Abstract
Application of level set method to optimize the topology of free damping treatments on plates is investigated. The objective function is defined as a combination of several desired modal loss factors solved by the finite element-modal strain energy method. The finite element model for the composite plate is described as combining the level set function. A clamped rectangle composite plate is numerically and experimentally analyzed. The optimized results for a single modal show that the proposed method has the possibility of nucleation of new holes inside the material domain, and the final design is insensitive to initial designs. The damping treatments are guided towards the areas with high modal strain energy. For the multimodal case, the optimized result matches the normalized modal strain energy of the base plate, which would provide a simple implementation way for industrial application. Experimental results show good agreements with the proposed method. The experimental results are in good agreement with the optimization results. It is very promising to see that the optimized result for each modal has almost the same damping effect as that of the full coverage case, and the result for multimodal gets moderate damping at each modal.
Highlights
In the automotive industry, the door, roof, dash, floor, and cab back panels of automobiles are always treated with damping materials to reduce the structure-borne noise. e effectiveness of damping treatments depends upon design parameters such as damping material types, locations, and size of the treatment
Here, we proposed an improved CAE methodology for location and size optimization of damping treatment, which is simple for industrial application. e normalized modal strain energy (MSE) can be expressed as
Treatments with shape (a) and shape (b) achieve max damping ratio at the 1st modal and 6th modal, respectively, for 50% coverage, and treatment with shape (c) gets moderate damping at each modal but total max damping ratio is achieved. e experimental results are in good agreement with the optimization results. e differences between full-covered case and optimized result for each modal are very small while 50% damping material is saved
Summary
The door, roof, dash, floor, and cab back panels of automobiles are always treated with damping materials to reduce the structure-borne noise. e effectiveness of damping treatments depends upon design parameters such as damping material types, locations, and size of the treatment. Zheng et al [4] studied the optimal layout of PCLD patches on beams for minimization vibration energy based on the analytical model using GA with penalty functions for constraints All of these studies mentioned above which performed shape or size optimization are at the level of macroscopic design, using a macroscopic definition of geometry given by, for example, dimensions or boundaries. E classical level set optimization method was adopted, which has the drawbacks that the optimization result is dependent on the initial design and has difficulty in solving Hamilton–Jacobi partial differential equation (H-J PDE) numerical problems. E main goal of this paper is to investigate the use of topology optimization based on a level set-based parameterization method to optimize free damping treatments with partial coverage to improve the damping characteristics of vibrating plates.
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