Bindi Saurabh Thakkar¹, Pradeep Kumar Karsh^2,*

CMC-Computers, Materials & Continua, Vol.86, No.2, pp. 1-22, 2026, DOI:10.32604/cmc.2025.072839 - 09 December 2025

Abstract This study investigates the uncertain dynamic characterization of hybrid composite plates by employing advanced machine-assisted finite element methodologies. Hybrid composites, widely used in aerospace, automotive, and structural applications, often face variability in material properties, geometric configurations, and manufacturing processes, leading to uncertainty in their dynamic response. To address this, three surrogate-based machine learning approaches like radial basis function (RBF), multivariate adaptive regression splines (MARS), and polynomial neural networks (PNN) are integrated with a finite element framework to efficiently capture the stochastic behavior of these plates. The research focuses on predicting the first three natural frequencies… More >

Salvatore Brischetto^*, Domenico Cesare, Tommaso Mondino

CMC-Computers, Materials & Continua, Vol.85, No.3, pp. 4491-4518, 2025, DOI:10.32604/cmc.2025.068518 - 23 October 2025

Abstract A three-dimensional (3D) analytical formulation is proposed to put together magnetic, electric and elastic fields to analyze the vibration modes of simply-supported layered piezo-electro-magnetic plates. The present 3D model allows analyses for layered smart plates in both open-circuit and closed-circuit configurations. The second-order differential equations written in the mixed curvilinear reference system govern the magneto-electro-elastic free vibration problem for multilayered plates. This set consists of the 3D equations of motion and the 3D divergence equations for the magnetic induction and electric displacement. Navier harmonic forms in the planar directions and the exponential matrix method in… More >

Jiaqing Jiang^*, Marco Amabili

The International Conference on Computational & Experimental Engineering and Sciences, Vol.33, No.2, pp. 1-1, 2025, DOI:10.32604/icces.2025.012283

Abstract This paper presents a novel mixed finite element method for the free vibration analysis of composite periodic beams. The governing state-space equations are derived based on the Hamilton's principle, treating both displacements and stresses as fundamental variables. This method uses transfer relations in the transverse direction and finite element discretization in the longitudinal direction of the beam, forming a semi-analytical computational framework. Therefore, it is able to handle general composite beam structures containing both transversely layered and axially jointed materials.
The proposed mixed finite element method ensures continuity of both displacements and stresses across material interfaces,… More >

Suppakit Eiadtrong^1,2,#, Tan N. Nguyen^3,#,*, Mohamed-Ouejdi Belarbi⁴, Nuttawit Wattanasakulpong^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.3, pp. 2819-2848, 2025, DOI:10.32604/cmes.2025.069481 - 30 September 2025

Abstract An improved meshfree moving-Kriging (MK) formulation for free vibration analysis of functionally graded material-functionally graded carbon nanotube-reinforced composite (FGM-FGCNTRC) sandwich shells is first proposed in this article. The proposed sandwich structure consists of skins of FGM layers and an FGCNTRC core. This structure possesses all the advantages of FGM and FGCNTRC, including high electrical or thermal insulating properties, high fatigue resistance, good corrosion resistance, high stiffness, low density, high strength, and high aspect ratios. Such sandwich structures can be used to replace conventional FGM structures. The present formulation has been established by using an improved More >

Boudjema Bendaho¹, Abdelhak Mesbah¹, Zakaria Belabed^1,2,*

CMC-Computers, Materials & Continua, Vol.85, No.2, pp. 2781-2805, 2025, DOI:10.32604/cmc.2025.069709 - 23 September 2025

Abstract A new quadrilateral finite element IQ4 is developed for the free vibration of carbon nanotube-reinforced composite (CNTRC) perforated plates with a central cutout. By enriching the membrane part and incorporating a projected shear technique, the IQ4 element is proposed to address the known limitations of the standard Q4 element, such as shear locking and limited consistency in the coupling of membrane-bending components. The proposed element is formulated within the FSDT-based framework and assessed through benchmark tests to verify its convergence and accuracy. The governing equations are obtained via the weak form of Hamilton’s principle. Particular… More >

Alireza Moradi, Alireza Shaterzadeh^*

CMC-Computers, Materials & Continua, Vol.82, No.1, pp. 223-257, 2025, DOI:10.32604/cmc.2024.059441 - 03 January 2025

Abstract For the first time, the linear and nonlinear vibrations of composite rectangular sandwich plates with various geometric patterns of lattice core have been analytically examined in this work. The plate comprises a lattice core located in the middle and several homogeneous orthotropic layers that are symmetrical relative to it. For this purpose, the partial differential equations of motion have been derived based on the first-order shear deformation theory, employing Hamilton’s principle and Von Kármán’s nonlinear displacement-strain relations. Then, the nonlinear partial differential equations of the plate are converted into a time-dependent nonlinear ordinary differential equation… More >

Yufeng Xing^*, Ye Yuan, Gen Li

CMES-Computer Modeling in Engineering & Sciences, Vol.142, No.1, pp. 329-355, 2025, DOI:10.32604/cmes.2024.056440 - 17 December 2024

Abstract The separation-of-variable (SOV) methods, such as the improved SOV method, the variational SOV method, and the extended SOV method, have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells. By taking the free vibration of rectangular thin plates as an example, this work presents the theoretical framework of the SOV methods in an instructive way, and the bisection–based solution procedures for a group of nonlinear eigenvalue equations. Besides, the explicit equations of nodal lines of the SOV methods More >

Lazreg Hadji^1,2,*, Fabrice Bernard³, Nafissa Zouatnia⁴

FDMP-Fluid Dynamics & Materials Processing, Vol.19, No.4, pp. 1043-1054, 2023, DOI:10.32604/fdmp.2022.022327 - 02 November 2022

Abstract The bending and free vibration of porous functionally graded (PFG) beams resting on elastic foundations are analyzed. The material features of the PFG beam are assumed to vary continuously through the thickness according to the volume fraction of components. The foundation medium is also considered to be linear, homogeneous, and isotropic, and modeled using the Winkler-Pasternak law. The hyperbolic shear deformation theory is applied for the kinematic relations, and the equations of motion are obtained using the Hamilton’s principle. An analytical solution is presented accordingly, assuming that the PFG beam is simply supported. Comparisons with More > Graphic Abstract

Qiuhong Li¹, Wenhao Huang^1,*, Joey Sanchez², Ping Wang¹, Qiang Ding³, Jiufa Wang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.3, pp. 2093-2121, 2023, DOI:10.32604/cmes.2022.021340 - 20 September 2022

Abstract Based on Kirchhoff plate theory and the Rayleigh-Ritz method, the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method (ICCM). The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate. The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method. From the continuity condition of the vibration displacement More >

Xiaojun Huang^1,2, Liaojun Zhang^1,*, Renyu Ge², Hanbo Cui², Zhedong Xu²

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.1, pp. 23-41, 2022, DOI:10.32604/cmes.2022.019765 - 02 June 2022

Abstract In the current research, an effective differential quadrature method (DQM) has been developed to solve natural frequency and vibration modal functions of circular section beams along radial functional gradient. Based on the high-order theory of transverse vibration of circular cross-section beams, lateral displacement equation was reconstructed neglecting circumferential shear stress. Two equations coupled with deflection and rotation angles were derived based on elastic mechanics theory and further simplified into a constant coefficient differential equation with natural frequency as eigenvalue. Then, differential quadrature method was applied to transform the eigenvalue problem of the derived differential equation… More >