Study On Inversion Method Of Acoustic Parameters Of Viscoelastic Materials

With the continuous development of underwater acoustic technology,viscoelastic material,as an acoustic material that is widely used on the surface of underwater vehicles and plays an important role in reducing vibration and noise,has attracted increasing attention.The characteristic of this material lies in the use of acoustic damping to convert incident sound energy into heat energy,thereby reducing the energy of reflected sound waves and reducing the target strength of itself.Mastering the key performance of materials is a prerequisite for efficient use of materials.The traditional inversion method is slow and inaccurate of viscoelastic acoustic material parameters based on sound tube measurement.In this paper,a method for inversion of complex longitudinal and shear wave velocities of viscoelastic materials based on multimodal decomposition and spherical harmonic domain transformation is proposed.The research work is as follows:1.Based on the viscoelastic material theory model and its longitudinal vibration mathematical model,the Sturm-Liouville(S-L)equation on the complex longitudinal wave velocity of the viscoelastic material is derived.Based on the multimodal decomposition method,the complex plane rooting problem of complex longitudinal wave velocity transcendental equation is transformed into the expansion coefficient system matrix eigenvalue decomposition problem,and the expansion coefficient system matrix in three typical backing cases is derived.The accuracy of the method was verified by theoretical calculation and finite element simulation of viscoelastic test samples with different thicknesses.The effects of the multimodal expansion truncation order and the measurement error of the complex reflection coefficient on the accuracy of the complex longitudinal wave velocity inversion are analyzed.2.Based on the theory of pure elasticity and the expansion of the normal series,an analytical model of the surface admittance of viscoelastic solid spheres is established.The correspondence between the incident and reflected sound waves on the solid spheres surface and their surface admittances is established by the spherical harmonic domain transformation.The mapping relationship is also established between the zero-order admittance in the harmonic domain and the shear wave velocity.The theoretical calculation and finite element simulation of viscoelastic solid balls with four radiuses are carried out to verify the accuracy of this method.On this basis,the effects of complex longitudinal wave number inversion error,spherical radius change under high hydrostatic pressure,and spherical harmonic domain zero-order surface admittance measurement error on shear wave velocity inversion results are analyzed.3.The measurement test of the complex reflection coefficient of the rubber cylindrical sample in the free backing of the acoustic tube and the impedance backing was carried out,and the complex longitudinal wave velocity was inverted based on the measurement results.The experiment analyzes the influence of the measurement error of the complex reflection coefficient on the inversion results.According to the multi-modal decomposition and spherical harmonic domain transformation methods,a new method for inversion of complex longitudinal and shear wave velocities of viscoelastic materials is proposed.Compared with the traditional complex plane rooting search method,the calculation efficiency is significantly improved,and the shear wave velocity inversion results also avoid the multivalued problem.Although the measurement accuracy of the complex reflection coefficient or the zero-order surface admittance in the spherical harmonic domain is put forward,it can still provide a theoretical basis and reference basis for the inversion of acoustic parameters of viscoelastic materials.