Analysis of Stability and Vibrations of Porous Power and Sigmoid Functionally Graded Sandwich Plates by the R-Functions Method

DOI https://doi.org/10.15407/pmach2023.04.038
Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher Anatolii Pidhornyi Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN  2709-2984 (Print), 2709-2992 (Online)
Issue Vol. 26, no. 4, 2023 (December)
Pages 38-49
Cited by J. of Mech. Eng., 2023, vol. 26, no. 4, pp. 38-49

 

Authors

Lidiya V. Kurpa, National Technical University “Kharkiv Polytechnic Institute” (2, Kyrpychova str., Kharkiv, 61002, Ukraine), e-mail: kurpalidia@gmail.com, ORCID:0000-0002-4459-8249

Tetyana V. Shmatko, National Technical University “Kharkiv Polytechnic Institute” (2, Kyrpychova str., Kharkiv, 61002, Ukraine), e-mail: ktv_ua@yahoo.com, ORCID: 0000-0003-3386-8343

Anna B. Linnik, National Technical University “Kharkiv Polytechnic Institute” (2, Kyrpychova str., Kharkiv, 61002, Ukraine), e-mail: linnik2105@gmail.com, ORCID: 000-0003-4227-3210

 

Abstract

In this paper, the R-functions method is used for the first time to study the stability and vibrations of porous functionally graded (FG) sandwich plates with a complex geometric shape. It is assumed that the face layers of the plate are made of functionally graded materials, and the middle layer is isotropic, namely ceramic. Differential equations of motion were obtained using the first-order shear deformation theory with a given shear coefficient (FSDT). Two models of porosity distribution according to the power (P-law) and sigmoid (S-law) laws were studied. Analytical expressions for calculating the effective mechanical characteristics of functionally graded materials with even and uneven porosity distribution were obtained. Proposed approach takes into account the fact that the subcritical state of the plate can be heterogeneous, and therefore, first of all, the stresses in the middle plane of the plate are determined, and then the eigenvalue problem is solved in order to find the critical load. To determine the critical load and plate frequencies, the Ritz method combined with the R-functions theory was used. Developed algorithms and software are tested on case studies and compared with known results obtained by another methods. A number of problems of stability and vibrations of the porous functionally graded sandwich plates with a complex geometric shape for various layer arrangement schemes, various boundary conditions and laws of porosity distribution have been solved.

 

Keywords: stability, vibrations, sandwich plates, porosity, functionally graded material, R-functions method, Ritz method.

 

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Received 08 August 2023

Published 30 December 2023