Research On Topology Optimization Methods For Low Noise Design Of Thin Plates Base On Damping Energy Dissipation

The method of increasing system damping energy dissipation is the most direct and effective approach in the design of low noise plate strucutres, as it not olny reduce the peak value of the structural resonance, but also enhance the vibration resistance and dynamic stability of the system. Light weight is very important in composite strucutre design, so the damping materials are only located on certain area partially. However, it is difficult to find the optimal location using traditional optimization methods considering the complexity of the system dynamic chacteristic. This dissertation analyze the finite element modeling and distribution characteristic of the composite plates with Passive constrained layer damping (PCLD) treatments or PZT shunt damping treatments, and use topology optimization method to find the optimal topology of damping layers. The features obtained in this dissertation are mainly as follows:A general, accurate, easy-to-use interface finite element that can directly couple together the base structure plate elements, the viscoelastic layer and the constraining layer plate elements, is introduced. The base layer and constraining layer is modeled with plate elements based on Love-Kirchhoff classical plate theory. The modal loss factor is calculated by means of modal strain energy method. Then, Numerical model is adopted to verify the modeling method. In order to speed up, the improved reduced system based on iteration is used. Then, the relation between the distribution of PCLD and the damping effects of a cantilever beam is analyzed.The finite element modeling is established based on the solid isotropic material with penalization (SIMP) model. To eliminate local mode, the penalization factors are analyzed. Then, the optimizer is chosen as the method of moving asymptote (MMA) approach. The design sensitivities filtering technology is applied to remove checkerboards and a mode-tracking method to avoid altering the order of the modal. The design sensitivities of the modal loss factor is then calculated. A general flow of topology optimization is proposed. The validation of the method is carried out by numerical cases.The sound radiation power of the PCLD damped composite plate is obtained by finite element method-boundary element method (FEM-BEM) approach, and its sensitivity is analyzed then. By using the SIMP model and MMA optimizer, the topology of the PCLD is optimized to minimize the sound power of plates at a certain frequency. The sound radiation modal of the plate is studied and another objection function for sound power optimization is proposed. This method can minimize the sound power peak value of a certain structural modal, but it just suit for the case that the modal is in very low frequencies.The layerwise linear of the laminated plates is assumed, and the displacements and transverse shear stresses in the interface of each layer are continuation. Then, the mechanical-electrical coupling model is deduced form Hamilton’s principle and the second type piezoelectric equation, and then verified by two numerical example. Considering the relation of the circuit voltage and the current, the equation of the PZT shunt damping system is given. Some common shunt circuits are analyzed numerically.A closed-loop quasi-static energy cycle method is introduced to demonstrate the meaning of the general electromechanical coupling coefficient (GEMCC. Then, the relation of the damping energy dissipation capability and the GEMCC is analyzed. The SIMP model and the topology optimization method of the PZT composite plate are proposed. After that, Two structures are studied numerically. The total charge of the polarization surface is calculated also. Considering the design connectivity of the PZT patch, a bionic topology optimization is proposed based on the growth process of root system of plants. The optimization flow is then illustrated. The feasibility of the method is validated by numerical examples.Finally, the experimental validation is carried out for the plates with topology optimized PCLD treatments. The experimental results show that the proposed topology optimization is an efficient method for damped composite plates low noise design.