Structural Dynamic Optimum Design Under Harmonic Force Excitations

The study of Structural dynamics optimization design plays an important role in the current structure design. It has a remarkable effect to make the natural frequency, vibration mode and displacement response of structure dynamic characteristics meet the design requirements by changing the structure of dimension parameters, geometrical, topology and layout. This paper briefly describes the research background of structure dynamic optimization. The development and present situation of study on structural dynamics optimization design in recent years are reviewed. And on this basis, topology optimization of structure under harmonic excitation are studied. Meanwhile, a new linear ultrasonic motor with reverse double foot is presented.The main research work in this paper are listed as follows:Firstly, The derivation process of the polynomial interpolation scheme and the Method of Moving Asymptotes are describes briefly. Through a classical case validates mesh dependency problems, and the value of penalty factor, filter radius, the keep score of material’s volume effect the result of topology optimization.Secondly, the minimum displacement amplitude at the designated spot of a structure is defined as the objective function subjected to the volume constraint based on the variable density method is studied, and a complete topological optimization model and method are established. Meanwhile, we study the displacement amplitude and optimum structural considering the effects of static loads. The displacement amplitude is calculated by using the modal superposition method, the sensitivity analysis of structural displacement response based on incomplete modal superposition method. In order to avoid localized modes, the polynomial interpolation scheme is used to relate material properties to element density variables. In order to avoid checkerboards, the grid filtration method is introduced. Finally, The feasibility of the proposed method is verified by numerical examples using the Matlab language programming.Thirdly, a new linear ultrasonic motor with reverse double foot is presented to precisely position a pair of micro components with inverse synchronized actions. The motor used the first longitudinal and the second bending vibration modes of rectangular plate in-plane as working mode.Excited vibrations amplified by triangular structure were superposed at double foot to form elliptical trajectories, which drive rotors to obtain linear output with opposite direction. Based onthe parameterized finite element method, parameter sensitivity analysis and structural optimization were carried out to achieve the consistency of working frequencies. Harmonic response was analyzed to verify the feasibility of motor design. Motor output performance simulation were performed by rigid-soft contact finite element model of stator and rotor. The simulation results for different pre-pressures and excitation voltages show that the motor presented has a desired stability,and the moving speed and the thrust force can reach 120mm/s and 30 N respectively.