Free vibration of multi-cracked beams

Abdellatif Selmi 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.79 No.4

A new method is presented to study the free vibrations of multi-cracked beams with arbitrary boundary conditions. In the literature, the method based on changes in modal strain energy was used to perform the dynamic analysis of beams with just one crack. In this paper, the changes in modal strain energy are used iteratively to study the dynamic behavior of beams with multiple cracks. The iterative method consists in finding the dynamic frequencies in steps by considering the effects of cracks one by one. First, the beam is assumed intact, for it a single crack is taken into account via the method based on changes in modal strain energy. Then, this procedure is repeated iteratively by taking at steps (i+1), the frequencies obtained at step (i). The end is detected when the total number of cracks is reached. This developed iterative approach is used to analyze the effect of multiple open cracks on the modal parameters of a cantilever beam subjected to free vibration. The results are in good agreement with finite element and experimental methods. This developed method may also be used to generate training data for pattern recognition approaches to health monitoring.

Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam

Abdellatif Selmi 국제구조공학회 2020 Smart Structures and Systems, An International Jou Vol.26 No.3

Exact solution for nonlinear behavior of clamped-clamped functionally graded (FG) buckled beams is presented. The effective material properties are considered to vary along the thickness direction according to exponential-law form. The in-plane inertia and damping are neglected, and hence the governing equations are reduced to a single nonlinear fourth-order partial-integraldifferential equation. The von Karman geometric nonlinearity has been considered in the formulation. Galerkin procedure is used to obtain a second order nonlinear ordinary equation with quadratic and cubic nonlinear terms. Based on the mode of the corresponding linear problem, which readily satisfy the boundary conditions, the frequencies for the nonlinear problem are obtained using the Jacobi elliptic functions. The effects of various parameters such as the Young's modulus ratio, the beam slenderness ratio, the vibration amplitude and the magnitude of axial load on the nonlinear behavior are examined.

Dynamic behavior of cracked ceramic reinforced aluminum composite beam

Abdellatif Selmi 국제구조공학회 2022 Smart Structures and Systems, An International Jou Vol.29 No.3

This paper presents the vibration analysis of cracked ceramic-reinforced aluminum composite beams by using a method based on changes in modal strain energy. The crack is considered to be straight. The effective properties of composite materials of the beams are estimated through Mori-Tanaka micromechanical model. Comparison study and numerical simulations with various parameters; ceramic volume fraction, reinforcement aspect ratio, ratio of the reinforcement Young's modulus to the matrix Young's modulus and ratio of the reinforcement density to the matrix density are taken into investigation. Results demonstrate the pronounced effects of these parameters on intact and cracked ceramic aluminum beams.

Dynamic behavior of axially functionally graded simply supported beams

Abdellatif Selmi 국제구조공학회 2020 Smart Structures and Systems, An International Jou Vol.25 No.6

This paper focuses on the free vibration analysis of axially functionally graded (FG) Euler-Bernoulli beams. The material properties of the beams are assumed to obey the linear law distribution. The complexities in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using the Differential Transformation Method (DTM). Natural frequencies and corresponding normalized mode shapes are calculated. Validation targets are experimental data or finite element results. Different parameters such as reinforcement distribution, ratio of the reinforcement Young's modulus to the matrix Young's modulus and ratio of the reinforcement density to the matrix density are taken into investigation. The delivered results prove the capability and the robustness of the applied method. The studied parameters are demonstrated to be very crucial for the normalized natural frequencies and mode shapes.

Free vibration of bi-dimensional functionally graded simply supported beams

Selmi, Abdellatif Techno-Press 2021 Advances in concrete construction Vol.12 No.3

This paper investigates the free vibration of bi-dimensional functionally graded simply supported beams by using the continuous element method. The material properties are considered to vary exponentially along the beam thickness and length. The characteristic frequency equations of simply supported beams are derived by transfer matrix method. Validation targets are other analytical methods. The effects of the gradient indexes and the beam slenderness ratio on the natural frequencies of bi-dimensional functionally graded beams are studied.

