Stochastic Responses Of Functionally Graded Material Beams

Functionally gradient materials(FGM)is a new type of non-homogeneous composite material made of ceramic and metal.Due to its excellent structural performance and potential application value,Scholars pay more attention to the study of mechanical behavior of FGM.In this paper,the functionally graded material beams whose material properties are distributed along the thickness direction according to the volume distribution of each component is selected as the research object.Based on the Euler beam theory,the linear stochastic response,the nonlinear stochastic response,the viscoelastic damping stochastic response and stochastic response of a piezoelectric energy harvesting system based on FGM beams are studied respectively,which includes the following four aspects:(1)Based on the Euler beam elasticity theory,the linear machine motion equation of FGM is established,and the Galerkin method is used to study the linear stochastic response of the functionally graded beams under random excitation.The influence of different material gradient index,load intensity and beam slenderness ratio on the system response was analyzed.(2)By introducing the influence of the axial force of the system,the nonlinear response of the functionally graded material beams is studied by using the equivalent linearization method.The results of a large deformed functionally graded material beams are compared with those of a degraded linear functionally graded material beams,and the influence of nonlinear terms on the mean square displacement response of the system is analyzed.The effects of different material gradient indices,beam slenderness ratio and load strength on the system vibration effects.(3)Considering the influence of viscoelastic damping,the first-order Galerkin approximation is used to analyze the nonlinear stochastic response of FGM beams.Based on the generalized harmonic transform,the viscoelasticity is approximated as quasilinear damping and quasi-linear stiffness,and the probability density function of the viscoelastic damping functionally graded material beam is studied by theequivalent nonlinear method.The effects of different relaxation time,viscoelastic force amplitude,material gradient index,beam slenderness ratio,excitation intensity and linear viscous damping coefficient on the system response were discussed.(4)Based on Euler beam theory and piezoelectric effect,the governing equations of energy collector for functional graded material piezoelectric beam are established respectively.By using generalized harmonic transformation,an equivalent linear system related to mechanical state is established,and the stochastic response of piezoelectric energy harvesting system with functionally graded material beam is studied.The effects of system material gradient index,beam slenderness ratio,excitation intensity and load impedance on the mean square voltage were analyzed.