Investigations On Bandgap Tuning And Sound Insulation Characteristics Of Metamaterial Structures

With the development of sicence and technology,the demand for the vibration and noise reduction technology has become increasingly urgent in aerospace,marine,transportation,construction and other engineering fields.At present,there are many mature theories and methods for the vibration and noise reduction,including active control,passive control and semi-active control.The passive control technology has some advantages such as its simple construction,low cost,and independent of external power.However,the disadvantages are also obvious.Once the structure is designed,it can only adapt to the certain working condition for vibration reduction.But the active and semi-active control can often meet the requirements of vibration reduction under various working conditions.In recent years,phononic crystals and metamaterial structures have attracted the attentions of many scholars.This is because phononic crystals or metamaterial structures will show the characteristic of frequency band gap.It means that the elastic wave in the band gap range can not propagate in the structure.This property provides a new idea for vibration and noise reduction technology.In this paper,based on the theory of phononic crystal and metamaterial structures,the metamaterial structures are designed by combining the piezoelectric patches with beam and plate structures.Adjustable band gap characteristic of metamaterial structure is realized by using the active control strategy.In addition,an acoustic metamaterial plate with spiral cavity is designed,and its sound and vibration isolation characteristics are investigated.The main works are as follows:A laminated piezoelectric metamaterial beam with the function of actively tuning the band gap is designed,and a displacement feedback active control strategy is proposed to provide active stiffness for metamaterial beam,which can be used to enhance the vibration bandgap characteristics of the laminated piezoelectric metamaterial beam.The equation of motion of metamaterial piezoelectric beam is established by using Hamilton's principle,and the spectral element method is used to solve the equation of motion to obtain the frequency responses of the structures.The frequency band gap characteristics of metamaterial piezoelectric beam are analyzed by the frequency response curves.The frequency band gap of the structure is tuned by adjusting the control gain.The results are verified by using the finite element software,and the feasibility of the control strategy is verified by experiments.In addition,the effects of cell number,fiber laying angle and displacement feedback gain on the band gap characteristics of the metamaterial piezoelectric beams are discussed.A displacement and acceleration feedback control strategy is proposed to provide active stiffness and inertia for the structure,the active tuning characteristics of the vibration band gap of the piezoelectric metamaterial plate structure is realized,and a local resonance band gap is obtained.The frequency response curves of the piezoelectric metamaterial plate are calculated by the spectral element method,and the frequency band gap characteristics are analyzed.From the investigations,it is found that the widths of the zero-frequency band gap and the band gaps in the middle and high frequency regions can be widened effectively by increasing the displacement feedback control gain,and due to the application of acceleration feedback active control strategy,a local resonance band gap can be generated.In addition,the influences of the main structure size and material parameters on the band gap characteristics are investigated.A laminated metamaterial plate with adjustable band gap properties is designed by periodically distributing the Macro fiber composites(MFC)piezoelectric patches along the plate.The MFC piezoelectric materials are used as actuators and sensors of the structure,and acceleration feedback active control strategy is used to adjust the frequency band gap characteristics of the MFC piezoelectric laminated metamaterial plate.Frequency response curves and attenuation constants of the structure are calculated by the spectral element method and transfer matrix method.The effects of parameters such as the fiber laying angles of MFC piezoelectric patch and laminated base plate on the frequency band gaps are analyzed.The investigation results show that the width of the zero-frequency band gap will become wider with the increase of the fiber laying angle of the laminated base plate,and better band gap characteristics can be obtained in the low and high frequency ranges when smaller fiber laying angles of the MFC piezoelectric patch are chosen.A displacement and velocity feedback active control strategy is proposed,which organically combines the band gap characteristics wtih the vibration active control function of the piezoelectric metamaterial Mindlin plate.The active stiffness and damping are provide to the structure,the active tuning of the band gap characteristics of the MFC piezoelectric metamaterial thick plate is realized,and the vibration responses of the structure in the passbands can be greatly reduced.From the investigations,it is found that the width and position of the band gaps can be tuned effectively by adjusting the displacement feedback gain,and with the increase of velocity feedback control gain,the pass bands in the middle and high frequency ranges will disappear,and the vibration of the structure will be greatly attenuated.The sound transmission loss of the MFC piezoelectric metamaterial thick plate is calculated by the finite element software.It is found that the structure has good sound insulation characteristics in the frequency band gap regions.A spiral cavity metamaterial lattice plate with super sound insulation performance is designed,and the influence of structural size and material parameters on the sound insulation characteristics of the structure is clarified.The vibration mode characteristics and the sound transmission loss curve of the structure are analyzed and calculated by the finite element software,and the results are verified by the acoustic experiment.The results show that the metamaterials plate with spiral cylindrical cavity has good sound and vibration insulation characteristics.The sound insulation performance of the structure can be improved by selecting the appropriate number of spiral turns and diameter.