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Finite Element-based Free Vibration Analysis of Power-Law, Exponential and Sigmoidal Functionally Graded Sandwich Beams

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Abstract

In the present work, a comparative study has been carried out between sandwich functionally graded beams made up of power law and exponential and sigmoidal laws under free vibration conditions. The study has been carried out using the recently proposed higher-order zigzag theory. The present formulation satisfies all important necessary conditions such as interlaminar transverse stress continuity condition at the interface. The present formulation incorporates transverse normal stress and hence is more efficient. Also, the present formulation satisfies zero transverse shear stress conditions at the top and bottom surface of the beam. Three-noded C-0 finite element having eight degrees of freedom per node is used during the study. The present formulation is free from any post-processing requirements. The efficiency of the present model has been carried out by comparing the present results for the power-law sandwich FGM beam with those available in the literature. Variation of stresses across the thickness for the first six modes in graphical form is also reported. Several new results have also been presented in the manuscript, especially for exponential and sigmoidal sandwich FGM beams, which will serve as the benchmark for future studies.

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Acknowledgements

The authors are thankful to MHRD, Government of India and National Institute of Technology Kurukshetra, India for providing financial assistance for the present work through the scholarship grant (2K17/NITK/PHD/6170004).

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Authors and Affiliations

  1. Department of Civil Engineering, National Institute of Technology Kurukshetra, Kurukshetra, 136119, India

    Aman Garg & H. D. Chalak

  2. Laboratoire de Génie Energétique Et Matériaux, LGEM, Université de Biskra, B.P. 145, Biskra, R.P. 07000, Algeria

    Mohamed-Ouejdi Belarbi

  3. Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Anupam Chakrabarti

  4. Laboratoire D’Etude Des Structures Et de Mécanique Des Matériaux, Département de Génie Civil, Faculté Des Sciences Et de La Technologie, Université Mustapha Stambouli, B.P. 305, Mascara, R.P. 29000, Algeria

    Mohammed-Sid-Ahmed Houari

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Appendices

Appendix 1

See Table 7.

Table 7 Brief about homogenization scheme
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Appendix 2

See Fig. 32.

Fig. 32
figure 32

Validation study for non-dimensional in-plane stress distribution for 1-1-1 s-s H-Type-A sandwich FGM beam with results obtained using model proposed by Chalak et al. [35] \(\left( {n = 1, l/h = 10} \right)\)

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Garg, A., Chalak, H.D., Belarbi, MO. et al. Finite Element-based Free Vibration Analysis of Power-Law, Exponential and Sigmoidal Functionally Graded Sandwich Beams. J. Inst. Eng. India Ser. C 102, 1167–1201 (2021). https://doi.org/10.1007/s40032-021-00740-5

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