Machine learning model for predicting ultimate capacity of FRP-reinforced normal strength concrete structural elements

Selmi Abdellatif,Ali Raza 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.85 No.3

Limited studies are available on the mathematical estimates of the compressive strength (CS) of glass fiberembedded polymer (glass-FRP) compressive elements. The present study has endeavored to estimate the CS of glass-FRP normal strength concrete (NSTC) compression elements (glass-FRP-NSTC) employing two various methodologies; mathematical modeling and artificial neural networks (ANNs). The dataset of 288 glass-FRP-NSTC compression elements was constructed from the various testing investigations available in the literature. Diverse equations for CS of glass-FRP-NSTC compression elements suggested in the previous research studies were evaluated employing the constructed dataset to examine their correctness. A new mathematical equation for the CS of glass-FRP-NSTC compression elements was put forwarded employing the procedures of curve-fitting and general regression in MATLAB. The newly suggested ANN equation was calibrated for various hidden layers and neurons to secure the optimized estimates. The suggested equations reported a good correlation among themselves and presented precise estimates compared with the estimates of the equations available in the literature with R2= 0.769, and R2 =0.9702 for the mathematical and ANN equations, respectively. The statistical comparison of diverse factors for the estimates of the projected equations also authenticated their high correctness for apprehending the CS of glass-FRP-NSTC compression elements. A broad parametric examination employing the projected ANN equation was also performed to examine the effect of diverse factors of the glass-FRP-NSTC compression elements.

Effectiveness of SWNT in reducing the crack effect on the dynamic behavior of aluminium alloy

Selmi, Abdellatif Techno-Press 2019 Advances in nano research Vol.7 No.5

This paper investigates the effectiveness of Single Walled Carbon Nanotubes, SWNT, in improving the dynamic behavior of cracked Aluminium alloy, Al-alloy, beams by using a method based on changes in modal strain energy. Mechanical properties of composite materials are estimated by the Eshelby-Mori-Tanaka method. The influence of SWNT volume fraction, SWNT aspect ratio, crack depth and crack location on the natural frequencies of the damaged 3D randomly oriented SWNT reinforced Al-alloy beams are examined. Results demonstrate the significant advantages of SWNT in reducing the effect of cracks on the natural frequencies of Al-alloy beams.

Vibration behavior of bi-dimensional functionally graded beams

Abdellatif Selmi 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.77 No.5

Based on Euler-Bernoulli beam theory and continuous element method, the free vibration of bi-dimensional functionally graded beams is investigated. It is assumed that the material properties vary exponentially along the beam thickness and length. The characteristic frequency equations of beams with different boundary conditions are obtained by transfer matrix method. The validity of the proposed method is assessed through comparison with available results. Parametric studies are carried out to analyze the influences of the gradient indexes and the beam slenderness ratio on the natural frequencies of bidimensional functionally graded beams.

Analytical vibration of FG cylindrical shell with ring support based on various configurations

Hussain, Muzamal,Selmi, Abdellatif Techno-Press 2020 Advances in concrete construction Vol.9 No.6

In this study, the impact of ring supports around the shell circumferential has been examined for their various positions along the shell axial length using Rayleigh-Ritz formulation. These shells are stiffened by rings in the tangential direction. For isotropic materials, the physical properties are same everywhere where the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. The influence of the ring supports is investigated at various positions. These variations have been plotted against the locations of ring supports for three values of length-to-diameter ratios. Effect of ring supports with middle layer thickness is presented using the Rayleigh-Ritz procedure with three different conditions. The influence of the positions of ring supports for clamped-clamped is more visible than simply supported and clamped-free end conditions. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. The Lagrangian functional is created by adding the energy expressions for the shell and rings. The axial modal deformations are approximated by making use of the beam functions. The comparisons of frequencies have been made for efficiency and robustness for the present numerical procedure. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped, simply supported-simply supported frequency curves are higher than that of clamped-simply curves. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

In-plane varying bending force effects on wave dispersion characteristics of single-layered graphene sheets

Cao, Yan,Selmi, Abdellatif,Tohfenamarvar, Rasoul,Zandi, Yousef,Kasehchi, Ehsan,Assilzahed, Hamid Techno-Press 2021 Advances in nano research Vol.10 No.2

An analytical investigation has been performed on the mechanical performance of waves propagated in a Single-Layered Graphene Sheet (SLGS) when an In-plane Varying Bending (IVB) load is interacted. It has been supposed that the Graphene Sheet (GS) is located on an elastic medium. Employing a two-parameter elastic foundation, the effects of elastic substrate on the GS behavior are modeled. Besides, the kinematic equations are derived by the means of a trigonometric two-variable refined plate theory. Moreover, in order to indicate the size-dependency of the SLGS, a Nonlocal Strain Gradient Theory (NSGT) was considered. The nonlocal governing differential equations are achieved in the framework of Hamilton's Principle (HP). Also, an analytical approach was used to detect the unknowns of the final eigenvalue equation. Finally, the effects of each parameters using some dispersion charts were determined.