Research On Displacement Field Reconstruction Algorithm Of Elastic Thin Plate Based On Measured Strain

Elastic thin plate is the most widely used structure in various engineering fields.In the area of structural control and health monitoring,the displacement field monitoring of structures is an important indicator of estimating the health of structures.With the rise of optical fiber sensing technology,FBG-based strain measurement is becoming more and more accurate,rapid and convenient.Therefore,monitoring structural displacement field through measured strain has a promising application prospect.In the existing strain-based displacement field reconstruction algorithms,modal matrix transformation method and inverse finite element method are the most prevalent.However,the modal matrix transformation method is not applicable to the case of non-linear vibration.The inverse finite element method has strict requirements on the number of strain measuring points and requires different strain components of a measuring point,which brings challenge the sensor layout.Besides,the algorithm is too complex and is not economical and convenient in practice.Some plate-specific methods do not have universality and only calculate the displacement in one direction,so the reconstructed displacement field is relatively rough.Based on the curves theory in differential geometry,a reconstruction algorithm for displacement field of square plates with classical boundary conditions is presented in this paper.The method first obtains the shape of a series of orthogonal deflection curves through the quadratic integral of curvature,and then make them bridge on each other by translation and rotation according to boundary conditions.Finally the orthogonal curvilinear network that reflecting the displacement field of the plate is established.The proposed method has high efficiency and accuracy,and is suitable for high frequency vibration and nonlinear vibration shape detection.The main works of this paper are:(1)The calculation formula of boundary strain is derived by using boundary conditions and strain interpolation function.According to the characteristics of different boundaries,the rotation and translation methods for determining the position of the deflection curves are given.For the special case of adjacent simply supported plate,the nonlinear optimization problem for solving the rotation angles of the orthogonal deflection curves is established.(2)Taking cantilever plate,opposite side simple support plate and adjacent side simple support plate as examples,the reconstruction algorithm of displacement field is verified.The reliability of the reconstruction algorithm of plate under natural frequency excitation,arbitrary frequency excitation and free vibration is analyzed.The reconstruction errors are obtained by comparing the reconstruction results with the calculation results of finite element.(3)Taking the nonlinear elastic material plate and the nonlinear elastic foundation plate as an example,the nonlinear vibration of cantilever plate and the opposite side simply support plate are simulated by ANSYS.The analysis result is taken as input to verify the reliability of the reconstruction algorithm when applying to nonlinear vibration shape measurement.Finally,the algorithm is applied to the nonlinear vibration mode detection of simply support plate buried in granular medium,and some of the nonlinear law is revealed.