| Acoustic coating is a important components for achieving acoustic stealth of underwater vehicles,mostly composed of rubber damping materials with periodic cavity structures,which play a role in reducing underwater vehicle noise and absorbing sonar sound waves.However,the sound absorption properties of periodic cavity structures under hydrostatic pressure will severely decrease.The multi-layer composite sound-absorbing material itself does not have a cavity structure,and the acoustic impedance design between each layer is formed through rubber layers with different mechanical properties to consume acoustic energy.It is considered to have good pressure resistance and acoustic performance.At present,there are still shortcomings in the research on multi-layer composite sound-absorbing materials in terms of simulation methods and optimization of sound-absorbing performance.Therefore,establishing a more comprehensive simulation method to explore the impact rules of sound-absorbing performance of multi-layer composite sound-absorbing materials,and optimizing the structure with excellent sound-absorbing performance is of great significance for the practical production guidance of acoustic sound-absorbing materials..This work establishes a transfer matrix mathematical model for calculating the acoustic properties of multi-layer acoustic coatings.Experimental samples are prepared to verify the accuracy of the model,and a Windows GUI application is developed for this model.Based on this mathematical model,the impact of dynamic modulus distribution,thickness distribution,Poisson’s ratio distribution,and the number of layers of the rubber layer of the multi-layer acoustic coating on the reflection coefficient,transmission coefficient,and sound absorption coefficient of the coating is investigated.During this process,a "modulus sandwich" structure with high internal storage modulus and low on both sides is discovered,and its sound absorption properties are superior to the traditional acoustic impedance gradient structure.Finally,the optimal solution for the sound absorption properties of the multi-layer acoustic coating is determined.The specific research contents and results are as follows:(1)Particle stress and particle vibration velocity are used as transfer parameters to construct a fourth-order transfer matrix mathematical model.This model can be used to calculate the reflection coefficient,transmission coefficient,sound absorption coefficient,and transmission loss of multi-layer composite acoustic coatings,as well as analyze the behavior of sound waves that are obliquely incident upon the coating.To make the model more user-friendly,a Windows GUI application has been developed.(2)The mathematical model is compared with the finite element method using the same working conditions established through the reference of other researchers.Results show that the accuracy of the mathematical model is equivalent to that of the finite element method.To further verify the model’s validity,two SBR samples with different carbon black mass fractions(0 and30)are prepared and compounded into a double-layer structure acoustic coating sample.The sample’s acoustic and dynamic mechanical properties are tested,and the average relative error between experimental and simulation values is 5.23%,within the allowable range,thus demonstrating the model’s effectiveness.(3)The dynamic modulus distribution,thickness distribution,and Poisson’s ratio distribution of rubber layers in a multi-layer composite acoustic coating are explored using this model,as well as the effects of layer number on the reflection coefficient,transmission coefficient,and sound absorption coefficient of the coating.The results show that the layer number of the multi-layer composite structure rubber has no significant effect on the sound absorption performance under the condition of fixed overall modulus gradient of the coating.The storage modulus is proportional to the acoustic impedance of the material and inversely proportional to the transmission loss,while the loss factor is proportional to the acoustic impedance and transmission loss of the material.The distribution of storage modulus has a greater impact on the sound absorption performance,acoustic impedance,and transmission loss of the material than the loss factor.In addition,appropriately increasing the thickness ratio of the low modulus layer in the material is beneficial to improving the sound absorption performance.The addition of a small amount of high Poisson’s ratio layer in the covering layer is beneficial for low-frequency sound waves to enter the covering layer,improving the sound absorption performance of the covering layer in the low-frequency range.(4)For the acoustic coating with acoustic impedance gradient structure,the sound absorption properties of the decreasing impedance layer by layer structure is higher than that of the traditional increasing impedance structure.On this basis,the design of increasing thickness layer by layer can make its sound absorption properties higher.After optimization design,the average sound absorption coefficient of the acoustic impedance gradient structure is31.1% higher than that of the SBR covering layer with 30 parts of carbon black.(5)For the acoustic coating with sandwich modulus structure,the acoustic impedance mismatch effect between the high-modulus layer in the middle and the low-modulus layer on both sides significantly improves the energy consumption of sound waves within the material,making its sound absorption properties better than that of the impedance gradient structure.On this basis,properly increasing the thickness of the low modulus layer on the back of the covering layer is more conducive to the sound absorption of the material.The average sound absorption coefficient of the optimized structure is 39.6% higher than that of the uniform structure SBR. |