Analysis Of Vibration Characteristics Of Functionally Graded Cylindrical Shell Pipe Conveying Fluid With Variable Velocity

Pipe conveying fluid plays an indispensable role in people's daily life,and has important applications in petroleum transportation and other projects.Pipe conveying fluid has become a research hotspot of scholars because it contains rich dynamics problems.Most of the existing study use beam model to study,while cylindrical shell model is helpful to study its dynamic characteristics more accurately and comprehensively.Functionally gradient materials(FGM)are new composites with the rapid development of aviation industry.They have good heat resistance and designable performance.Therefore,the free vibration of FGM cylindrical shells and the dynamic characteristics of FGM cylindrical shells with uniform flow velocity and variable flow velocity are studied in this paper.The main work is as follows:1.For the free vibration of FGM cylindrical shells with simply supported boundary at both ends,an FGM with exponential distribution is selected.Using Hamiltonian method,the kinetic energy and strain energy of cylindrical shells are given,and the Lagrange function is obtained.Hamiltonian canonical equation is derived,and the problem is transformed into solving eigenvalues of Hamiltonian matrix.The variation of natural frequencies with the circumferential wave number and volume fraction is analyzed.2.Based on the study of free vibration of FGM cylindrical shells,a uniform velocity fluid is introduced into the cylindrical shells.The kinetic energy of fluid flow,the kinetic energy and strain energy of cylindrical shells are given,the Lagrange function of the system is obtained,and the Hamiltonian canonical equation is derived.The natural frequencies are obtained by solving the characteristics of Hamiltonian matrix,and the variation of critical velocity and natural frequency with each parameter is analyzed.3.For the dynamics problems of FGM cylindrical shells with variable velocity,the distribution of fluid velocity along the cross section of the pipeline is assumed.Lagrange function of cylindrical shell pipeline with variable velocity is obtained.Hamiltonian canonical equation is derived and the natural frequency of the system is obtained.By numerical calculation,the variation law of critical velocity and natural frequency affected by variable velocity effect is analyzed.The main conclusions are as follows:Compared with the FGM cylindrical shell pipeline with the uniform velocity,the critical velocity of the FGM cylindrical shell pipeline with the variable velocity increases,the imaginary part of the natural frequency of the slender cylindrical shell pipeline decreases,and the imaginary part of the natural frequency of the pipeline with small thickness-diameter ratio increases.