Finite Element Analysis And Application For Functionally Graded Piezoelectric Cantilever Beams With Different Moduli In Tension And Compression

The sensors with piezoelectric cantilever beam as basic element are widely used in the field of health monitoring of civil engineering structures.This piezoelectric element,which is made up of traditional piezoelectric ceramics and metals,often resulting in inaccurate readings or damage of sensors due to the problem of bonding between materials.Therefore,as a new kind of composite material,functionally graded piezoelectric materials have emerged as a new research hotspot.This composite materials can maintain the mechanical and electrical coupling characteristics of the original piezoelectric material,and the material components of this composite materials can also present gradient changes along the thickness direction of the element,in order to eliminate the interface effect and achieve the perfect combination of functional gradient characteristics and piezoelectric effect.Besides,existing studies have shown that composite material will exhibit significantly different properties when stretched and compressed(i.e.bimodulus effect).However,if the influence of the bimodulus effect is ignored to analyze the stress and deformation of the structure due to the complexity of the analysis will produce a great error with the actual situation,which will eventually affect the practical application of the piezoelectric cantilever beam as the basic element of the sensor.In this paper,we use analytical method and numerical method respectively to study the functionally-graded piezoelectric cantilever beam with different moduli in tension and compression in both static force and vibration.The application of analytical method focuses on the derivation of one-dimensional solution.On the basis of the deformation characteristics of euler-bernoulli beam,the equivalent elastic modulus and bending stiffness of the piezoelectric beam in the one-dimensional case are derived,and the one-dimensional static solution for stress,displacement and electrical displacement of the beam are acquired,as well as the analytical solutions of the free damping vibration of the cantilever beam are obtained.Moreover,the static and vibration problems of bimodulus functionally-graded piezoelectric cantilever beam are simulated effectively by ABAQUS software based on the simplified mechanical model of tension-compression subarea and the laminated theory of composite materials,and the two-dimensional numerical solutions are obtained.The results show that both the one-dimensional theoretical solution and the two-dimensional numerical solution are in good agreement with two-dimensional theoretical solution in the existing studies,and the validity of the solution in this paper are verified.The equivalent modulus of elasticity derived in this paper includes the flexibility coefficient,piezoelectric coefficient and dielectric coefficient in the constitutive equation of the coupling of force and electricity.The formulation of this physical quantity simplifies greatly the whole solving process,and the attempt of equivalence is the application of the basic idea of homogenization,essentially.At the same time,the results also show that considering the bimodulus effect of functionally graded piezoelectric materials will affect the final response of the structure to a certain extent.Thus,taking the bimodulus effect into account in the mechanical analysis is worth weight in gold.In addition,the relative magnitude between the tensile modulus and compression modulus may have effect on the attenuation speed of vibration.In a word,for the piezoelectric sensor based on the cantilever beam,the work of this paper has certain guiding significance for its theoretical analysis and design.