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 >

Preeti Agarwal^*, Priyaranjan Pal, Pradeep Kumar Mehta

Sound & Vibration, Vol.56, No.2, pp. 105-125, 2022, DOI:10.32604/sv.2022.014874 - 25 March 2022

Abstract The free vibration analysis of simply supported box-girder bridges is carried out using the finite element method. The fundamental frequency is determined in straight, skew, curved and skew-curved box-girder bridges. It is important to analyse the combined effect of skewness and curvature because skew-curved box-girder bridge behaviour cannot be predicted by simply adding the individual effects of skewness and curvature. At first, an existing model is considered to validate the present approach. A convergence study is carried out to decide the mesh size in the finite element method. An exhaustive parametric study is conducted to… More >

Mohammad Arefi¹, Masoud Mohammadi¹, Ali Tabatabaeian¹, Timon Rabczuk^{2, *}

CMC-Computers, Materials & Continua, Vol.62, No.3, pp. 1001-1023, 2020, DOI:10.32604/cmc.2020.08052

Abstract This study focuses on vibration analysis of cylindrical pressure vessels constructed by functionally graded carbon nanotube reinforced composites (FG-CNTRC). The vessel is under internal pressure and surrounded by a Pasternak foundation. This investigation was founded based on two-dimensional elastic analysis and used Hamilton’s principle to drive the governing equations. The deformations and effectivemechanical properties of the reinforced structure were elicited from the first-order shear theory (FSDT) and rule of mixture, respectively. The main goal of this study is to show the effects of various design parameters such as boundary conditions, reinforcement distribution, foundation parameters, and More >

Chih-Ping Wu, Ruei-Yong Jiang

CMC-Computers, Materials & Continua, Vol.46, No.1, pp. 17-56, 2015, DOI:10.3970/cmc.2015.046.017

Abstract An asymptotic meshless method using the differential reproducing kernel (DRK) interpolation and multiple time scale methods is developed for the three-dimensional (3D) free vibration analysis of sandwich functionally graded material (FGM) circular hollow cylinders with combinations of simply-supported and clamped edge conditions. In the formulation, we perform the mathematical processes of nondimensionalization, asymptotic expansion and successive integration to obtain recurrent sets of motion equations for various order problems. Classical shell theory (CST) is derived as a first-order approximation of the 3D elasticity theory, and the motion equations for higher-order problems retain the same differential operators… More >

Hao Zuo^1,2, Zhi-Bo Yang^1,2,3, Xue-Feng Chen^1,2, Yong Xie⁴, Xing-Wu Zhang^1,2, Yue Liu⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.6, pp. 477-506, 2014, DOI:10.3970/cmes.2014.100.477

Abstract The application of B-spline wavelet on the interval (BSWI) finite element method for static, free vibration and buckling analysis in functionally graded (FG) beam is presented in this paper. The functionally graded material (FGM) is a new type of heterogeneous composite material with material properties varying continuously throughout the thickness direction according to power law form in terms of volume fraction of material constituents. Different from polynomial interpolation used in traditional finite element method, the scaling functions of BSWI are employed to form the shape functions and construct wavelet-based elements. Timoshenko beam theory and Hamilton’s… More >

Da-Guang Zhang^1,*, Hao-Miao Zhou¹

CMC-Computers, Materials & Continua, Vol.40, No.1, pp. 21-34, 2014, DOI:10.3970/cmc.2014.040.021

Abstract Nonlinear symmetric free vibration analyses are first presented for super elliptical isotropic thin plates with simply supported edge and clamped edge based on classical plate theory. Approximate solutions of super elliptical thin plates are obtained by Ritz method, and the validity can be confirmed by comparison with related researchers’ results. Numerical results confirm that the characteristics of nonlinear vibration behaviors are significantly influenced by different boundary conditions, vibration amplitudes, the power of the super ellipse, as well as ratio of major to minor axis. More >

W.L.A. Pereira¹, V.J. Karam², J.A.M. Carrer³, C.S.G. Monteiro¹, W.J. Mansur¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.2, pp. 117-130, 2013, DOI:10.3970/cmes.2013.096.117

Abstract In this work, the BEM is applied to obtain the numerical solutions for free vibration analysis of thick square plates with two edges simply supported or clamped, and the other two edges free. A formulation based on Reissner’s theory is used here, which includes the contribution of the additional translational inertia terms to the integral equation of displacements and internal forces. The boundary element method is used to discretize the space, where it is employed the static fundamental solution. In literature, the responses for the kind of problem addressed here are very important in the More >

Chih-Ping Wu^1,2, Hao-Yuan Li²

CMC-Computers, Materials & Continua, Vol.19, No.2, pp. 155-198, 2010, DOI:10.3970/cmc.2010.019.155

Abstract The Reissner mixed variational theorem (RMVT)- and principle of virtual displacements (PVD)-based finite layer methods (FLMs) are developed for the quasi-three-dimensional (3D) free vibration analysis of simply-supported, multilayered composite and functionally graded material (FGM) plates. The material properties of the FGM layers are assumed to obey either an exponent-law exponentially varied with the thickness coordinate or the power-law distributions of the volume fractions of the constituents. In these formulations, the plate is divided into a number of finite layers, where the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations… More >

Wei-Ming Lee¹, Jeng-Tzong Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 141-160, 2009, DOI:10.3970/cmes.2009.050.141

Abstract This paper presents the multipole Trefftz method to derive an analytical model describing the free vibration of a circular plate with multiple circular holes. Based on the addition theorem, the solution of multipoles centered at each circle can be expressed in terms of multipoles centered at one circle, where boundary conditions are specified. In this way, a coupled infinite system of simultaneous linear algebraic equations is derived for the circular plate with multiple holes. The direct searching approach is employed in the truncated finite system to determine the natural frequencies by using the singular value More >