Investigation On The Dynamic Modeling And Energy Transmission Characteristics Of Acoustic Black Hole Structure And Its Coupling System

Elastic beam/plate structures and their coupling systems are widely used in many engineering fields.Under the excitation of mechanical force or acoustic field,these structures will generate vibration and acoustic radiation.The nature of the vibration and noise is the bending wave propagating in the elastic structure and its interaction with the surrounding medium.It is of great engineering significance to study structural vibration and noise attenuation technology.Structural vibration and noise have always been the focus of attention in various fields.In recent years,a kind of passive noise reduction structure Acoustic Black Hole(ABH),which has the geometric parameters of thin-walled structure or the gradient of material characteristic parameters to reduce to zero gradually according to the specific power function changing law has attracted much attention.And bending waves in it can be zero-reflected,so that the bending waves can be controlled in the structure,which has a wide application prospect in the vibration and noise attenuation field to control and gather the vibration energy carried by the bending wave.Due to the current research on the ABH structure is mainly confined to the analysis of the vibration characteristics and the sound radiation in free space,the research on the vibration energy transmission in the ABH structure and its coupling system with other structures and the enclosed sound field is not enough,the understanding and application design of the ABH structure is limited.It is necessary to investigate the power flow analysis of the ABH beam/plate structure with complex boundary conditions and its coupling systems.And revealing the vibration power flow transmission characteristics of the ABH structure with complex boundary conditions and the behavior mechanism of its coupling system is an important foundation for people to fully understand the ABH structure and realize the effective design and implementation of the vibration and noise attenuation in complex environments.Based on the Euler-Bernoulli beam theory and the modified one-dimensional Fourier Series is adopted as the admissible function to describe the lateral vibration displacement.using the energy principle,a semi-analytical model for the dynamics and power flow analysis of a onedimensional ABH beam with elastic constraints is established.It provides an effective tool for a power flow analysis of one-dimensional ABH beams,which can explore the characteristics of vibration energy transmission and the influence of the damping layer on energy transmission in ABH beams from the energy perspective.And the characteristic parameters of the ABH cross-section are analyzed.Given the application of ABH structure in rotating machinery,the power flow analysis model of a one-dimensional ABH beam is combined with the spinning hardening effect,and a dynamic and power flow analysis model of a spinning cantilever ABH beam is established to investigate the effect of spinning on the ABH beam from the dynamic response and vibration energy transmission perspectives.The essential dynamic and energy-transmitting characteristics of spinning ABH beams are revealed.The one-dimensional ABH structure is extended to two dimensions,based on the Kirchhoff thin plate theory and the improved two-dimensional Fourier Series as the transverse vibration displacement description admissible function,and the energy principle is adopted,a semianalytical model for the dynamics and power flow analysis of two-dimensional ABH plate with elastic constraints is established,the effect of ABH on energy transmission in plate structure is investigated.According to the vibration attenuation characteristics of the coupling system composed of ABH plate and uniform plate,the bending vibration and in-plane vibration of the twodimensional structure are considered.based on the improved two-dimensional Fourier Series,the bending vibration and in-plane vibration displacements of the plate structures in the system are expanded,and an ABH coupling plates with elastic constraints dynamic and power flow analysis model are established.The vibration characteristics of acoustic black hole coupled plate structure are analyzed,the influence law of coupling boundary on vibration level suppression of coupled plate system is revealed,and the influence law of coupling boundary on energy transmission is explored.Based on the semi-analytical model of the two-dimensional ABH plate and the continuous condition of the vibration velocity at the interface between the elastic plate and the acoustic field,the energy equation of the vibroacoustic coupling system is constructed.Based on the energy principle,an ABH plate-cavity vibroacoustic coupling system model with elastic constraints is established.The model is used to investigate the effect of the ABH plate on the noise attenuation in the cavity,and the energy transformation and transmission characteristics of the system are analyzed.The present work in this paper provides a new analytical tool for the application of ABH beam/plate structure in the field of vibration and noise attenuation.And the ABH structure characteristics are discussed and analyzed in more practical and complicated application environment,such as spinning and coupling systems.