Thin Cylindrical Shell Forced Vibration Displacement Response And Crack Detection

Thin cylindrical shell is a space surface structure with excellent mechanical properties,and is widely used in production and life.Vibration and noise will be generated when cylindrical shell is excited externally,and long-term vibration shock will easily cause structural damage.Therefore,it is of great significance to study the vibration response characteristics of cylindrical shell to detect and evaluate the damage.In view of the above problems,this paper studied the vibration characteristics of thin cylindrical shell.By analyzing the vibration displacement response characteristics of cracked shells,a damage identification method based on displacement amplitude characteristics is proposed.The main work and results are as follows:(1)Based on the Flügge shell theory,a free vibration equation of cylindrical shell was established.The wave propagation method was used to study the coefficients of the characteristic equations of the coupled system.The natural frequencies of each mode are obtained by solving the sixth-order algebraic equation.The comparison with the calculation results of the finite element method and other literatures verified the reliability of the theoretical calculations,and the relationship between the geometric parameters of thin cylindrical shell and the natural frequency of each mode was also given..The dimensionless axial characteristic wave number of thin cylindrical shell was obtained by solving the eighth algebraic equation.The dispersion characteristics of thin cylindrical shell in different circumferential mode are analyzed.The dispersion characteristics of the propagating waves were discussed in detail,and the wave propagation characteristics of three propagating waves in the circumferential modes of each order were given.The study found that the attenuation standing wave will only appear in relatively low frequency bands.As the dimensionless frequency increases,thin cylindrical shell system will eventually contain three propagating waves and one near-field wave,and the three propagating waves reflect their bending,torsional and tensile properties respectively.(2)The circumferential cosine distribution excitation as the excitation source,the Fourier transform method was used to transform the system characteristic equation to the wavenumber domain for solving.Based on the residue theorem,the infinite domain integral problem was transformed to solve the characteristic root problem,and then the specific expression of the forced vibration displacement response of the thin-walled cylindrical shell was obtained.The displacement response amplitude characteristics of thin-walled shells in different circumferential modes were analyzed,and the decoupling characteristics of the axial and radial displacements of the shells in the breathing mode were obtained.Furthermore,the dimensionless input power flow characteristics of the thin cylindrical shell were studied,and the fluctuation characteristics of dimensionless input power flow in frequency domain and the distribution pattern of its peak position were obtained.(3)Based on the Rankine vortex model,combined with the Helmholtz solution method,the critical conditions for vortex penetration were obtained,Efluid-structure coupling model was established,and the response characteristics of forced vibration of shells with different pipe diameters under vortex impact were analyzed.The results show that the catastrophic characteristics of shell are related to the critical penetration state of the vortex(4)Based on the linear spring theory,the effects of straight cracks on the local stiffness of cylindrical shell and the discontinuities of displacement at the cracks were analyzed.a finite element model of thin cylindrical shell with straight cracks was established,according to modal analysis of cracked shells with different crack parameters,and the relationship between the first third order natural frequency of the shell and the crack parameters was given.Taking the circumferentially uniform excitation as the external excitation source of cracked cylindrical shell,the forced vibration response of cracked shell was studied,and the propagation modes of stress wave on perfect shell and cracked shell were compared and analyzed.Discussed the displacement response of cylindrical shell in axial,circumferential and radial directions,and analyzed the relationship between the radial displacement response characteristics and crack circumferential position in detail.Finally,according to the natural frequency characteristics and radial displacement amplitude characteristics of cracked cylindrical shell,the circumferential position,axial position and relative depth of the crack were effectively identified.The research results can provide technical support for related research on vibration and damage identification of thin cylindrical shells.