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An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study. Mechanical properties of MFG porous plates change according to the length, width, and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology. Especially, new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work. Applying Hamilton’s principle and the refined higher-order shear deformation plate theory, the governing equation of motion of an MFG porous rectangular plate in a fluid medium (the fluid-plate system) is obtained. The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass. The Galerkin-Vlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium. The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature. The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail. These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium. Thereby, they offer appropriate operational approaches for the structure when employed in various mediums.

In this work, free vibration and transient response of porous metal foam magneto-electro-elastic (PMF-MEE) curved nanobeam with elastic boundary conditions (BCs) using an isogeometric analysis (IGA) based on nonlocal elastic and refined higher-order shear beam theories (HSDT) are investigated. The variation of electric and magnetic potentials through the thickness direction of the curved nanobeam is determined by the Maxwell equation and the magneto-electric boundary condition. The new point of this paper is that it does not use traditional boundary conditions, but instead, the first and last positions of the curved nanobeam are linked by an elastic system consisting of transrational springs and rotational springs with stiffness controlled to give arbitrary boundary conditions. Besides, the nonlocal coefficients vary with thickness like other material properties. Hamilton’s principle is applied to establish the governing equations of motion. The Newmark direct integration method is applied to derive the dynamic responses including deflection and phase trajectory. A comprehensive parametric study is carried out to evaluate the influence of input factors on the natural and forced oscillation capabilities of PMF-MEE curved nanobeams. The findings may benefit for the analysis and design of intelligent structures made of magneto-electro-elastic materials.

In the present paper, the combination of mixed interpolation of tensorial components technique of triangular elements (MITC3) based upon the first-order shear deformation theory (FSDT) is developed to research the free and forced vibration of the unsymmetrical functionally graded porous (UFGP) folded sandwich plates. The MITC3 element still uses the triangular mesh and avoids the shear-locking phenomena that occur when using the classical triangular elements. Based on the basic formula of the MITC3 element for analyzing plates, the twisted angle (φz) is added to the node displacement vector to solve for folded plates. Material properties of folded sandwich plates are unsymmetric with an FGP core layer, a metal bottom layer, and a ceramic top layer. The motion equations for UFGP folded sandwich plates are derived from Hamilton's principle. Some examples are conducted to verify the accuracy and reliability of the present method. Then, the new numerical results on the free and forced vibrations of UFGP folded sandwich plates are provided.

This paper uses isogeometric analysis (IGA) based on higher-order shear deformation theory (HSDT) to study the dynamic response of bio-inspired helicoid laminated composite (B-iHLC) plates resting on Pasternak foundation (PF) excited by explosive loading. IGA takes advantage of non-uniform rational B-spline (NURBS) basic functions to exactly represent the structure geometry models and the attainment of higher-order approximation conditions. This method also ensures a C1 continuous function in the analysis of transverse shear deformation via HSDT. Furthermore, IGA eliminates the requirement for correction factors and delivers accurate results. Pasternak foundation with two stiffness parameters: springer stiffness (k1) and shear stiffness (k2). The derivation of the governing equations is based on Hamilton's principle. The proposed method is validated through numerical examples. A comprehensive analysis of the impact of geometrical parameters, material properties, boundary conditions (BCs), and foundation stiffness on dynamic response of B-iHLC plates is carried out.

In this article, vibration characteristics of sandwich plates with an auxetic honeycomb core and laminated three-phase skin layers subjected to blast load are studied. Higher-order ES-MITC3 element based on higher-order shear deformation theory (HSDT) to achieve the governing equations. The sandwich plates with the ultra-light feature of the auxetic honeycomb core layer (negative Poisson's ratio) and reinforced by two laminated three-phase skin layers. The obtained results in our work are compared with other previously published to confirm accuracy and reliability. In addition, the effects of parameters such as geometrical and material parameters on the vibration characteristics of sandwich plates with an auxetic honeycomb core and laminated three-phase skin layers are fully investigated.

The main objective of this article is to propose a new shear continuous function used for the free vibration analysis of functionally graded (FG) nanoplates with the presence of internal porosity (so-called FGP nanoplates) by employing isogeometric analysis (IGA). The small-scale effect that appears in nanostructures is included by using the nonlocal elasticity theory (nonlocal theory). Functionally graded materials consist of mechanical properties varies along z-directions. The porosity occurring in the material matrix is described by the trigonometric function. Furthermore, an artificial neural network (ANN) model is created by Matlab software to predict the natural frequencies of FGP nanoplates. The performance of the proposed formula is confirmed by comparing the obtained results with those of previous publications. Finally, some examples are conducted to provide novel results in the free vibration of FGP nanoplates.

