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Free vibration analysis of sandwich beam with porous FGM core in thermal environment using mesh-free approach

Hung Tran Quang, Tu Tran Minh, Duc Do Minh

Archive of Mechanical Engineering

2022

LXIX, nr 3

471--496

Thermally induced free vibration of sandwich beams with porous functionally graded material core embedded between two isotropic face sheets is investigated in this paper. The core, in which the porosity phase is evenly or unevenly distributed,has mechanical properties varying continuously along with the thickness according to the power-law distribution. Effects of shear deformation on the vibration behavior are taken into account based on both third-order and quasi-3D beam theories. Three typical temperature distributions, which are uniform, linear, and nonlinear temperature rises, are supposed. A mesh-free approach based on point interpolation technique and polynomial basis is utilized to solve the governing equations of motion. Examples for specific cases are given, and their results are compared with predictions available in the literature to validate the approach. Comprehensive studies are carried out to examine the effects of the beam theories, porosity distributions, porosity volume fraction, temperature rises, temperature change, span-to-height ratio, different boundary conditions, layer thickness ratio, volume fraction index on the vibration characteristics of the beam.

An efficient analysis of steady-state heat conduction involving curved line/surface heat sources in two/three-dimensional isotropic media

Mohammadi M., Hematiyan M. R., Shiah Y. C.

Journal of Theoretical and Applied Mechanics

2018

Vol. 56 nr 4

1123--1137

In this paper, a new formulation based on the method of fundamental solutions for two/three- -dimensional steady-state heat conduction problems involving internal curved line/surface heat sources is presented. Arbitrary shapes and non-uniform intensities of the curved heat sources can be modeled by an assemblage of several parts with quadratic variations. The presented mesh-free modeling does not require any internal points as in domain methods. Four numerical examples are studied to verify the validity and efficiency of the proposed method. Our analyses have shown that the presented mesh-free formulation is very efficient in comparison with conventional boundary or domain solution techniques.