Vibration Analysis Of Mico-structure Based On The Couple Stress Theory

The mechanical properties of the fluid-conveying magneto-electro-elastic(MEE)mico-tube and the bi-directional(2D)functional graded material(FGM)nano-beam are investigated in this paper.The concrete contents are composed as follows:Firstly,the nonlinear free vibration of a MEE mico-tube is investigated.Based on the Euler-Bernoulli beam model and the modified couple stress theory,the nonlinear governing equation of a fluid-conveying pined-pined MEE micro-tube is derived and analyzed by the direct multiple scales method.The geometric nonlinearity caused by axial deformation is considered.The model of micro-tube can be reduced to the model of classical Euler-Bernoulli beam.Numerical results show the effects of some parameters on the vibration.Then,the nonlinear forced vibration analysis of a MEE micro-tube conveying fluid is discovered.According to the model of the free vibration of a MEE mico-tube,the mathematical modeling of the nonlinear forced vibration is developed.The results can be solved by direct multiple scales method.The influences of some parameters,such as vibration,are discussed in detail.Finally,the nonlinear buckling of 2D FGM nano-beam is analyzed.The equation of governing is derived based on Euler-Bernoulli beam theory,von Kármán geometric nonlinearity and nonlocal elasticity theory.The nonlinear buckling behavior of the nano-beam with size effect is investigated.The 2D FGM introduces an additional stiffness term in governing equation,therefore it cannot be solved by classical methods.The differential quadrature method(DQM)used to solve the nonlinear buckling problem.The effects of different material parameters,boundary conditions and size scale on nonlinear buckling behavior are discussed.