A finite element modeling combined with the strain gradient theory (SGT) and the refined higher-order shear deformation beam theory is developed to study the dynamic instability of magnetically embedded functionally graded porous (FGP) nanobeams. Nanobeams with elastic foundation (EF) subjected to an axially oscillating load are analyzed. Nanobeams are made of functionally graded material (FGM) with an uneven porosity distribution. A three-node beam element with 8 degrees of freedom (DOFs) for two outer nodes and 2 DOFs for the middle node, which has the C1 and C2 continuous Hermite shape functions, is used to simulate nanobeams. Besides, Bolotin’s method is employed to determine the instability region of FGP nanobeams. The accuracy of the proposed method is tested by comparing it with other published works. In addition, the influences of various parameters such as magnetic potential, small-scale parameter, porosity coefficient, stiffness foundation, boundary conditions (BCs) on the dynamic instability of nanobeams are studied in detail.

This paper proposes a new finite element formulation based on Shi’s third-order shear deformation theory (TSDT) for controlling the vibration of piezoelectric functionally graded porous (PFGP) plates integrated with piezoelectric sensors and actuators under dynamic loading in the high temperature environment. The properties of the PFGP core vary through the plate’s thickness according to the power-law index k and porosity factor Ω, while the electric potential is a linear function via the piezoelectric sublayer thickness. To actively control the vibration of PFGP plates, a closed-loop control algorithm based on displacement and velocity feedback is applied. The motion equation of PFGP plate under mechanical and thermal load is established based on based on Galerkin weak formulation. The proposed method is evaluated through several numerical examples to demonstrate its effectiveness. Furthermore, the active vibration control of FPGP plates is detail presented.

This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate change in both the thickness and length directions via power-law distributions and Mori-Tanaka model. The governing equation of motion of BDFG plate in the fluid-plate system is formulated basing on Hamilton's principle and the refined quasi three-dimensional (3D) plate theory with improved function f(z). The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to determine the added mass. The discrete system of equations is derived from the Galerkin weak form and numerically analyzed by IGA. The accuracy and reliability of the proposed solutions are verified by comparing the obtained results with those published in the literature. Moreover, the effects of the various parameters such as the interaction boundary condition, geometric parameter, submerged depth of plate, fluid density, fluid level, and the material volume control coefficients on the free vibration behavior of BDFG plate in the fluid medium are investigated in detail. Some major findings regarding the numerical results are withdrawn in conclusions.

This paper extends isogeometric analysis (IGA) based on third-order shear deformation theory (TSDT) for vibration analysis of functionally graded porous (FGP) plates in the thermal environment resting on Kerr foundation. IGA is based on non-uniform rational B-spline (NURBS) basic functions, so it can represent exact geometry and satisfy higher-order approximation (C1 continuous function) conditions of TSDT. This combination ensures high accuracy, including transverse shear deformation, without having to use any correction factors. The temperature field via the plate thickness satisfies the steady‐state heat transfer equation. The governing equations are derived from Hamilton's principle. Then, numerical examples are conducted to validate the effectiveness of the proposed method. Finally, the effects of geometrical parameters, material properties, boundary conditions (BCs), temperature change and foundation stiffness on the thermal vibration of FGP plates are fully considered.

In this paper, the free vibration of the functionally graded porous (FGP) non-uniform annular-nanoplates lying on Winkler foundation (WF) is studied by using the smoothed finite element method based on the first-order shear deformation theory (FSDT). The combination of the mixed interpolation of the tensorial components for the three-node triangular element (MITC3 element) and the edge-based smoothed finite element method (ES-FEM) creates the ES-MITC3 element. This element is employed to avoid the shear locking problem as well as to improve the accuracy of the original MITC3 element. The small-scale effect is considered based on the nonlocal theory. Applying Hamilton's principle, the governing equation of the FGP non-uniform thickness annular-nanoplate is derived. Material properties of the nanoplate are characterized by two parameters: power-law index (k) and maximum porosity distributions (Ω) in the forms of cosine functions. The results of the present work are compared with other published work to verify accuracy and reliability. Moreover, the effects of geometry parameters and material properties on the free vibration of FGP non-uniform annular-nanoplates are comprehensively investigated.

This article develops a new C1 rectangular element based on Shi's third-order shear deformation plate theory (TSDT) for the static and dynamic analysis of functionally graded porous (FGP) sandwich plates. Although the plate theory is attractive, it cannot be exploited as expected in finite element analysis due to the difficulties associated with satisfying the zero shear stress boundary condition. In this work, the proposed element has four nodes with seven degrees of freedom (DOFs) per node. The performance of this element is confirmed by conducting various examples, showing its accuracy and range of applications. Then, some studies are performed to present the effects of input parameters on the static and dynamic response of FGP sandwich plates.

