Natural Vibration Of Functionally Graded Cylindrical Shells In The Multiple Physical Fields

Functionally graded materials(FGM)is a new type of material composed of metal and ceramic,which can maintain good mechanical properties in high temperature environments.Cylindrical shells are often important basic components in mechanical devices and equipment,which inevitably face various complex environments such as high temperature and strong magnetism during service,which places higher demands on the stability and safety of shell structures in extreme environments.Therefore,it is of great theoretical and engineering importance to investigate the natural vibration characteristics of cylindrical shells functional gradients.In this paper,the classical plate and shell theory and non-linear vibration analysis methods are used to study the natural vibration of metal-ceramic functional gradient cylindrical shell in multiple physical field with magneto-thermoelastic coupling.The physical model of functionally graded cylindrical thin shell in magnetic field and temperature field is established.Based on Love shell theory and geometric nonlinear relationship,the expression of internal force and internal moment are derived based on generalized Hooke’s law.According to the theory of electromagnetic solid mechanics,electromagnetic force and electromagnetic torque are derived,and the expressions of kinetic energy,potential energy,and virtual work of electromagnetic force are obtained.Using Hamilton’s principle,the nonlinear magneto-thermoelastic coupled vibration equation of functionally graded cylindrical shells in multiple physical fields is derived.The linear natural vibration of functionally graded cylindrical thin shells is studied.The nonlinear magneto-thermoelastic coupled vibration equation is degenerated to obtain the linear magneto-thermoelastic vibration equation for functionally graded cylindrical shells.Set displacement solutions for boundary conditions to obtain the vibration characteristic equation.Through numerical calculation,the relationship between the natural frequency and parameters such as temperature field,magnetic field,and geometric size is plotted,and its impact on the natural frequency is analyzed.Compare and analyze the results of this paper with those of the literature to verify the rationality of the research method in this paper.The nonlinear vibration of functionally graded cylindrical thin shells in the magnetic field is studied.Based on the magnetoelastic coupling vibration equation,the nonlinear magnetoelastic lateral vibration equation is obtained.For the functionally graded cylindrical thin shell that satisfies the boundary conditions of simply supported at both ends,assuming displacement function,the Galerkin integral method is used to derive the differential equation for the free vibration of the functionally graded cylindrical thin shell.Using the multiscale method to introduce small parameters for solving,and the nonlinear natural natural frequency expression of the shell in the magnetic field is obtained.By analyzing numerical examples,draw the effect of different parameters on the natural frequency.By drawing the power spectrum,and comparing the numerical and analytical solutions of the natural frequency,the reliability of the results in this paper is verified.The nonlinear vibration of functionally graded cylindrical thin shells in magnetic and temperature fields is studied.Based on the nonlinear magneto-thermoelastic coupling vibration equation,the magneto-thermoelastic vibration equation expressed by lateral displacement is obtained.The nonlinear ordinary differential equation of the system is obtained by the Galerkin method of space-time separation.Apply the multiscale method for analytical solutions at different time scales to obtain the expression of natural frequency.Draw curve graph of the natural frequency changing with parameters such as temperature,magnetic field,thickness to diameter ratio,and circumferential wave number.Compare the numerical solution with the analytical solution to verify the rationality of the results in this paper.