Study On Flexural Wave Band Gaps And Vibration Characteristics Of Periodic Acoustic Black Hole Structure

The vibration and noise reduction level of ship structures can greatly affect the working performance of ships.How to effectively improve the vibration and noise reduction level is of great significance in the field of ships.As a continuous variable cross-section structure,acoustic black hole has the characteristics of gradual impedance,which can effectively control the elastic wave.It is a new vibration-proof structure.The phononic crystal is an artificial periodic composite structure,which can generate elastic wave band gap and obtain better vibration characteristics at the corresponding frequency.In order to further improve the vibration reduction performance of acoustic black hole structure for its application in the field of ships,a periodic acoustic black hole structure is constructed by combining acoustic black hole with phononic crystal.The bending band gaps and vibration characteristics of periodic acoustic black hole structure are studied from the perspective of phononic crystal.It aims to provide a new type of vibration reduction measures to improve the vibration suppression ability of ship structureFirstly,the calculation methods of bending wave band gap of periodic acoustic black hole beam are studied based on Euler-Bernoulli beam theory.Periodic acoustic black hole beam belongs to one-dimensional phononic crystal,so the transfer matrix method and plane wave expansion method are selected to calculate the band gap of the structure,and the band gaps given by the two methods are compared.When using the transfer matrix method to calculate the band gap,due to the variable cross-sectional characteristics of the acoustic black hole,the acoustic black hole cell needs to be divided into countless small pieces,and the deformation and force of the structure are selected as the initial parameters to reduce the amount of calculation.The plane wave expansion method uses the consistency of reciprocal space and wave vector space to expand the structural parameters and displacement solutions of acoustic black hole in the wave vector space by Fourier series.The dispersion curve is obtained by solving the wave equation.The results show that the band gaps obtained by the two methods are completely consistent,which verifies the accuracy of the methods and provides a theoretical basis for the following analysis of the band gap characteristics of structures.The bending wave band gap of the periodic acoustic black hole beam structure is calculated according to the given methods,and the vibration transmission characteristics of the finite periodic structure are compared and analyzed by using the finite element method.The periodic constant cross-section beam and periodic wedge beam are selected as the comparison objects to verify the advantages of periodic acoustic black hole beam in vibration characteristics.The effects of beam width,period number and material parameters on the structural band gap and vibration characteristics are analyzed.The influence of damping layer position and thickness on vibration characteristics is analyzed by combining damping with acoustic black hole,which improves the vibration reduction characteristics of periodic acoustic black hole structure.To further broaden the band gap of periodic acoustic black hole structure and make the vibration suppression frequency adjustable,the piezoelectric shunt circuit is introduced into the periodic acoustic black hole beam.Piezoelectric materials have the electromechanical conversion ability.Through the external circuit,the vibration energy of the structure is converted to electrical energy and consumed,so the vibration damping capacity is improved.When the circuit contains inductance components,the circuit will resonate,and the periodic acoustic black hole structure will produce a locally resonance band gap at the corresponding frequency,and the flexural wave will be greatly suppressed when it propagates in this frequency band.Through the piezoelectric equation,the mechanism of the locally resonant band gap generated by the piezoelectric shunt circuit is studied and the influence of different circuits and parameters on the band gap of the structure is analyzed.The results show that the introduction of negative capacitance can effectively broaden the locally resonant band gap and attenuation coefficient,and greatly improve the vibration damping characteristics of the structure.Slab structure is a common structure in ship structure.The study of vibration reduction performance of plate structure has a strong reference for improving the vibration reduction performance of ship structure.Therefore,the periodic acoustic black hole is extended to the grillage structure,and the finite element method is used to analyze the vibration characteristics of the grillage structure.For thin plates,the periodic acoustic black hole beams are laid on the plate at a certain interval to form a periodic acoustic black hole grillage structure.Compared with light plate and constant cross-section beam-slab structure,acoustic black hole beam-slab structure has great advantages in vibration reduction performance in partial frequency bands.For the thick plate,the periodic acoustic black hole plate is formed by the periodic reduction of the internal thickness.The analysis shows that the vibration attenuation of the plate structure is obvious.In order to improve the stiffness of the structure,a certain number of stiffeners are laid on the acoustic black hole plate,and the configuration of the stiffened structure is designed and improved,so that the stiffened acoustic black hole plate structure has good vibration damping characteristics on the basis of considering the stiffness.The periodic acoustic black hole beam and plate frame structure studied in this paper combines the advantages of acoustic black hole and phononic crystal,and introduces new vibration reduction measures such as piezoelectric shunt damping,which has good band gap characteristics and vibration damping performance in a relatively low frequency band.It provides guidance for structural vibration reduction in practical ship engineering,and also provides reference for the application of acoustic black hole in ship engineering.