Research On Constrained Layer Damping Topology Optimization Based On Bi-directional Evolutionary Structural Optimization Method

The thin plate structures are widely used in the modern engineering field,but the vibration problems caused by the characteristics of large area and low rigidity of the thin plate structures are also very common.Constrained damping has very good energy dissipation characteristics.It is an important means to suppress structural vibration by laying constrained damping on the thin plate structure,which is widely used in the design of vibration reduction of thin plate structures in the engineering.Scholars’ researches on the constrained damping mainly focuses on the overall laying of damping materials.However,many thin plates structural designs in engineering often has special requirements.The overall laying of constrained damping not only increases production costs and structural weight,but also does not meet the lightweight design guidelines on structures.Therefore,it is of great significance to study the optimization of the placement of the constraining layer damping on the surface of the thin plate structure.This paper studies the optimal damping material distribution of the constrained damping structure,including the following main contents:Establish a finite element model of constrained damping structure.A finite element model of rectangular element with constrained damping structure is established.The deformation relationship of the constrained damping structural element is analyzed.The complex modulus model is used to describe the constitutive law of the damping material,and the modeling of the finite element model of the constrained damping structure is completed based on the energy method.The accuracy of the established finite element model is verified by comparing with the relevant literature.Topological optimization designs is performed on the optimal distribution of the constrained damping attached to the thin plate structure.First,a mathematical model of topology optimization based on the bi-directional evolutionary structural optimization method is established.The optimized objective function is to maximize the modal loss factor of the constrained damping structure,and the amount of the constrained damping material is the constraint condition of the mathematical model.Based on the modal strain energy method,the elements sensitivity of the topology optimization progress is derived.The meshindependent filter method is used to reduce the checkerboard pattern problem of the optimization process.The update strategy and convergence conditions of the topology optimization model are analyzed.According to the analysis of the basic theory of the bidirectional evolutionary structural optimization method,the topology optimization process of the constrained damping structure is compiled.The topology optimization design of the constrained damping layout of cantilever beams and four-sided fixed supported plates is given.A frequency response test system was establishing,and the modal test of the cantilever beam and the four-sided fixed plate damping structure was carried out by the force hammer excitation method,which verified the accuracy and effectiveness of the optimization results.For a certain commercial vehicle floor structure,the transmission loss of the vehicle floor is studied based on the reverberation-anechoic chamber method and the modal participation factor method,and the first-and the sixth-order mode has main effects on the transmission loss of the cab floor.The constrained damping treatments are performed on these two main modes to improve the transmission loss of the vehicle floor,and the bi-directional evolutionary structural optimization method is used to realize the optimal treatment of the constrained damping.The simulation results show that the restraint damping treatment for the cab floor structure can improve its transmission loss.With full-coverage constrained damping,the transmission loss of the floor at the first-and sixth-order modes are 4.8d B and7.5d B,respectively,which is increased by 2.7d B and 3.9d B compared to the floor that uncovered constrained damping.When the first-and sixth-order modes are optimized respectively,the transmission loss at the first-and sixth-order modes after optimization is reduced by 0.7d B and 1.1d B respectively compared with the floor with full coverage constrained damping.When the first-order and sixth-order modes are optimized at the same time,the transmission loss at the first-and sixth-order modes after optimization is reduced by 1.2d B and 1.7d B respectively compared with the floor with full coverage constrained damping.The difference between the optimized cab floors transmission loss and the fully covered constrained damping is smaller,but the amount of material is reduced by 75%compared to the fully covered constrained damping,which effectively improves the use of constrained damping materials.