An approach for the Pasternak elastic foundation parameters estimation of beams using simulated frequencies

Abstract

As a first attempt, a mix of differential quadrature (DQ) and simplex (S) method for the Pasternak elastic foundation parameters estimation of beams using simulated frequencies is presented. The method is applied for the parameters estimation of functionally graded (FG) beams. The first-order shear deformation theory is employed to derive governing equations of FG beam on the Pasternak elastic foundation. The equations are discretized by utilizing the DQ method and frequencies of the beam are calculated. Then, the simulated frequencies are obtained by applying random error to the calculated frequencies. The simulated frequencies are used as input data for estimating parameters of the problem. An objective function as a root-mean-square error between the calculated and simulated frequencies is defined. The DQ method and simplex technique as a classical optimization technique are coupled to minimize the function via finding the best foundation parameters, iteratively. Some examples are solved to show applicability, robustness and accuracy of the mixed method for elastic foundation parameters estimation of the beam. Also, it has been found that using only the first simulated frequency of the beam cannot give correct parameters of the foundation.