived the expression of modal damping ratio. Analysis the sensitivity of Structure. Proposed the method of independent acuity filtering to suppress the checkerboard numerical instability phenomenon, and introduces MAC matrix to track the optimization of modal shape, in order to ensure the smooth progress of the optimization process. Through the example is given to analysis the optimization effect of variable density method to optimize freedom damping and constraint damping structures. When optimized, design the modal damping ratio maximum as objective function, volume for 50% of raw materials as the constraint conditions. Finally obtain a good optimization results. Compared with freedom damping, the effect of constrained damping’ optimization is better.(4) Based on the topological evolutionary optimization method to achieve topology optimization layout of constrained damping plate viscoelastic damping material, and compared with the variable density method. Establish topology optimization model of constrained damping plate. Derived the sensitivity of modal loss factors for the design variables, using the independent grid filtering technique to suppress the numerical instability phenomenon. Finally, through the example shows the effect of evolutionary optimization method and compared with variable density method. Through these two methods can get a good topology optimization configuration, and can effectively improve the dynamic performance of structure, and achieve the damping effect. The optimized results obtained are closely related with the properties of the material itself(thickness, density, elastic modulus and Poisson’s ratio, etc.) and external constraints conditions.