Theoretical And Finite Element Analysis Of Nonlinear Thermoelastic Coupling Vibration

The basic equations of elliptic plate, when temperature and stress fields are coupled, are developed, which include transverse thermal vibration equation , the compatibility equation and energy equations. In order to solve them easily, we introduced the dimensionless quantities and non-dimensionlized the obtained equations. A nonlinear ordinarydifferential equations are obtained by Galerkin's method. The numericalresults are presented by employing Runge-Kutta method. The important results are given as follows: The coupling coefficient the amplitude of temperature, the parameter, the ration of length of long axis to that of short axis and initial displacement are main factors which influence the thermoelastic vibration of elliptic plate; When the initial displacement is smaller, thermoelastic coupling makes the frequency of the elliptic plate larger and when the initial displacement is larger, thermoelastic coupling makes the frequency of the elliptic plate smaller; The boundary conditions has strong influence on the coupling effect, the stronger it is, the smaller frequency of free vibration is but the larger amplitude is. Second, the thermoelastic coupling vibration of cylindrical shell are discussed by means of the same method. The coupling coefficient, amplitude of temperature, initial displacement, ratio of length to radius and that of radius to thickness are main factors which influence the thermoelastic vibration of cylindrical shell; The higher the coupling coefficient is, the lower the axial force, the axial stress and the axial moment are.The finite element code LS_DYNA is used to investigate the response of the axisymmetry cylindrical shell under the thermal impact, and the curves of displacement vs time and that of stress vs time are obtained. The results from simulation agree well with the conclusions ofconference [21], and indicate that the boundary conditions have no obvious effect on the displacement and stress; that the displacement and stress increase with linear heat expanding ratio, and those decrease with the specific heat of material; that the displacement increases with the heat transfer ratio, but the stress does not .