Research On Statics And Dynamics For The Piezoelectric Beam Reinforced With BNNTs Under Electro-Thermo-Mechanical Loadings

In recent years,with the development of science and technology,a piezoelectric nature of the new intelligent nano-composite materials,i.e.,the matrix of the beam is PVDF and the reinforced material is BNNT,attracting the interest of the scientific community.The static and dynamic research and application of the piezoelectric beam reinforced with Boron nitride nanotubes(BNNT)has gradually emerged.In this paper,the constitutive relations of piezoelectric beam reinforced with BNNTs is established by using the strain displacement relationships and the piezoelectric theory considering the temperature effect.Under electro-thermo-mechanical loadings,the constitutive equations of the buckling,nonlinear bending,dynamic stability and nonlinear dynamic response are deduced by energy-variation principle respectively.The effects of voltage,temperature,boundary condition and volume ratio on the buckling load,nonlinear bending,dynamic stability and nonlinear dynamic response of piezoelectric beam reinforced with BNNTs are discussed in detail in numerical examples.First,the axial load is applied at both ends of the piezoelectric beam.The results show that the buckling load of the piezoelectric beam can be increased or decreased by applying negative or positive voltage at both ends of the beam.The buckling load of the BNNTs reinforced piezoelectric beam increases while the temperature rise decreases,and the volume ratio increases.Secondly,the transverse dynamic load is applied across the piezoelectric beam considering the geometrical nonlinearity.The results show that the deflection and bending moment of the nonlinear bending of the beam are less than the deflection and bending moment of the linear bending,and when the dimensionless load is less than 200,the BNNTs However,with the increase of load,the difference between the two increases gradually.When the dimensionless load is more than 500,the nonlinear bending effect is very obvious.It is necessary to consider the nonlinearity of piezoelectric beam reinforced with BNNTs.Then,the axial dynamic load is applied at both ends of the piezoelectric beam,and the nonlinear dynamic response of the piezoelectric beam is analyzed.The Governing equations is a set of Mathieu equations,which is used to describe the vibration behavior of the piezoelectric beam.The Boltin's method is used to transform the constitutive equation into a homogeneous linear algebraic equation,and the influence of various parameters on the vibration fundamental frequency and unstable region of the beam is analyzed.Finally,a transverse dynamic load is applied across the piezoelectric beam,the numerical solution of the nonlinear dynamic response of the piezoelectric beam is obtained by using the finite difference method and Newmark method.The results show that the dynamic response of the beam in the linear case is greater than that in the nonlinear case.The non-linear dynamic response amplitude of piezoelectric beam reinforced with BNNTs increases with the increase of voltage,temperature rise and mechanical load.When the volume ratio of BNNT in matrix increases,the response amplitude decreases.