Research On Mechanical Properties Of Piezoelectric Stack Clamped Beam Based On State Space Method

Smart materials show a good application prospect in the safety and development of large structures and projects,especially in health monitoring and diagnosis of large structures. In civil engineering,piezoelectric smart materials have played a significant role in structural monitoring,controlling and intelligent regulation and so on.Among a large number of structures, since the stacked member of piezoelectric smart materials is one of the common components, it is necessary to study the mechanical properties of different piezoelectric laminated materials under different support and stress conditions,in order to seek a more accurate, more convenient and more rapid method of solving, provide a theoretical basis for the design and manufacture of structures.The general elastic material, laminated elastic materials, piezoelectric materials, single-layer piezoelectric smart laminated material clamped beam as the mechanical model in this paper respectively.Based on the three basic equations of elasticity (constitutive equations, the equations of motion and gradient equation),In this paper, using the state space method, the matrix is derived and calculated, established the corresponding state equation, combined with the corresponding boundary conditions for solving the state transfer matrix. The upper surface of the beam is distributed with uniform load as an example, the exact solution of the state variables at any height of the beam is obtained by using the algebraic operation.In solution of piezoelectric laminated composite state space, consider the piezoelectric effects of piezoelectric materials, ignore the physical, body charge, current, based on piezoelectric effect equation, transfer matrix is obtained, finally obtains the exact solution of piezoelectric laminated beam each state variable.This method is suitable for the single beam and laminated beam, without limitation of thickness, which can be widely used in solving the layered component.At the end of this paper, the MATLAB software is used to calculate the composite beams with different span depth ratio, and the laminated beams of the common elastic material, the laminated beams, the elastic piezoelectric materials and the elastic piezoelectric materials.From the comparison of the results, it is concluded that both the single beam and the laminated beam, or the same kind of material and a variety of materials, the calculation results are very similar.In the case of different high span ratio, the deviation of the calculated results and the FEM simulation results are also within the allowable range. It can be known that the assumption of the boundary conditions of clamped beam is very accurate in this paper,and based on the theory of state space, the method of piezoelectric material structure is very accurate for the calculation results of single beam and laminated beam of different materials.This method also can applied to the stacking structure and computer programming...