Steel and Composite Structures

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A hybrid inverse method for small scale parameter estimation of FG nanobeams

  • Darabi, A. (Department of Civil and Environmental Engineering, School of Engineering Shiraz University) ;
  • Vosoughi, Ali R. (Department of Civil and Environmental Engineering, School of Engineering Shiraz University)
  • Received : 2015.09.20
  • Accepted : 2016.01.12
  • Published : 2016.04.10
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Abstract

As a first attempt, an inverse hybrid numerical method for small scale parameter estimation of functionally graded (FG) nanobeams using measured frequencies is presented. The governing equations are obtained with the Eringen's nonlocal elasticity assumptions and the first-order shear deformation theory (FSDT). The equations are discretized by using the differential quadrature method (DQM). The discretized equations are transferred from temporal domain to frequency domain and frequencies of the nanobeam are obtained. By applying random error to these frequencies, measured frequencies are generated. The measured frequencies are considered as input data and inversely, the small scale parameter of the beam is obtained by minimizing a defined functional. The functional is defined as root mean square error between the measured frequencies and calculated frequencies by the DQM. Then, the conjugate gradient (CG) optimization method is employed to minimize the functional and the small scale parameter is obtained. Efficiency, convergence and accuracy of the presented hybrid method for small scale parameter estimation of the beams for different applied random error, boundary conditions, length-to-thickness ratio and volume fraction coefficients are demonstrated.

Keywords

References

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