Stability Analysis Of Functionally Graded Material Beams With Surface-bonded Magnetostrictive Layers Under Thermal Loads

The giant magnetostrictive materials(GMM) have many excellent characteristics, like large magnetostriction, high electromechanical coupling coefficient, response speed, and it also can work in a wider frequency range. In this paper, the model of functionally graded materials beams surface-bonded magnetostrictive layer is established and the effect of the magnetic field intensity, magnetostrictive layer thickness, functionally graded material beam thickness and power law index on the critical buckling temperature and post-buckling configuration are investigated.1. Considering the properties of functionally graded materials with the beam thickness is a power series change, the physical parameters (elastic modulus E, thermal expansion coefficient α) as a function of thickness coordinate. Magnetostrictive functionally graded material beams model is established under Cartesian coordinate system.2. Based on the Euler Bernoulli beam theory, the stress and displacement equation is derived according to the geometric equation and physics equation of magnetostrictive materials and functionally gradient materials. The governing equations of magnetostrictive functionally graded material beams in temperature field are deduced from the elastic equations. Using the adjacent equilibrium criterion and the control equations to get the function expression of displacement, the critical thermal force in a given magnetic field intensity is obtained through the eigenvalue method under different boundary conditions. We can get critical thermal force by set the critical buckling temperature as an unknown fundamental quantity in three kinds of temperature environment. To comparison of the two cases of critical thermal force, so as to obtain the expression of critical buckling temperature.3. The nonlinear governing equation of functionally graded materials beams surface-bonded magnetostrictive layer is established and the numerical solutions are adopted by using the shooting method. The numerical solution of the nondimensional critical buckling temperature and static nonlinear post-buckling configuration at one end of simply supported and fixed supported at the other end are obtained. The post-buckling configuration with different magnetostrictive layer thickness, power law index and the other parameters is given. The effect of the parameters on the post-buckling configuration and dimensionless critical buckling temperature are examined.