Analysis Of Reflection Coefficient Of One Dimensional Acoustic Black Hole Structure

The acoustic black hole structure,abbreviated as ABH,is a new and efficient structure for vibration reduction and noise reduction.Its exquisite structure form can effectively control the elastic wave,which is expected to replace the traditional vibration reduction and noise reduction method with large-area attached damping layer.The ideal one-dimensional acoustic black hole structure is a power-law wedge-shaped structure based on the basic smoothing assumption.When the wave is transmitted to the end structure above the second power,there is no reflection.However,in practical engineering,the acoustic black hole structure inevitably has truncation due to processing accuracy and other factors,and the reflection of wave is inevitable at the truncation.In order to measure the performance of the acoustic black hole structure,the reflection coefficient of the acoustic black hole structure becomes an important evaluation index.At present,there are mainly geometric acoustic method and impedance method to solve the reflection coefficient of acoustic black hole in theory,but most of them are applied to single solution to verify the experimental results,lack of expansion analysis and rule summary of multiple examples,and rely on basic smoothing assumption,the results are not completely accurate.Although the impedance method does not rely on the basic smoothing assumption,due to the complexity of the algorithm,there is a lack of accurate algorithms and examples.In order to sum up the variation rule of reflection coefficient based on ABH by using the geometric acoustic method,it is necessary to increase the realizability of the geometric acoustic method.In this paper,the longberg method and the geometric acoustic method are combined to realize the fast solution of reflection coefficient of acoustic black hole.Based on the software of this method,the reflection coefficient curve of acoustic black hole can be obtained by inputting any parameter.On this basis,the influence of various parameters on the reflection coefficient of acoustic black hole is analyzed,and the variation rule of stable length and thickness of stable damping layer with the geometric parameters of ABH structure is determined.Finally,we get the properties of acoustic black holes,which can guide the optimization design of acoustic black holes.In order to solve the complex variable differential equation in the impedance method,this paper combines the Runge Kutta method and the smooth curve method to solve the reflection coefficient,and obtains a curve similar to the geometric acoustic method.According to the lack of stability of the explicit method of Runge Kutta method(RKF4-5),the implicit algorithm of RKFGI4-6 is extended by combining the adaptive idea of fairberg and the implicit method of Gauss,so that the program can automatically carry out multiple iterations to solve the implicit nonlinear equation.To some extent,this method increases the accuracy of impedance calculation,and through the combination of Runge Kutta method(RK)and smoothing method to eliminate the oscillation,a more accurate reflection coefficient curve of acoustic black hole structure is obtained.The size of the end of the ABH structure is too thin and easy to deform,while increasing the overall thickness of the ABH structure will make the reflection coefficient rise sharply,so that the ABH structure fails.Therefore,it is difficult to find the ABH structure which can be machined and make the reflection coefficient reach the effect of vibration absorption.In order to improve the machining feasibility of the ABH structure,this paper combines the machining and the procedures and laws obtained from the geometric acoustic method to find a method that can not only obtain good machinability but also greatly affect the reflection coefficient,and obtains two improvement schemes with high feasibility.