Wave Based Vibration Control Method For Flexible Structures

Due to the features of light weight,high efficiency,and high precision,light flexible structures are becoming commonly used in aerospace engineering and intel igent robot manufacturing.Vibrations in the light-weighted flexible structures are easy to form and hard to be suppressed,vibration suppression of flexible structures is important to improve their working performance and to extend their service life.This thesis is devoted to the research on the wave propagation in different kinds of flexible structures and proposes the vibration control strategy based on wave theory.The main contributions of the thesis are summarized as the following:(1)For 1D gantry cranes,the wave based control methods are developed to suppress the vibration caused by the motion of loading mass based on the idea of wave absorption.First,wave based control methods are proposed based on different launch velocities for a single pendulum system.It is found that the control method based on an exponential launch velocity shows a smooth velocity curve and good robustness.Second,wave based open-loop control strategies are examined for gantry crane motion to reduce swings of a double pendulum and load hoist models,which are purposely considered to examine the influence of wave scattering and configuration change with the wave based method.For the double pendulum model,wave reflection and transmission in the system were analyzed.The gantry crane motion is determined by absorbing both the reflected waves from the mid-load mass and end-load mass through adjustment of the trolley velocity.The numerical simulation demonstrates a high efficiency for swing motion aleviation,the experimental measurement is also conducted to validate the proposed control strategy.It is also found that the suspended rigid rod model can be considered as a special case of a double pendulum model.In the load hoist model,the string length changes during the displacement of the trolley,which can be simply taken into account by modifying the wave travel ing time in a single pendulum model.The experiment is also performed to validate this model.Last,a close-loop control method is proposed for a single pendulum model.By using the feedback of the trolley and swing angle,the vibration caused by motion or residual vibration can be efficiently eliminated.(2)The utilization of coordinate transformation method to net structure is explored.For lowfrequency flexural waves,the net structure can be homogenized as a thin membrane with effective stiffness and density.For the net structures with regular triangle,square and regular hexagon lattices,their effective stiffness matrices and density matrices can be simplified to isotropic forms.As the governing wave equation of a membrane keeps form invariance,the coordinate transformation method can be used in the design of microstructure for wave propagation control.Based on a compression,“white hole” and Maxwell fisheye transformations,the required effective material parameters are obtained through the transformation method for each function.The wave propagations in the designed net structures are computed numerically to validate the proposed design method.(3)The influence of lattice configuration change on the band structure is investigated.Three kinds of flexible periodic net structures,string lattice,folded beam and folded plate are examined in detail.The dispersion relations of the string lattices with different unit cells are studied analytically.It is shown that the bandgap frequency and the wave propagation direction can be tuned by adjusting the lattice configuration.The wave dispersion and propagation features of the folded beam and folded plate models with different folding angles are examined analytically and numerically.It is shown that the structural folding gives rise to the coupling of the orthogonal waves,like transverse and longitudinal waves,creating bandgaps in the folded beam and directional bandgaps in the folded plate.The width of bandgaps changes with the folding angle.Benefiting from the coupling of wave modes,the resonance of additional stubs can easily absorb the energy of the coupled waves and form complete bandgaps.