Research On Band Gap Characteristics Of One-dimensional Periodic Structures With Resonant Element And Elastic Support

Beam and rod structures are widely used in practical engineering,which not only play the role of connection and bearing,but also the transmission medium of vibration.The beam not only propagates vibration,but also is affected by vibration itself.The presence of vibration not only has a negative impact on mechanical equipment,but also affects people’s physical and mental health.At present,it is still difficult to realize vibration control in low frequency range.In recent years,phononic crystal theory provides a new guiding idea for vibration and noise reduction in low frequency range.The feature of "small size controlling large wavelength" of locally resonant phononic crystals has been favored by researchers.The one-dimensional phononic crystal beam with resonant element and elastic support has better performance,so it is necessary to study the band gap characteristics of the beam.Taking the Euler beam with local resonance of a single oscillator as the object,the transfer matrix method is used to derive the band gap calculation formula caused by the reaction force of the oscillator,and the spectral element method is used to calculate the band gap characteristics,it is found that the dynamic reaction force of the oscillator causes two kinds of band gaps,namely Bragg type and local resonance type.Research on the regulation law of the band gap indicates that there is a transformation phenomenon between the two kinds of band gaps,the finite element software COMSOL is used to verify the correctness of the theoretical calculation of band gap.The band gap characteristics of phononic crystal chains with resonant elements and elastic supports are studied theoretically,and the corresponding relationship between band gap formation and attenuation factor is revealed.The introduction of equivalent parameters simplifies the research model,verifies the correctness of theoretical calculation,and reveals the correlation between band gap formation and dynamic equivalent parameters.The solution of transmittance provides theoretical guidance for the study of finite-period structure and the practical application of phononic crystals,the influence of the change of related parameters on the attenuation factor of phononic crystal chain is explored by using the normalization processing method.The spectral element method is used to study the phononic crystal Euler beam model with resonant element and elastic support.The results show that the first band gap starts from 0 Hz,and the first two band gaps only change the width and position of the band gap,and the type of the band gap will not change.The phononic crystal beam with resonant element and elastic support is applied to the vibration reduction of diesel generator base.The results show that this model has a certain effect on the low frequency vibration reduction of diesel generator base,and the maximum vibration reduction effect can reach 100dB in the band gap section.