| Elastic shell structures are widely used in shipbuilding industry,aerospace,civil architecture and other engineering fields.Scholars have carried out a lot of research on the vibration of elastic shell structures.In recent years,with functional and light-weight design requirements,the popularization and application of periodic structures and new acoustic black hole stuctures are drawing more and more attention.Elastic shell structures with arbitrary thickness characteristics have become an important research object of vibration control.The unified dynamics model of elastic shell structure with arbitrary variable thickness is insufficent,and the vibration characteristics and mechanism research remains to be further enriched.In this paper,the dynamic modeling and vibration mechanism analysis of elastic shell structures with arbitrary variable thickness are studied and verified by relevant experiments.The main work is as follows:The thickness function is expanded in the dual Fourier series and the thickness variation information is compressed into into the corresponding Fourier coefficients.Based on the Love shell theory and Rayleigh-Ritz energy method,a semi-analytical uniform model for vibration analysis of cylindrical shells with arbitrary thickness under elastic boundary conditions is established.Artificial springs is used to simulate elastic boundary conditions,and an improved Fourier series is used to construct the vibration displacement function of cylindrical shells.The vibration characteristics of cylindrical shells with linear thickness,stepped thickness and arbitrary power exponential thickness are analyzed,and the influence of boundary conditions,slope,step thickness ratio and step thickness location on the vibration characteristics are obtained.The results show that the natural frequencies of linear cylindrical shells decrease gradually with the increase of slope,and the center of the distribution of overall mode shapes moves to the thinner port,except for the simply-supported and free-free boundaries.The natural frequencies of the axial stepped cylindrical shell show antisymmetric/symmetric changes with respect to the step thickness location under the same boundaris.The natural frequencies of axial stepped cylindrical shells increase monotonically with the increase of the step thickness ratio,and local modes appear in the thinner port.The natural frequencies of cylindrical shells with power function increase with the exponential constant,but the speed is slower and slower.The wave propagation model of cylindrical shells with infinite period and arbitrary thickness is established based on the wave finite element method.The unified dynamic model of cylindrical shells with finite period and arbitrary thickness is established based on the Fourier expansion method and the semi-analytical Rayleigh-Ritz method.The band gap characteristics of elastic wave propagation are obtained.The influences of periodic elastic support,elastic boundary and periodic variable thickness on the band gap characteristics are analyzed.The local resonance mechanism of the band gaps of cylindrical shells with arbitrary periodic thickness is further lucidated and relevant measures to control the band gaps are given.The results show that the periodic radial support spring and the periodic rotational support spring have more influence on the band gap characteristics than the periodic axial support spring and the periodic circumferential support spring.The boundary conditions at both ends have little effect on the band gap characteristics The variation of step thickness ratio and step thickness location can fully evoke the dynamic evolution process of band gaps.The band gap characteristics of cylindrical shells with periodic arbitrary thickness arise from the local resonance mechanism and are closely related to the natural frequency determined by the internal stiffness and mass distribution in the unit cell.Considering the specific power exponential constant and damping layers,a semi-analytical vibration model of elastic ABH cylindrical shells is established.The energy terms of damping layers are added to the whole system equation by fully coupled method.By introducing the power flow analysis,the vibration reduction mechanism of elastic ABH cylindrical shell structures is studied.The energy flow of ABH shells is analyzed,and the failure phenomenon of acoustic black hole effect at the frequencies of global modal excitation is explained.The influence of parameters such as truncation thickness,power exponent,damping layer length and thickness on vibration energy concentration and dissipation of ABH cylindrical shells with damping layers is given.The results show that the absorbed power ratio decreases with the decrease of the modal loss factor at the acoustic black hole failure frequencies.The absorbed power ratio in ABH region is sensitive to the truncation thickness at low frequencies while that is insensitive to the power parameter at middle and high frequencies.The increase of the damping layer length and thickness can enhance the acoustic black hole effect.Considering the influence of half-cone angle,a dynamic model of elastic conical shells with arbitrary thickness under elastic boundary conditions is established based on the Fourier expansion method and the semi-analytical Rayley-Ritz method.The vibration characteristics of conical shells with linear thickness,stepped thickness,power exponential thickness and ABH profile are analyzed.Based on the power flow analysis,the energy transfer characteristics of ABH conical shell are studied,and the influence of parameters such as half-cone angle and thick-diameter ratio on the vibration energy concentration and dissipation of ABH conical shells with damping layers is revealed.The results show that the dimensionless natural frequencies of stepped conical shells increase monotonically with the increase of the step thickness ratio,except for the free-free boundary.The damping layers increase significantly the absorbed power ratio in ABH region.The increase of half-cone angle leads to the shift of absorbed power ratio curve,and the increase of thick-diameter ratio leads to the shift of absorbed power ratio and the decrease of acoustic black hole effect in ABH region.Based on the foregoing research work,the modal experiments and vibration response tests are carried out for cylindrical shells with uniform thickness,linear thickness,stepped thickness,ABH profile and periodic thickness,respectively.The dynamic characteristics of different thickness types of cylindrical shells are compared and analyzed,as well as the band gap characteristics of cylindrical shells with periodic variable thickness.The experimental results show that the modal shape shifts of linear cylindrical shells,stepped cylindrical shells and ABH cylindrical shells predicted by the present method appear.The mechanism of band gap generation of cylindrical shells with periodic variable thickness explained by the proposed method is further verified by experiments. |