The aim of this paper is to present the hygro-thermal vibration behavior of bidirectional functionally graded porous (BDFGP) curved beams resting on two-layer elastic foundations (EF) using the generalized finite element method (GFEM). In which, one of these two layers is composed of Winkler springs with the variation of modulus, while the other is composed of shear springs with a fixed modulus. The enrichment is accomplished by constructing the enriched mathematical space using an enriched FE shape function. Moisture causes tensile stresses in the x-axis direction without affecting mechanical characteristics of the material, while temperature changes Young's modulus of elasticity and thermal expansion coefficients. The free vibration equation for the curved beam is developed that relied on the k-order shear deformation beam theory and Hamilton's principle. The correctness of the proposed model is evaluated by comparing obtained numerical results of the present work to the findings of credible publications in the literature. By considering the free vibration responses of the curved beam, the effects of parameters such as the grading power indexes, the porosity coefficient, the temperature and moisture change, the opening angle of the curved beam, stiffness of the EF, boundary conditions, and the thickness-to-length ratio are investigated.

The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous (FGP) variable-thickness plates by using an edge-based smoothed finite element method (ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element (MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index (k) and maximum porosity distributions (Ω) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.

This article proposes a finite element method (FEM) based on a quasi-3D nonlocal theory to study the free vibration of functionally graded material (FGM) nanoplates lying on the elastic foundation (EF) in the thermal environment. By applying Hamilton's principle, the governing equations of FGM nanoplates on the EF are obtained. Using the FEM helps solve many complicated problems that analytical solution (AS) cannot be performed yet, such as complex structures, asymmetric problems, variable thickness, etc. The numerical results of this work are compared with those of other published researches to verify accuracy and reliability. In addition, the effects of geometrical parameters, material properties such as the thickness, material exponents, nonlocal coefficients, elastic foundation stiffness, boundary conditions (BCs), and temperature on the free vibration of nanoplates are comprehensively investigated.

In this article, some numerical results from the free vibration analysis of functionally graded material (FGM) plates resting on the elastic foundation (EF) in the thermal environment are presented. An ES-FEM combining with the MITC3 is used to improve the accuracy as well as eliminate the shear locking phenomena for the classical triangular element. The EF is modeled from the Winkler-Pasternak foundation with stiffness two-parameter. Numerical examples are compared with published works to prove the reliability and accuracy of the proposed method. The effects of volume fraction index (n), temperature (T), and two-parameter of the EF on the free vibration of FGM plates are also investigated. Furthermore, an artificial neural network (ANN) is trained to predict exactly the fundamental frequency of FGM plates.

The paper presents the extension of an edge-based smoothed finite element method using three-node triangular elements for dynamic analysis of the functionally graded porous (FGP) plates subjected to moving loads resting on the elastic foundation taking into mass (EFTIM). In this study, the edge-based smoothed technique is integrated with the mixed interpolation of the tensorial component technique for the three-node triangular element (MITC3) to give so-called ES-MITC3, which helps improve significantly the accuracy for the standard MITC3 element. The EFTIM model is formed by adding a mass parameter of foundation into the Winkler–Pasternak foundation model. Two parameters of the FGP materials, the power-law index (k) and the maximum porosity distributions (Ω), take forms of cosine functions. Some numerical results of the proposed method are compared with those of published works to verify the accuracy and reliability. Furthermore, the effects of geometric parameters and materials on forced vibration of the FGP plates resting on the EFTIM are also studied in detail.

The main goal of this article further extends the ES-MITC3 element based on first-order shear deformation theory (FSDT) for the free vibration analysis of functionally graded porous (FGP) plates resting on the partially supported elastic foundation (PSEF). The ES-MITC3 element is the union between the mixed interpolation of tensorial components (MITC) technique and an edge-based smoothed finite element method (ES-FEM). The elastic foundation (EF) is a Winkler-Pasternak’s model with two parameters consisting of Winkler-stiffness (k1) and Pasternak-stiffness (k2). The porosity distribution in plates is assumed to vary according to the even distribution (case 1) and uneven distribution (case 2) rules. The governing equation is derived from Hamilton's principle. Numerical examples are performed to verify the accuracy and reliability of the present method. In addition, the effects of types of PSEF, material properties and geometry characteristics on the free vibration behavior of FGP plates are fully investigated.