Investigations Of The Acoustic Properties Of The Helmholtz Resonators

With the development of the acoustic metamaterials(AMMs),Helmholtz resonators(HRs)can be used to realize the negative mass density(ρ)in combination with the porous materials,to directly possess the negative or infinite bulk modulus(B)by itself-designed structures,and to obtain the double-negative parameters in combination with thin-film structures.Besides,HRs are also one of the in-dispensable “raw materials” of the positive parameter acoustic metamaterials and absorption metamaterials.In this letter,the acoustic double zero refractive index metamaterial(DZIM)is designed by a single negative bulk modulus of the HRs.Then,the effective medium theory and Green’s function are used to study and verify the mechanism and physical phenomenon of the ρ≈0 and 1/ B ≈0 at the same frequency.Furthermore,the relevant array with a hard defect is designed to study the cloaking effect of the artificial surface acoustic waves,which opens a new vision for the structural design and application of acoustic DZIM.In addition,as for the HRs with the characteristics of the frequency selection in acoustic absorption,the porous aerogel materials are embedded in the HRs to achieve the non-resonant region,wide-band absorption performance.The dissertation is divided into following chapters:In the first chapter,we review the effective constitutive parameters property and research progress of AMMs,analyze the function of the HRs in the above-mentioned AMMs,and then introduce the current application situation and prospect of the HRs in the acoustics.In the second chapter,we analyze the acoustic characteristics of the HRs in the plane wave incidence,such as the transmission coefficient,the impedance matching condition and the resonance frequency formulations,etc.Then,the physical significances of ρ and B of the wave equation is given by the three basic equations.The boundary conditions for solving the relevant definite solution problems are introduced.The effective medium theory at a subwavelength scale and the Green’s function based on the eigenmode analysis in one-dimensional systems are analyzed.Finally,the eigenmodes,transmission and phase of a single HR and double HRs are simulated and calculated by the Green’s function and the effective medium theory,which can be used to provide the theoretical foundation for the design of the DZIM unit cell.In the third chapter,we report the theoretical understanding and experimental realization of acoustic DZIM induced by the coupling between two HRs via a connecting tube at subwavelength scale.Owing to the presence of a connecting tube,the system can generate the dipolar mode that is independently tunable and monopolar mode that is virtually unchanged.It thereby makes ρ and 1/.B.simultaneously crossing zero,where the overlapping regions of dipolar mode and monopolar mode can be readily tuned.Then we experimentally validate the acoustic cloaking by grafting a 5×9 array of unit cells in a two-dimensional defective waveguide.Passing through the defect,the phase distribution of the plane waves maintains unchanged and the impedance matches well with the background air medium.Finally,a relatively broadband acoustic cloaking is experimentally demonstrated in the frequency band of 1865-1925 Hz.Surprisingly,the designed DZIM cloaking system has no intrinsic limit to the number of unit cells,so the corresponding array can be designed according to practical demand and assembly for further real-world applications.In the fourth chapter,we present a composite structure for acoustic absorption,which is constructed by filling the designed HRs by three types of granular aerogels with various thicknesses(5,10,15 and 20 mm).The transmission loss and absorption coefficient are investigated at low frequency range from 200-2500 Hz.The measurement results show that the absorption performance,including the intensity and working frequency bands,can be effectively manipulated not only by modulating the thickness of infilled aerogels,but also by the structure design of HRs,where the strongly coupled double HRs design shows superior absorption than the simple single HR.This novel combination of resonant structure and aerogels paves the route towards designing highly tunable and efficient acoustic composite devices for noise absorption in vent and pipeline systems.In the fifth chapter,the conclusion is given and the direction of further work is briefly discussed.In summary,we propose two novel structures based on the acoustic properties of the HRs and systematically investigate the acoustic propagation properties in these structures by theoretical,numerical and experimental methods,which are meaningful in perspective of both theoretical exploration and practical application.