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

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 the open literature are implemented… 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

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 function at the cutout, the… 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

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 into a set of algebraic… More >

Preeti Agarwal^*, Priyaranjan Pal, Pradeep Kumar Mehta

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

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 determine the fundamental frequency of… 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 aspect ratio on the free… More >

E. Viola¹, F. Tornabene²

Structural Durability & Health Monitoring, Vol.1, No.2, pp. 155-170, 2005, DOI:10.3970/sdhm.2005.001.155

Abstract In this paper, generalized differential quadrature techniques are applied to the computation of the in-plane free vibrations of thin and thick non-uniform circular arches in undamaged and damaged configurations, when various boundary conditions are considered. Structural damage is represented by one crack in different positions and with various damage levels. The crack present in a structural member can be considered as a local stiffness reduction at the fracturing section, which changes the dynamic behaviour of the structure. Much effort has been devoted to dealing with in-plane free vibration analysis of circular arches, but only a few researchers have studied cracked… More >

Kazunori Shinohara¹

CMES-Computer Modeling in Engineering & Sciences, Vol.115, No.2, pp. 149-215, 2018, DOI: 10.3970/cmes.2018.02179

Abstract Exact solutions of the cubic Duffing equation with the initial conditions are presented. These exact solutions are expressed in terms of leaf functions and trigonometric functions. The leaf function r=sleafn(t) or r=cleafn(t) satisfies the ordinary differential equation dx2/dt2=-nr2n-1. The second-order differential of the leaf function is equal to -n times the function raised to the (2n-1) power of the leaf function. By using the leaf functions, the exact solutions of the cubic Duffing equation can be derived under several conditions. These solutions are constructed using the integral functions of leaf functions sleaf2(t) and cleaf2(t) for the phase of a trigonometric… More >

A. Alaimo¹, A. Milazzo¹, C. Orlando¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.15, No.4, pp. 137-144, 2010, DOI:10.3970/icces.2010.015.137

Abstract The axial and flexural natural frequencies of magneto-electro-elastic bimorph beam devices are analyzed in the framework of the third-order shear deformation theory (TSDT). Although the assumption of parabolic transverse shear strain distribution along the thickness leads to higher order stress resultants the use of the TSDT allows to avoid the need for shear correction factor. Moreover, since the electric and magnetic potentials strictly depend on the shear strains, a more accurate modeling of the magneto-electric coupling can be achieved by expanding the kinematical model up to the cubic term. The natural frequencies for different mechanical boundary conditions are computed by… More >

G. Davì¹, A. Milazzo¹, C. Orlando¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.15, No.4, pp. 129-136, 2010, DOI:10.3970/icces.2010.015.129

Abstract A dual reciprocity based boundary element approach for the analysis of magneto-electric laminates free vibration behavior is presented. The problem is formulated employing generalized displacements, that is displacements and electric and magnetic scalar potentials, and the corresponding generalized tractions. The generalized boundary integral representation is deduced by extending the reciprocity theorem to magneto-electro-elasticity problem and the multidomain boundary element technique is used to model multilayer structures. The magneto-electro-elastic static fundamental solutions are used jointly with the dual reciprocity method to transform the inertia domain integral into a boundary integral. Numerical results are presented focusing on the effects of the electro-magnetic… More >

A Milazzo¹, C. Orlando², A. Alaimo³

The International Conference on Computational & Experimental Engineering and Sciences, Vol.11, No.2, pp. 55-62, 2009, DOI:10.3970/icces.2009.011.055

Abstract A magneto-electro-elastic Timoshenko beam model is presented and employed to study the effect of the shear strain on the free vibration behavior of the beam. Once the differential governing equation for Timoshenko magneto-electro-elastic beam is derived, the Euler-Bernoulli model is obtained by letting be zero some of the governing equation coefficients. Results for the Timoshenko and Euler-Bernoulli beam are presented in comparison with two-dimensional finite element computation. More >