Analysis Of Vibration And Wave Characteristics In Multilayer Annular Sector Plate

As an important branch of mechanical structure,plate structure has been paid large attention.In order to ensure the reliability of the whole mechanical structure,the mechanical properties,especially the vibration characteristics,of plate structures must meet certain requirements.Single layer annular sector plate has single structural characteristics and relatively limited application.As a new type of material,multilayer annular sector plate can not only maintain some characteristics of its original laminated materials,but also have properties that the original laminated materials do not have.In actual situation,annular sector plate structures are often used to achieve the purpose of vibration and noise reduction.Therefore,it is necessary to analyze the vibration and wave characteristics of the multi-layer annular sector plate,and obtain the time and frequent domain analytical solution of the displacement and stress,which provides a theoretical basis for the structural design and material selection.In this paper,the multi-layer sector is a research object to explore the vibration characteristics in the face,and the highly coupled plane motion differential equation is decoupled by means of Helmholtz decomposition method and separation variable method.With the Bessel equation,the displacement,stress expression,and the natural frequency analytic solution and the mode of the structure are obtained.Taking a double-layer sector board as an example,the natural frequency is calculated,and the finite element simulation verifies the correctness of the theoretical solution method and analyzes the variation of the natural frequency during the distinct angle of the fan ring.With the help of the theoretical analysis idea of the in-plane vibration of the multi-layer fan-ring plate,the wave of the multi-layer fan-ring plate is studied.Taking the double-layer fanring plate as an example,the wave function expansion method is used to expand the expressions of incident P and SV waves into series form.By solving the wave equation,the standing wave field in the multi-layer fan ring plate is obtained.Combined with the boundary conditions,the unknown parameters in the solution are obtained,and the expressions of the stress and displacement of each layer are obtained.Finally,the dynamic stress concentration factors of the standing wave field under the incidence of P and SV waves are obtained respectively,and the influence of the changes of the incident frequency and the incident angle on the dynamic stress concentration factors is analyzed.Based on the wave characteristics research,taking the double-layer fan ring plate as the unit cell,the vibration reduction characteristics of the multi-layer fan ring plate in the case of periodic arrangement are studied by exploring the band gap characteristics of the finite periodic radial one-dimensional generalized phononic crystals.Based on the expressions of displacement and stress of each layer of double-layer fan ring plate,the characteristic matrix describing its transfer characteristics is obtained by using the transfer matrix method based on mechanical state vector,and then the band gap characteristics of the structure are obtained.The band gap characteristics of the model are parameterized from four aspects: incident direction,boundary conditions,material parameters and structural parameters,which provides theoretical calculation means and research ideas for the analysis of vibration characteristics and wave characteristics of multilayer annular sector plates.