Mechanical Analysis Of Size-dependent Laminated Piezoelectric Beams

At present,intelligent structure system is widely applied in many fields such as machinery,aerospace,aviation,biomedicine and so on,because of its outstanding advantages in ensuring structural safety,improving structural performance,lightening structural weight and reducing energy consumption.Because of its fast response,high linearity and low power consumption,piezoelectric materials have broad application prospects in intelligent structure systems.Usually,they are embedded or embedded in piezoelectric elastomers or piezoelectric actuators in conventional elastic materials.It is necessary to study the mechanical properties of this micro structure when the piezoelectric material is used in the microstructural system.The scale effect should not be negligible when the size of the structure is in the order of micron or nanometers.At present,many scholars have put forward the theory of scale effect of small structure.Based on the modified couple stress theory,a piezoelectric composite laminated beam model considering scale effect is established in this article.The scale correlation analysis of the deformation of piezoelectric laminated beams under different loads and different boundary conditions.First,based on the new modified couple stress theory that only produces a size parameter for the anisotropic material,the scale dependent constitutive equation of composite laminated beam is obtained by using the Timoshenko beam assumption.Then the scale dependent constitutive equation of composite laminated beam is obtained.Combined with the effect of piezoelectric layer on the stress strain relationship,the constitutive relation of laminated composite beam is derived.Secondly,the equation of motion and the boundary conditions are dimensionless,and the displacement and angle of the five possible boundary conditions are solved.The influence of different size parameters on beam displacement under different voltage is analyzed,and the relationship between maximum displacement and voltage under different size parameters is verified,and the scale correlation of piezoelectric microstructures is verified.Finally,a model of variable length of the piezoelectric driving layer is established,a certain analysis and summary of the deformation of the model under the internal size parameters of different sizes is made,deformation obtained was compared with that without considering the size effect by traditional mechanics theory.It is concluded that the deformation of the structure will change when the internal scale parameters of the material are considered.