Research Articles | Challenge Journal of Structural Mechanics

Natural frequencies of porous orthotropic two-layered plates within the shear deformation theory

Ferruh Turan


DOI: https://doi.org/10.20528/cjsmec.2023.01.001
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Abstract


This paper analyzes the natural frequencies of porous orthotropic laminated composite plates with two different porosity models based on the higher-order shear deformation theory. The fundamental relations of natural frequency analysis are derived by using the virtual work principle and hyperbolical shear deformation theory. The obtained partial differential equations system is reduced to an ordinary differential equations system via approximation functions suitable for simply supported boundary conditions and the Galerkin method. After some mathematical operations, the natural frequency equation of porous orthotropic laminated composite plates is obtained in the framework of hyperbolical shear deformation theory. The natural frequency equation based on the classical laminated plate theory can be determined by ignoring the shear strains in the theoretical formulations. After two validation studies by using appropriate results in the literature, parametric analyses are performed to show the sensitivity of natural frequencies to shear deformation, porosity model, orthotropy, layer sequence, and geometric properties.


Keywords


porosity; porous plate; laminated composite; vibration; shear deformation; orthotropy

References


Arshid E, Amir S, Loghman A (2020). Static and dynamic analyses of FG-GNPs reinforced porous nanocomposite annular micro-plates based on MSGT. International Journal of Mechanical Sciences, 180, 105656.

Aydogdu M (2009). A new shear deformation theory for laminated composite plates. Composite Structures, 89(1), 94-101.

Chen Z, Qin B, Zhong R, Wang Q (2022). Free in-plane vibration analysis of elastically restrained functionally graded porous plates with porosity distributions in the thickness and in-plane directions. The European Physical Journal Plus, 137(1), 1-21.

Esen I, Özmen R (2022). Thermal vibration and buckling of magneto-electro-elastic functionally graded porous nanoplates using nonlocal strain gradient elasticity. Composite Structures, 296, 115878.

Esmaeilzadeh M, Kadkhodayan M, Mohammadi S, Turvey GJ (2020). Nonlinear dynamic analysis of moving bilayer plates resting on elastic foundations. Applied Mathematics and Mechanics (English Edition), 41(3), 439-458.

Fares M, Zenkour A (1999). Buckling and free vibration of non-homogeneous composite cross-ply laminated plates with various plate theories. Composite Structures, 44(4), 279-287.

Hung P, Phung-Van P, Thai CH (2022). A refined isogeometric plate analysis of porous metal foam microplates using modified strain gradient theory. Composite Structures, 289, 115467.

Kumar P, Harsha SP (2022). Static and vibration response analysis of sigmoid function-based functionally graded piezoelectric non-uniform porous plate. Journal of Intelligent Material Systems and Structures, 1045389X221077433.

Kumar Y, Gupta A, Tounsi A (2021). Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model. Advances in Nano Research, 11(1), 1-17.

Lahdiri A, Kadri M (2022). Free vibration behaviour of multi-directional functionally graded imperfect plates using 3D isogeometric approach. Earthquakes and Structures, 22(5), 527-538.

Li S, Zheng S, Chen D (2020). Porosity-dependent isogeometric analysis of bi-directional functionally graded plates. Thin-Walled Structures, 156, 106999.

Mahi A, Adda Bedia EA, Tounsi A (2015). A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates. Applied Mathematical Modelling, 39(9), 2489-2508.

Pan H-G, Wu Y-S, Zhou J-N, Fu Y-M, Liang X, Zhao T-Y (2021). Free vibration analysis of a graphene-reinforced porous composite plate with different boundary conditions. Materials, 14(14), 3879.

Pham Q-H, Nguyen P-C, Tran V-K, Nguyen-Thoi T (2021). Finite element analysis for functionally graded porous nano-plates resting on elastic foundation. Steel and Composite Structures, 41(2), 149-166.

Reddy JN, Phan ND (1985). Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory. Journal of Sound and Vibration, 98(2), 157-170.

Safaei B, (2020). The effect of embedding a porous core on the free vibration behavior of laminated composite plates. Steel and Composite Structures, 35(5), 659-670.

Shi P, Dong C, Sun F, Liu W, Hu Q (2018). A new higher order shear deformation theory for static, vibration and buckling responses of laminated plates with the isogeometric analysis. Composite Structures, 204 342-358.

Teng Z, Xi P (2021). Analysis on free vibration and critical buckling load of a FGM porous rectangular plate. Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University. 39(2), 317-325.

Turan F, Başoğlu MF, Zerin Z (2017). Analytical solution for bending and buckling response of laminated non-homogeneous plates using a simplified-higher order theory. Challenge Journal of Structural Mechanics, 3(1), 1-16.

Wang W, Xue G, Teng Z (2022). Analysis of free vibration characteristics of porous FGM circular plates in a temperature field. Journal of Vibration Engineering & Technologies, 1-12.

Xu K, Yuan Y, Li M (2019). Buckling behavior of functionally graded porous plates integrated with laminated composite faces sheets. Steel and Composite Structures, 32(5), 633-642.

Yuan Y, Zhao K, Xu K (2019). Enhancing the static behavior of laminated composite plates using a porous layer. Structural Engineering and Mechanics, 72(6), 763-774.

Zenkour AM, Radwan AF (2016). Free vibration analysis of multilayered composite and soft core sandwich plates resting on Winkler–Pasternak foundations. Journal of Sandwich Structures & Materials, 20(2), 169-190.

Zhong R, Qin B, Wang Q, Shao W, Shuai C (2021). Prediction of the in-plane vibration behavior of porous annular plate with porosity distributions in the thickness and radial directions. Mechanics of Advanced Materials and Structures, 1-25.

Zhou C, Zhan Z, Zhang J, Fang Y, Tahouneh V (2020). Vibration analysis of FG porous rectangular plates reinforced by graphene platelets. Steel and Composite Structures, 34(2), 215-226.


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