Thermo-mechanical Free Vibration Analysis Of Bi-dimensional FGM Beams By Using Different Beam Theories

Functionally graded material(FGM)is a new type of composite based on a new design theory,FGM not only has excellent thermal shock resistance of traditional composites,but also can alleviate or even avoid inter-facial stress concentration in ultra high temperature environment.It is a potential material in many fields such as aeronautics and Astronautics,nuclear industry and so on.It has great application value,FGM has the extremely broad application prospect.In this paper,the two-dimensional FGM beam is chosen as the object of study.It is assumed that the material properties are distributed along the transverse and axial directions of the beam in two directions according to the power function.Based on the principle of virtual work,the free vibration control equations of euler-bernoulli beam theory,Timoshenko beam theory and high order shear deformation beam theory are derived.Finally,the model is discretized and solved by the finite element method.Numerical examples show that:(1)With the increase of the material gradient index,the natural frequency of the FGM beam will decreases.(2)As the temperature difference increases,the FGM beam will undergo thermal buckling,When the temperature difference is less than the critical temperature,the natural frequency increases with the increase of porosity.When the temperature difference is greater than the critical temperature,the natural frequency will decrease with the increase of porosity.Temperature has an important influence on the frequency of FGM beam.(3)Because the shear deformation effect can be considered,the HOBT theory has less frequency than the EBBT theory,and this trend is more obvious when the span height of the beam is relatively small.(4)With the change of the axial material gradient exponent,the formation of the two-dimensional FGM beam has no symmetry.