Research On Low Frequency Vibration And Noise Reduction Of Plate Structure Based On Local Resonance Theory

Noise problems are widely existed in the cabins of running cars,planes and high spead rails etc.However,the broadband low frequency noise problems in those cabins are difficult to be suppressed by existing noise and vibration control methods such as surface reinforcement,laying of damping material and utilization of sound absorption material.Locally resonant structures proposed in the field of acoustic physics provided a new idea for broadband low frequency noise suppression.Analogy to the locally resonant theory,the locally resonant structures can be formed by installing distributed locally resonant unit on the beam and plate to realize noise and vibration suppression.In view of the above background,the noise and vibration supression characteristics of the locally resonant plate are sdudied in this paper.And,the locally resonant plates are used to suppress the broadband low frequency noise in the cabins.By transfer metrix method,the locally resonant band gaps generated by the dynamic reaction force and reaction torque of the resonators in the locally resonant beams are calculated and analyzed.Analysis results clarified that the dynamic reaction torque type resonators should be used in the design of wide band locally resonant band gap.The lower mode vibration reduction performance of the locally resonant band gaps is analyzed.The results showed that the locally resonant beam has several vibration peaks in the band arrounding the locally band gap.And,those vibration peaks seriously weakend the wide band vibration suppression effect of the locally resonant band gaps.Effective suppression of the two vibration peaks on both outsides of the band gap is the key to realize the broadband low frequency vibration control performance.The corresponding multi-DOF vibration system of the “base plate-distributed resonators”is established,and the eignvalue problem and the vibration response of the locally resonant plate subject to external force are calculated b ased on modal expansion method.The vibration shape peroperties of the distributed resonat ors are analyzed and revealed:vibration shapes of the distributed resonators at the vibration peaks frequecies are same with the corresponding mode shape of the base plate.Based on this vibration shape property of the resonators,the vibration displacement of a reference resonator and the vibration shape matrix of the resonators are introduced into the multi-DOF vibration system.Then,equivalent system describing the vibrations of the locally resonant plate is established.With the fixed points theory in dynamic vibration absorber optimization procesure,the resonator parameter optimization formula for wide band vibration reduction of the locally resonant plate is proposed.Then,the optimization formula is verified by numerical method.The influnce of the resonators installation position on the vibration reduction performance of the locally resonant plate is analyzed and the results showed that the installing of resonators at each maximum modal displacement point is the optimal distribution method to achive the wideband vibration reduction performance.The sound radiation power and sound radiation effective calculation method of the locally resonant plate is proposed with the use of far field sound radiation theory of plate structures.The analysis of sound radiation characteristics reveals th at fixed point phenomena also exisit in the sound radiation curve of locally resonant plates.By using mathematical method of series expansion and the expression of the equivalent vibration system,the equivalent sound radiation system describing sound radiation of the locally resonant plate is established.The resonator parameter optimization formula for wide band noise reduction of the locally resonant plate is proposed according to fixed point theory.Then,the optimization formula is verified by numerical method.The influnce of the resonators installation position on the noise reduction performance of the locally resonant plate is analyzed and the results show that the installing of resonators at each maximum modal displacement point is the optimal distribution method to achive the wideband nosie reduction performance for any complicated mode shapes.The locally resonant plate can have sound absorption function if the locally resonant unit is membrane type resonator.The sound absorption coefficient calculation method of the locally resonant plate carrying membrane resonators is proposed based on mode expansion method.The sound absorption tunning characteristics of the membrane parameters are analyzed.The results show that the sound absorption peaks of the locally resonant plate can be tuned to low frequency range by lossiing tension of the membrane,adding weight of the central metal block and increasing the distance between membrane resonator and back plate.More over,the adding of the damping of membrane can broaden the sound absorption band.In order to further broaden the sound absorption band of the locally resonant plate,a compound sound absorber consisted of locally resonant plate and perforated plate is proposed.The wideband low frequency sound absorption is examined through theoretical and experimental study.Based on theoretical analysis results of low frequency noise and vibration reduction peroperties of locally resonant plate,the method of redusing the low frequency noise in cabin structures using locally resonant plate is proposed.According to the noise and vibration characteristics of the real enginearing cabin structure,the cabin structure sample is prepared under laborotary condition.Besides,the corresponding sound radiation suppressive and sound absorptive locally resonant plate sample are also prepared.The nosie source plate can be designed as locally resonant type plate to suppresse the vibration of the noise source plate and suppress the radiated noise into the cabin.Experiment results show that this method can afford averaged 19.8d B inner noise reduction effect in 0-400 Hz range.The non-noise source plate can be designed as sound absorptive locally resonant plate to further reduce the inner noise.Noise test results show that the combination of the two above methods reached averaged 24 d B noise reduction effect in 0-500 Hz range.