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Vibration analysis of different material distributions of functionally graded microbeam
Youcef Tlidji,Mohamed Zidour,Kadda Draiche,Abdelkader Safa,Mohamed Bourada,Abdelouahed Tounsi,Abdelmoumen Anis Bousahla,S. R. Mahmoud 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.69 No.6
In the current research paper, a quasi-3D beam theory is developed for free vibration analysis of functionally graded microbeams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by three functions, power function, symmetric power function and sigmoid law distribution. The modified coupled stress theory is used to incorporate size dependency of micobeam. The equation of motion is derived by using Hamilton’s principle, however, Navier type solution method is used to obtain frequencies. Numerical results show the effects of the function distribution, power index and material scale parameter on fundamental frequencies of microbeams. This model provides designers with guidance to select the proper distributions and functions.
Youcef Tlidji,Rabia Benferhat,Hassaine Daouadji Tahar 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.77 No.2
The effect of distribution shape of porosity using a quasi-3D theory for free vibration analysis of FG microbeams is studied analytically in the present paper. The microbeams are simply-supported and nonhomogeneous, with power function variation of Young’s modulus along their thickness. The modified coupled stress theory is utilized to consolidate size dependency of microbeam. Both even and uneven distribution shape of porosity are considered and the effective properties of porous FG microbeams are defined by theoretical formula with an additional term of porosity. The equation of motion is obtained through Hamilton’s principle, however, Navier type solution method is used to obtain frequencies. The influences played by many parameters are also investigated.
New state-space approach to dynamic analysis of porous FG beam under different boundary conditions
Tlidji, Youcef,Benferhat, Rabia,Trinh, Luan Cong,Tahar, Hassaine Daouadji,Abdelouahed, Tounsi Techno-Press 2021 Advances in nano research Vol.11 No.4
This paper investigates dynamic behavior of porous functionally graded beams under various boundary conditions using State-space approach. The material parameters of FG beams change continuously along the thickness direction according to the power-law function (PFGM) or sigmoid function (SFGM). The porous FG beams are assumed to have even and uneven distributions of porosities over the beam cross-section. The classical beam theory, first-order and higher-order shear deformation theories are employed to consider beams of various boundary conditions. Hamilton's principle are employed for derivation of the equations of motion. Fundamental frequencies are calculated numerically for different boundary conditions, gradient index, volume fraction of porosity, distribution shape of porosity, and span-to-depth ratios. The results show that the variation of the distribution shape of porosity has an effect on the fundamental frequencies.
Tlidji, Youcef,Benferhat, Rabia,Daouadji, Tahar Hassaine,Tounsi, Abdelouahed,Trinh, L.Cong Techno-Press 2022 Advances in nano research Vol.13 No.5
This paper aims to investigate the vibration analysis of functionally graded porous (FGP) beams using State-space approach with several classical and non-classical boundary conditions. The materials properties of the porous FG beams are considered to have even and uneven distributions profiles along the thickness direction. The equation of motion for FGP beams with various boundary conditions is obtained through Hamilton's principle. State-space approach is used to obtain the governing equation of porous FG beam. The comparison of the results of this study with those in the literature validates the present analysis. The effects of span-to-depth ratio (L/h), of distribution shape of porosity and others parameters on the dynamic behavior of the beams are described. The results show that the boundary conditions, the geometry of the beams and the distribution shape of porosity affect the fundamental frequencies of the beams.
A simple analytical model for free vibration and buckling analysis of orthotropic rectangular plates
Souad Sellam,Kada Draiche,Youcef Tlidji,Farouk Yahia Addou,Abdelkader Benachour 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.75 No.2
In the present paper, a simple analytical model is developed based on a new refined parabolic shear deformation theory (RPSDT) for free vibration and buckling analysis of orthotropic rectangular plates with simply supported boundary conditions. The displacement field is simpler than those of other higher-order theories since it is modeled with only two unknowns and accounts for a parabolic distribution of the transverse shear stress through the plate thickness. The governing differential equations related to the present theory are obtained from the principle of virtual work, while the solution of the eigenvalue problem is achieved by assuming a Navier technique in the form of a double trigonometric series that satisfy the edge boundary conditions of the plate. Numerical results are presented and compared with previously published results for orthotropic rectangular plates in order to verify the precision of the proposed analytical model and to assess the impacts of several parameters such as the modulus ratio, the side-to-thickness ratio and the geometric ratio on natural frequencies and critical buckling loads. From these results, it can be concluded that the present computations are in excellent agreement with the other higher-order theories.
Free vibration responses of nonlinear FG-CNT distribution in a polymer matrix
Mohamed Zidour,Rachid Zerrouki,Ahmed Hamidi,Youcef Tlidji,Abdelkader Karas,Abdelouahed Tounsi 국제구조공학회 2022 Smart Structures and Systems, An International Jou Vol.30 No.2
The object of this paper is to investigate the free vibration behavior under the effect of carbon nanotube distribution in functionally graded carbon nanotube-reinforced composite (FG-CNTRC) by using higher-order shear deformation theories. In this work, we present a novel distribution method for carbon nanotubes in the polymer matrix by using a new exponential power law distribution of carbon nanotube volume fraction. It is assumed that the SWCNTs are aligned along the beam axial direction and the distribution of the SWCNTs may vary through the thickness of the beam with different patterns of reinforcement. The rule of mixtures is used in order to obtain material properties of the CNTRC beams. Hamilton's principle is used in deriving the equations of motion. The validity of the free Vibration results is examined by comparing them with those of the known data in the literature. The results that obtained indicate that the carbon nanotube volume fraction distribution play a very important role on the free vibrations characteristics of the CNTRC beam.