Theory Of The Band-gap Property And The Low-impedance-baffle Effect On Noise-control Mechanism

The noise radiated from the elastic structures is decided by both the structural vibration response and radiation efficiency.The theory of the band-gap property and the low-impedancebaffle effect on the noise-control mechanism is carried out in the dissertation.On the one hand,the theory of vibro-acoustic performance is expanded in the study of the multi-band-gap locally resonant(LR)plate.On the other hand,the low-impedance-baffle effect is proposed to reduce the radiation efficiency.The theory and the corresponding findings can guide the structural design for noise control.Firstly,the theoretical model to calculate band structures of the multi-band-gap LR plate is established.By the new method,the band-gap property can be obtained for the multi-bandgap LR plate periodically attached with an arbitrary number of single-degree-freedom resonators with different spring-mass parameters.The effect of the sub-cell sequence on the form of complete band gaps is discussed,and the formation mechanism of the multiple LR band gaps is explored.The results show that,except for the LR band gaps,the Bragg-scattering band gaps are also introduced into the multi-band-gap LR plate due to the structural periodicity itself.The number of both kinds of band gaps,as well as their frequency ranges,are affected by the sub-cell sequence.The appearance of the LR band gaps depends on the locally strong resonant mode of the periodic cell,of which the eigenfrequency decides the lower frequency of the LR band gaps.The upper frequency of the LR band gaps is decided by the eigenfrequency of the periodic-cell mode whose mode shape is analogous to the spring-mass resonator.The theoretical method developed can quickly determine the band-gap frequency ranges and provide support for the band-gap design of finite periodic structures to meet the demand for vibration reduction in specified frequency bands in practical engineering.On the basis of the study on the band-gap simulation of the multi-band-gap LR plate,the theoretical model to obtain the analytic solution of vibro-acoustic responses of the double-bandgap LR plate is established,suitable for different boundary conditions of the plates.The effect of the band-gap property on the vibro-acoustic characteristics is then studied.The results show that,for the infinite LR plate,the vibration response is forbidden in the band gaps,while in the same frequency ranges,the acoustic radiation could be most effective,displaying similar featuress as passbands.For the double-band-gap LR plates of the finite size,the vibration response is all effectively attenuated in both the band-gap frequency ranges,however,the radiation efficiency is significantly increased in the same bands.The vibrational band-gap effect plays an important role in the LR plates with constrained boundary conditions,and the acoustic power in the band-gap frequency ranges is significantly reduced.However,the acoustic power radiated from the LR plate with fully free boundary conditions exceeds that from the equalmass-loaded plate near the band-gap frequencies.It can be seen that the vibrational band-gap effect can help to realize low-frequency vibration attenuation,however,to achieve the noisecontrol goal,further consideration of the structural radiation efficiency,vibration response distribution,and boundary conditions have to be optimized.Furthermore,the structural low-radiation property based on phase offset mechanism(POM)is studied,aiming to achieve the noise-control goal by reducing the structural radiation efficiency rather than depending on the vibration attenuation.Multi-piston line sources are selected to verify the effect of POM patterns on decreasing radiated power by changing the initial vibration phases of constituent sources.The theoretical model is built to calculate the radiation efficiency and the acoustic directivity in the far field.The acoustic energy density flux near the sources is further simulated by the finite element method.As can be found from the swerve of the density flux directions,the phase difference of the sources in POM patterns blocks acoustic energy out at lower frequencies,leading to radiation cancellation in the far field.Inspired by the idea of POM,sound radiation from plates with elastic boundary conditions embedded in an infinite perforated rigid baffle(PRB)is further analyzed.The radiation efficiency of the plates embedded in the PRB(named ‘PRB-ed plate’ in the following)is derived theoretically.It can be found that the PRB-ed plates behave like the dipole source radiation in the fundamental mode region as the perforation in PRB introduces communication of the sound field,and the radiation efficiency is lower than the baffled plate.With the decrease of the PRB thickness and the hole diameter,or the increase of the PRB perforation ratio,the sound power radiated from PRB-ed plates is decreased below the critical frequency.Moreover,the band-gap property is also applied to the plate embedded in the PRB,and the results show that both the band-gap property and the low-impedance baffle effect can broaden the noisecontrol band and reach better low-frequency noise control.This research could possibly provide ideas on the design of noise control for plate-like structures.Finally,the low-radiation acoustic boundary design of the LR plate and the corresponding experiments are carried out.The experimental results of the root-mean-square velocity level,sound power level,and radiation index of the homogeneous plate are obtained when setting high impedance acoustic boundary,low impedance acoustic boundary,and no baffle.It is found that in both cases of high and low impedance acoustic boundaries,as the change of frequency,the theoretical results of the radiation index of the homogeneous plate are consistent with the experimental results,reflecting the correctness of the theoretical model of sound radiation from the PRB plate.On the basis of verification of the noise reduction effect from the low impedance acoustic boundary,the experimental sample of the low-radiation band-gap plate is prepared.The comparative results show that the sample has both the low-radiation and band-gap properties,and the radiated noise of the sample is decreased by 6.5 dB in the frequency range of 50 Hz - 1 kHz.