Vibro-Acoustic Characteristic Analysis Of Acoustic Metamaterial-Acoustic Cavity Coupling Systems

By arranging artificial microstructures at the sub-wavelength scale and placing them in a particular order,the acoustic metamaterial obtains extraordinary mechanical or acoustical properties like low-frequency bandgap,negative refraction,and anomalous transmission,demonstrating abundant physical insights.Interior noise control is a promising application of acoustic metamaterials,and it is one of the hot topics among ongoing the acoustic metamaterial researches.Understanding the interaction mechanisms between an acoustic metamaterial and an acoustic cavity is a premise for improving the vibration-suppression and noise-insulation capacities of acoustic metamaterial plates,making it a fundamental problem in the vibro-acoustic analysis of acoustic metamaterial-acoustic cavity coupling systems.In this thesis,the vibro-acoustic characteristics of acoustic metamaterial-acoustic cavity coupling systems are studies.Based on an efficient numerical method proposed for vibro-acoustic analysis of the coupling system,the interaction mechanisms between an acoustic metamaterial plate and a closed acoustic cavity are,under both deterministic and uncertain conditions,studied thoroughly.Using the interaction mechanisms as guidelines,a lightweight,low-frequency design of acoustic metamaterial is proposed and its effects on the interior noise control is verified by both experimental studies and industrial applications.The main works and conclusions of this thesis are introduced as follows:(1)Based on the variational principle of energy functional and the orthogonal polynomial expansion,an efficient numerical method for vibroacoustic analysis of acoustic metamaterial-acoustic cavity coupling system is proposed.The isogeometric projection is introduced into the coordinate transformation between the physical domain and the parametric domain,making the energy functional of an arbitrarily-shaped acoustic cavity built directly,thus eliminating the complicated mathematical manipulations caused by domain decomposition.Furthermore,by exploiting the locally distributed feature of uncertain parameters in the coupling system,a localized uncertainty quantification and propagation analysis method is proposed through extending the deterministic variational method to the uncertain context.Numerical examples demonstrate that the variational method is of high accuracy and efficiency,and has fast convergence rate as well as good geometric adaptivity.Meanwhile,the localized uncertainty analysis method significantly speeds up the uncertainty analysis of acoustic metamaterials,with an accuracy comparable to the benchmark Mote-Carlo simulations.(2)For the acoustic metamaterial plate-cavity coupling system,the mean squared velocity of the plate,the mean squared sound pressure of the cavity,the radiated sound power,and the radiation directivity are calculated;for the acoustic metamaterial plate-cavity-plate coupling system,the sound transmission loss is calculated with different incidence angles,cavity depths,and arrangements of local resonators.By analyzing the varying tendencies of above vibro-acoustic responses,the interaction mechanisms between an acoustic metamaterial and an acoustic cavity are proposed,based on which the low-frequency coincidence-induced sound insulation valley and the way to improve that valley are studied.The results show that the vibro-acoustic characteristic of the acoustic metamaterial-acoustic cavity coupling system is successively governed by the local resonance effect and the low-frequency coincidence effect.Moreover,by carefully designing and allocating the local resonators,the vibration-suppression and noise-insulation capacities of acoustic metamaterial are significantly enhanced.(3)A cantilever-like,acrylic-made local resonator is design and a noise insulation test kit is produced.Specimens of the acoustic metamaterial platecavity system and the acoustic metamaterial plate-cavity-plate system are also fabricated.The experimental studies of the acoustic metamaterial-acoustic cavity systems are conducted,in which the vibration velocity of the plate,the sound pressure inside the test kit,the sound insertion loss and sound transmission loss are measured.The experimental results are in good agreement with the theoretical predictions,which validates the proposed interaction mechanisms between an acoustic metamaterial plate and a closed acoustic cavity.Particularly,the wavenumber transformation of the plate velocity demonstrates that the wavenumber circle of the elastic wave coincides with that of the acoustic wave after the bandgap,providing a strong evidence for the existence of the low-frequency coincidence phenomenon.(4)Towards the need for noise reduction in aviation cabins,a logical flow for acoustic metamaterial design and several basic principles for local resonator design are proposed.To alleviate the conflict between the added mass of local resonators and the weight limitation in the aviation industry,a new type of local resonator is designed by coming the inertial amplification mechanism and the regular cantilever-like resonator.The bandgap property of this inertially-amplified,cantilever-like local resonator is numerically analyzed and experimentally validated.The results show that by simultaneously adjusting the inertial amplification factor and the lever-beam connection location,the proposed local resonator achieves a much wider frequency-tuning range than the regular one.Meanwhile,the new local resonators,when periodically attached to the roof of a helicopter cabin,are found capable of significantly reducing the interior noise of the cabin,even under uncertain conditions.This thesis conducts an in-depth study on the vibro-acoustic characteristics of acoustic metamaterial-acoustic cavity coupling systems from five aspects,including theoretical formulation,numerical calculation,characteristic analysis,experimental measurement,and industrial application.This study reveals the interaction mechanisms between an acoustic metamaterial and an acoustic cavity,which helps enriching and broadening the vibro-acoustic theory of acoustic metamaterial.Meanwhile,this thesis summaries the design guidelines of acoustic metamaterial for interior noise control of aviation cabins,based on which a lightweight,low-frequency design of acoustic metamaterial is proposed.These practices offer meaningful references for the realization of lightweight,engineering-oriented acoustic metamaterials.