Dynamic Analysis of Functionally Graded Porous Beams Using Complementary Functions Method in the Laplace Domain

Noori, Ahmad Reshad; Aslan, Timuçin Alp; Temel, Beytullah

doi:10.1016/j.compstruct.2020.113094

Cited by 38 publications

(20 citation statements)

References 40 publications

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“…k w = k s = 0, and ∆T = 0. The material properties of the porous beam are E m = 200 GPa, ρ m = 7850 kg/m 3 , ν m = 0.33 and e o = 0.5 [27]. Some values of the first non-dimensional frequency are reported and compared with the previous publish of Noori et al [27] in Table 5.…”

Section: Validationmentioning

confidence: 90%

Free vibration of piezoelectric FGM sandwich beam with porous core embedded in thermal environment and elastic foundation

Hung

Tú

Duc

2021

STCE

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This paper aims to present thermo-electrical free vibration characteristics of functionally graded material (FGM) sandwich beam placed on the two-parameter elastic foundation. The beam is constructed of a foam core, two middle FGM layers, and two outer piezoelectric layers. It is assumed that the beam is subjected to a constant voltage and a uniform/linear temperature distribution. Physical properties of the core and two middle layers vary smoothly through the thickness according to the cosine and power-law forms, respectively. Lagrange equations in conjunction with the Reddy third-order beam theory is employed to derive the governing equations of motion. A simple polynomial trial function-based Ritz method is adopted for the approximation of the displacement field to obtain the vibration response. The correctness of the study is verified by comparisons with other authors’ published results. Influences of geometry parameters, material property distribution, applied voltage, elastic foundation, temperature distribution, temperature change, porosity coefficient, span-to-height ratio, and boundary conditions are investigated through parametric studies.

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Section: Validationmentioning

confidence: 90%

Free vibration of piezoelectric FGM sandwich beam with porous core embedded in thermal environment and elastic foundation

Hung

Tú

Duc

2021

STCE

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“…Roberts et al [15,16] proposed general formulations for elastic modulus and mass density for random 3D closed-cell and open-cell porous materials based on the Voronoi tessellations [18] and Gaussian random fields theories [19,20] using finite element method. The developed formulations are consistent with the experimental data and successful when used for modeling of porous structures, and have been used by many researchers to study behavior of porous structural forms [5,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. A brief literature review on porous beams is presented hereinafter.…”

Section: Introductionmentioning

confidence: 89%

Nonlinear vibration analysis of bidirectional porous beams

Keleshteri

Jelovica

2021

Engineering with Computers

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This paper presents nonlinear vibration behavior of shear deformable bidirectional porous beams with non-uniform porosity distribution. A new porosity distributions are proposed to maximize natural frequencies of the porous beam. It is assumed that closed-cell voids are distributed along the thickness and length of the beam. Hamilton principle is used to derive nonlinear governing equations using Reddy beam theory considering von Karman geometrical nonlinearity. Generalized differential quadrature method, harmonic balance approach along with the Picard iterative approach are used to discretize and solve the nonlinear dynamic equations. The variation of nonlinear frequency versus the vibration amplitude is highlighted considering various influential factors such as geometrical parameters, porosity distributions, beam theories and boundary conditions. It is shown that the newly defined porosity distribution can increase the frequencies in comparison to the conventional porosity distribution. Comparing beams of the same weight shows that porosities near the center of the beam further increases frequencies in comparison to the other porosity distributions. Moreover, bidirectional porosity increases the frequencies in comparison to the unidirectional porosity. Frequencies of the bidirectional porous Reddy beam depend not only on the bending stiffness, as in the case of unidirectional porous beam, but also on the first derivative of the bending stiffness.

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“…The CFM has been applied to several problems in applied mechanics. [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] Details of the CFM are presented in the Appendix. The matrix form of the governing equations ( 58) to (63) can be written as follows |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}…”

Section: Application Of the Cfmmentioning

confidence: 99%

“…The method can be applied to any arbitrary continuous function. This method has been applied in the analysis of several structures [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] and compared with other available methods like FEM, shooting method, etc. The shooting method uses the trial and error method to determine the initial conditions.…”

Section: Introductionmentioning

confidence: 99%

A powerful numerical approach for the axisymmetric bending response of shear deformable two-directional functionally graded (2D-FG) plates with variable thickness

Noori

Temel

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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In the present article, a powerful numerical approach is applied to the axisymmetric bending of 2 D-FG circular and annular plates with variable thickness. The mechanical properties of the materials of the plate are assumed to vary continuously both in the radial and thickness directions. The principle of minimum total potential energy is used to obtain the governing equations. Shear deformation is considered based on the first-order shear deformation theory (FSDT). These ODEs are solved via the Complementary Functions Method (CFM) for the first time. The novelty of this paper is the infusion of the CFM to the axisymmetric bending of a wide range of annular or circular plates, with variable thickness, radially FG (RFG), FG in thickness direction, or 2D-FG. In addition to adopting this effective numerical approach to the present class of problems, various parametric studies are presented to show the influence of material variation parameters and geometric constants on the axisymmetric bending response of the considered structures. Results of the proposed approach are validated with those carried out by FEM and those of the available published literature. An excellent agreement is observed.

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Dynamic Analysis of Functionally Graded Porous Beams Using Complementary Functions Method in the Laplace Domain

Cited by 38 publications

References 40 publications

Free vibration of piezoelectric FGM sandwich beam with porous core embedded in thermal environment and elastic foundation

Free vibration of piezoelectric FGM sandwich beam with porous core embedded in thermal environment and elastic foundation

Nonlinear vibration analysis of bidirectional porous beams

A powerful numerical approach for the axisymmetric bending response of shear deformable two-directional functionally graded (2D-FG) plates with variable thickness

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