Dynamic Analysis Of Axially Moving Functionally Graded Cylindrical Shell With Time-dependent Velocity Based On Absolute Nodal Coordinate Formulation

Axially moving cylindrical shell structures are widely used in aerospace field.However,the common materials are not suitable for high temperature working environment in this field.Functionally graded materials overcome the shortcoming of common materials not being able to resistant high temperature by their excellent thermomechanical properties.Based on this,the dynamic characteristics of axially moving functionally graded cylindrical shells with time-dependent velocities are analyzed by absolute nodal coordinate formulation in this paper.The main work is as follows:1.The vibration characteristics of functionally graded cylindrical shells are analyzed.By means of the absolute nodal coordinate formulation,the functionally graded cylindrical shell element model is established,the absolute position vector expression of any point on the middle surface of the cylindrical shell is obtained,which can express the strain and curvature.The kinetic energy and strain energy of the element are obtained.Substituted the energy expressions into Lagrange equation,and the vibration differential equation of the structure is obtained.Numerical calculation of a single-material thin-walled cylindrical shell is carried out,the accuracy of the calculation method is verified.The vibration differential equation of a stainless steel-alumina functionally graded cylindrical shell is solved,and the influence of the length to radius ratio,the thickness to radius ratio and the volume fraction on the natural frequency is analyzed.The results show that,as the length to radius ratio and volume fraction increase,the natural frequency of the functionally graded cylindrical shell decreases;as the thickness to radius ratio increases,the natural frequency continues to increase,and frequency veering occurs in many positions.2.The dynamic characteristics of the uniformly axially moving functionally graded cylindrical shell are analyzed.For the uniformly axially moving functionally graded cylindrical shell,the kinetic energy expression and the strain energy expression are deduced by the absolute nodal coordinate formulation,and the dynamic differential equation with damping is obtained.The influence of length to radius ratio,thickness to radius ratio and volume fraction on the complex frequency of stainless steel-alumina functionally graded cylindrical shell is analyzed.The results show that:the axial velocity reduces the complex frequency of the functionally graded cylindrical shell;the volume fraction has the greatest influence on the imaginary part of the first-order complex frequency under the condition of clamped-free boundary,and the length to radius ratio and the thickness to radius ratio have the least influence on it;the increase of velocity has no effect on the position of the frequency veering phenomenon.3.The dynamic characteristics of the axially moving functionally graded cylindrical shells with time-dependent velocity are analyzed.Extend the uniformly axially moving to the axially moving with time-dependent velocity,the kinetic energy and strain energy expressions of the system under the time-dependent velocity state are deduced,and the dynamic differential equation obtained,whose damping and stiffness are time-dependent.The vibration characteristics of different time-dependent velocity state are analyzed.The results show that:when the time-dependent velocity is uniformly accelerated,the stainless steel-alumina functionally graded cylindrical shell has a critical velocity,and the higher the frequency order,the greater the critical velocity.When the velocity is larger than the critical velocity,the system has divergent instability.As the volume fraction and thickness to radius ratio increase,the critical velocity decreases;as the length to radius ratio increases,the critical velocity gradually increases.When the time-dependent velocity changes as a sine function,the imaginary part of the first-order complex frequency of the Stainless steel-Zirconia functionally graded cylindrical shells is greatly affected by the velocity and less affected by volume fraction,length to radius ratio and thickness to radius ratio.