A Stochastic Investigation of Effect of Temperature on Natural Frequencies of Functionally Graded Plates

  • P. K. KarshEmail author
  • T. Mukhopadhyay
  • S. Dey
Conference paper
Part of the Lecture Notes in Civil Engineering book series (LNCE, volume 38)


The present paper deals with thermal uncertainty quantification in the free vibration of functionally graded materials (FGMs) cantilever plate by using the finite element method coupled with multivariate adaptive regression splines surrogate (MARS) model. The combined effects of uncertainty in material properties on the natural frequency are examined. The power law is employed for gradation of material properties across the depth of FGM plate, while the Touloukian model is used to evaluate temperature effects on the material properties. In finite element analysis (FEA), eight noded iso-parametric elements are considered with each element having five degrees of freedoms. In MARS, Sobol sampling is employed to train the model, which results in better convergence and accuracy. The results of MARS model are validated with Monte Carlo simulation results. The results reveal that MARS model can achieve a significant level of accuracy without compromising the accuracy of results.


Finite element method Monte Carlo simulation Multivariate adaptive regression splines Free vibration Thermal uncertainty Functionally graded plates 



P. K. Karsh received financial support from the MHRD, Government of India, during this research work.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentNational Institute of Technology SilcharSilcharIndia
  2. 2.Department of Engineering ScienceUniversity of OxfordOxfordUK

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