Research On The Control Of Flexural Waves In The Thin Plates Metamaterial Based On The Coordinate Transformation Theory

Acoustic materials is a kind of artificial periodic structure which is composed of units in subwavelength scales.In accordance with manipulation of the unit structure on the elastic wave,the work aims to achieve an unusual physical effect,like band-gap in low-frequency,acoustic focusing on plates and so on.The noise and vibration control for the structure is an urgent problem to be solved in the engineering field.The acoustic metamaterials provide a new concept and way for the research of the noise and vibration control and the engineering design.The theory of acoustic transformation guides a significant direction for the exploration of the application of the acoustic metamaterials,which can help to achieve an elastic wave control featuring delicate and complex in the investigation of invisible cloak and acoustic wave spin,so to improve the design flexibility greatly.The paper studies the feasibility of employing the acoustic transformation theory to the design of the elastic plate composed of metamaterials,and then to control the plate’s flexural wave to spread in a free manner.The work deeply analyzes the mechanism of the control of the elastic wave,and the influencing factor and laws.Further work experimentally validates the feasibility of the theory.The conclusions and the main contents are presented as follow:1.The study introduces the coordinate transformation design into the basic theory of the flexural wave control for the plate,and then analyzes the stability of the formula of the flexural dynamics in coordinate transformation.Based on the continuous coordinate transformation and the finite-embedded coordinate transformation,the work deduces the property equation for the flexural wave cloaking and the flexural waveguide at a free angle.The model is established on the basis of the flexural wave cloaking and sound-waveguide design with the multi-layer medium theory.2.Based on the finite element model,the work studies the influence and laws of the flexural waveguide for the plate-metamaterials,finding that the property can help control the wave-spreading in band-frequency.It deeply reveals the mechanism of the broad-band control.3.The investigation comes up with the way to employ the homogenous medium to conduct the metamaterial flexural waveguide design.The samples are fabricated.Further work experimentally validates the control effect of the flexural wave for the plate metamaterial based on the coordinate transformation design.In conclusion,the paper clarifies the feasibility of the way by employing the coordinate transformation theory into the control of the flexural wave for the plates.Meanwhile,the study paves a new road for the vibration and noise control on the plate-structures,and it is of great theoretical and practical importance for further exploration of the acoustic metameterial.