Analysis Of Dynamic Characteristics Of Axially Moveing Cylindrical Shell Made Of Functionally Graded Material With Time-dependent Velocity

The application of thin-walled cylindrical shell structures has gradually expanded from the original aerospace field to other engineering fields,such as civil engineering,mechanical manufacturing engineering and biomedical engineering.The free vibration and forced vibration of the cylindrical shells will not only affect its performance of system,but also its strength and service life.Functionally graded materials(FGM)are a new type of materials with the development of aviation industry and the increasing requirements of materials since 1984.They have good thermal stress relaxation characteristics and designable performance.Therefore,the vibration characteristics of FG cylindrical shells,the dynamic characteristics of axially moving FG cylindrical shells with constant velocity and with time-dependent velocity are studied in this paper.The main work is as follows:(1)Under the boundary conditions of clamped-clamped and clamped-free boundary,the free vibration characteristics of FG cylindrical shells are an alyzed.An FGM along the wall thickness with exponential function distributed is used,using Rayleigh-Ritz method,the displacement component as the product of admissible functions and generalized coordinate vectors is selected,the kinetic and strain energy of FG cylindrical shells are given,and the Lagrange function is obtained and substitute it into the Lagrange equation,the homogeneous algebraic equation of the FG cylindrical shells is derived.The main conclusions are as follows:under both boundary conditions,the natural frequency increases with the increase of the thickness-to-diameter ratio,the natural frequency gradually decreases with the increase of the length-to-diameter ratio,the circumferential wave number doesn't influence the natural frequency after the volume fraction is greater than four.(2)Under the three boundary conditions of simply supported and clamped at both ends,and clamped-free boundary,the dynamic characteristics of axially moving FG cylindrical shells with constant velocity are analyzed.Based on the free vibration and increased the axially moving with constant velocity,the kinetic energy and strain energy of axially moving cylindrical shells are given,substitute to the Lagrange equation and the differential equation of motion of axially moving FG cylindrical shells with constant velocity is obtained.The critical velocity of cylindrical shells under three boundary conditions are analyzed,the complex frequencies versus velocity and each parameter is discussed.The main conclusions are as follows:the imaginary part of the dimensionless complex frequency gradually decreases with the increase of moving velocity until it decreases to zero,and the real part begins to branch,the curves of vibration frequency with thickness-diameter ratio and circumferential wave number is basically same to compare with free vibration.(3)The dynamic characteristics of axially moving FG cylindrical shell with time-dependent velocity are analyzed.It is assumed that the axially moving of cylindrical shells is variable velocity,the kinetic energy and strain energy are given,substitute to the Lagrange equation and the discretization motion differential equation of axially moving cylindrical shells with time-independent velocity is obtained.Take simply supported boundary at ends as example,the time-frequency curve of the imaginary part of the first-order complex frequencies of cylindrical shells is analyzed,the variations of dimensionless complex frequencies with velocity and other parameters under the influence of variable velocity is discussed under the three boundary conditions.The main conclusions are as follows:the volume fraction of cylindrical shells doesn't influence the period of imaginary part of the first-order complex frequencies,the change of the dimensionless complex frequencies versus velocity is same to compare with the axially moving with constant velocity,and the variable velocity only improves the critical speed of the cylindrical shells system.