Properties Of Wave Propagation And Vibration In Multistable Mechanical Metamaterials

Structural vibration deteriorates the performance,safety,reliability and service life of equipment,and thus vibration control is a vital way to improve product quality.However,achieving the low-frequency and broadband vibration control of structures remains a major challenge,which calls for new theories and technologies.Mechanical metamaterials are artificial periodic structures with extraordinary mechanical properties whose properties depend on the geometry of the micro units rather than the material composition.Mechanical metamaterials have exotic mechanical properties including negative effective mass,negative Poisson’s ratio,negative modulus,folding,and chirality.Moreover,the bandgaps in metamaterials for stopping elastic waves provide a new technical approach for elastic wave control and a novel idea for breaking through the bottleneck of vibration reduction technology.Multistable mechanical metamaterials have attracted extensive attention from academia and engineering areas owing to their broad design space,excellent deformability,unconventional mechanical properties,and wide application prospects.Aiming at the requirements of tunable,ultra-low frequency and ultra-wideband vibration reduction of equipment,this thesis studies the elastic wave propagation,dynamic properties,vibration isolation and vibration reduction characteristics of metastable mechanical metamaterials.The main contributions of this thesis are as follows:1.The phenomenon of 1/2 sub-harmonic resonance in bistable structure is clarified,and the parameter effect law of its vibration isolation characteristics is analyzed.For a typical bistable structure,i.e.,the bistable buckling structure,the generation process and parameters influence of the 1/2 sub-harmonic resonance are studied based on analytical,numerical and experimental methods.Harmonic balance and numerical integration method are used to reveal the influence of parameters such as negative stiffness coefficient,nonlinear coefficient,and excitation amplitude on the vibration isolation characteristics of bistable structures.2.The properties,including the tunable and amplitude-dependent bandgaps and the oscillator snap-through behavior in bistable periodic structure are studied.Based on the numerical integration method,the steady harmonic and shock wave propagation in the infinite bistable period structure are studied.The regularity and local intrinsic randomness of the oscillators’ snap-through sequence under harmonic and shock wave are analyzed,and the influences of parameters are clarified.The distribution law of energy in bistable periodic structure is analyzed.The low frequency and broadband wave attenuation properties and mechanism of bistable periodic structure are revealed.3.The asymmetric deformation mechanism of the symmetric multistable configuration is revealed.Based on finite element simulation and experiment,the thesis presents the intrinsic static asymmetric deformation phenomenon of symmetric multistable configuration.Based on analytical analysis,the asymmetric deformation mechanism caused by unstable bifurcation is revealed.Furthermore,a variable stiffness element with symmetrical deformation properties is proposed and its symmetric deformation and stable tuning properties are verified.4.The wave propagation and vibration suppression properties of tunable metamaterials are studied.A multistable mechanical metamaterial with tunable bandgap was designed based on the local resonance mechanism.The longitudinal wave in 1D tunable metamaterials and the flexural wave in both 1D and 2D tunable metamaterials are analyzed.The mechanisms for tunable wave propagation and vibration of the bandgap are revealed.The tunable vibration properties of tunable metamaterials are verified by vibration experiments.In summary,we systematically investigate the properties and mechanism of elastic wave propagation in multistable mechanical metamaterials and present several design techniques,which provide new method for elastic wave regulation,and preliminarily realizes the tunable,low-frequency,broadband vibration suppression of 1D and 2D metamaterials.The results provide an important theoretical and technical basis for the field of multistable mechanical metamaterials,and provide a new technical approach for the vibration reduction of equipment and structures.