Bending Analysis Of Functionally Graded Microcantilever Beam With Surface Stress

Microcantilever sensors usually use the surface stress-induced deformation to monitor environmental molecules/atoms,viruses,cells,etc.in real time.The relatively low signal-tonoise ratio and accuracy limit their application range.The accuracy could be improved by applying gradient materials for the microcantilever or selecting an appropriate geometric shape.Therefore,in this thesis,functionally graded materials,with arbitrary change of the material properties,are introduced into the surface stress model of the microcantilever,and the size effect(the structures are in micro/nano scale)is also considered.Then,based on the nonlocal elastic theory and the classical continuum theory,the effects of size effect,material property,gradient parameter and different section shapes on the beam bending are analyzed,respectively.The main results are summarized as follows:(1)Based on the principle of virtual work and the theory of small deformation EulerBernoulli beam,the mechanical model of the functionally graded rectangular microcantilever beam with arbitrary varying material properties and along the axial direction under the action of surface stress is established,and the surface stress model is optimized.Then,a general method,Taylor series expansion method,is used to get the analytical relationship between the surface stress and the bending deformation(deflection,slope,curvature)of the microbeam.The effects of gradient parameter and elastic modulus ratio on the dimensionless deformation induced by surface stress are discussed.The design of atomic force microscope and micromechanical sensor is optimized by selecting appropriate gradient variation forms and parameters.(2)Based on the theory of the Euler-Bernoulli beam with small deformation,the mechanical model of a functionally graded microcantilever beam with variable cross-section under surface stress is established.The material properties and beam width vary arbitrarily along the axial direction,and the Taylor series expansion method is used to solve the problem.The effects of different cross section shapes and material properties on the adsorption capacity of microcantilever beams are discussed based on numerical examples.(3)Considering the size effect of the microstructure,based on the nonlocal elastic theory and the Euler beam theory,the nonlocal theoretical model of the surface stress for the functionally graded microcantilever beam is established.The solution is obtained by using the Taylor series expansion method,and the relationship between the bending deformation and the surface stress is also obtained.The influence of length scale parameters and gradient parameters on the adsorption capacity of microcantilever beams is discussed.The proposed method and derived solution in this paper can guide the improvement of the sensitivity of the surface stress-based microcantilever sensor,and provide a theoretical basis for the practical application and optimal design of the microcantilever sensor.