Papers by mohamed trabelssi
Journal of sound and vibration, Jul 1, 2024
Journal of sound and vibration, Jul 1, 2024
Applied condition monitoring, 2023
This manuscript aims to study a misaligned rotor using a new approach to solving nonlinear rotor ... more This manuscript aims to study a misaligned rotor using a new approach to solving nonlinear rotor equations of motion based on the Harmonic Quadrature Method (HQM). The present rotor system is supported by ball bearings with a squeeze film damper. The dynamic model representing this rotor yields a system of nonlinear equations of motion with time-dependent coefficients.HQM is a periodic discretization technique that does not involve costly Galerkin integrals while providing high-order computational accuracy and efficiency. The different steps of its implementation were presented, and a validation study was carried out. A good agreement was found between the numerical results found in the literature and those obtained by the HQM method. Numerical simulations of the dynamic misaligned rotor behavior generated by the HQM method were also performed. These simulations show the non-synchronous and chaotic motions (bifurcated response) generated by the non-linear interaction between the rotor misalignment and the fluid film forces induced by the damper.
Archive of Applied Mechanics, 2020
The purpose of this paper is to provide a high-order finite element method (FEM) formulation of n... more The purpose of this paper is to provide a high-order finite element method (FEM) formulation of nonlocal nonlinear nonlocal graded Timoshenko based on the weak form quadrature element method (WQEM). This formulation offers the advantages and flexibility of the FEM without its limiting low-order accuracy. The nanobeam theory accounts for the von Kármán geometric nonlinearity in addition to Eringen’s nonlocal constitutive models. For the sake of generality, a nonlinear foundation is included in the formulation. The proposed formulation generates high-order derivative terms that cannot be accounted for using regular first- or second-order interpolation functions. Hamilton’s principle is used to derive the variational statement which is discretized using WQEM. The results of a WQEM free vibration study are assessed using data obtained from a similar problem solved by the differential quadrature method (DQM). The study shows that WQEM can offer the same accuracy as DQM with a reduced com...
Composite Structures, 2018
In this paper the torsional vibration of size-dependent viscoelastic nanorods embedded in an elas... more In this paper the torsional vibration of size-dependent viscoelastic nanorods embedded in an elastic medium with dierent boundary conditions is investigated. The novelty of this study consists of combining the nonlocal theory with the strain and velocity gradient theory to capture both softening and stiening size-dependent behavior of the nanorods. The viscoelastic behavior is modelled using the so-called KelvinVoigt viscoelastic damping model.Three length-scale parameters are incorporated in this newly combined theory, namely, a nonlocal, a strain gradient, and a velocity gradient parameter. The governing equation of motion and its boundary conditions for the vibration analysis of nanorods are derived by employing Hamilton's principle. It is shown that the expressions of the classical stress and the stress gradient resultants are only dened for dierent values of the nonlocal and strain gradient parameters. The case where these are equal may seem to result in an inconsistency to the general equation of motion and the related non-classical boundary conditions. A rigorous investigation is conducted to prove that that the proposed solution is consistent with physics. Damped eigenvalue solutions are obtained both analytically and numerically using a Locally adaptive Dierential Quadrature Method (LaDQM). Analytical results of linear free vibration response are obtained for various length-scales and compared with LaDQM numerical results.
Archive of Applied Mechanics, Feb 21, 2022
The free and forced vibration of a graded geometrically nonlinear Timoshenko nanobeam supported b... more The free and forced vibration of a graded geometrically nonlinear Timoshenko nanobeam supported by on a nonlinear foundation is considered in this paper. The main contribution of this study is to propose a new formulation for the dynamic response of this beam by combining nonlocal and surface elasticity in addition to employing the physical neutral axis method which eliminates the quadratic nonlinearity from the equation of motion. Using the principle of virtual work, a fourth-order nonlinear partial differential equation is formulated and Galerkin technique is employed to yield a fourth-order ordinary differential equation with cubic nonlinearity in the temporal domain. The method of multiple scales is employed to obtain the analytical expression of the nonlinear frequency of the beam and its frequency response curve from a primary resonance analysis. To assess the accuracy of this analytical solution, it is compared with a numerical solution obtained using the differential quadrature method. The obtained analytical results are successfully validated for particular cases of the considered problem with results published by other authors. The effects of surface elasticity, nonlocality, the physical neutral axis, the beam aspect ratio, the power-law index and the elastic foundation coefficients on the free and forced vibration response of the graded Timoshenko nanobeam are thoroughly investigated for different types of boundary conditions. Keywords Functionally graded Timoshenko nanobeam • Nonlocal theory • Surface effects • Nonlinear vibration • Physical neutral axis • Method of multiple scales • Differential quadrature method 1 Introduction Miniature beams have been used in many electromechanical systems such as biosensors, ultra-thin films, microswitches, micro-actuators, nanowires, micro-electromechanical systems (MEMS) and nanoelectromechanical system (NEMS) as the primary structural elements [1-4]. It is well known that a classical continuum model S. El-Borgi (B) Mechanical Engineering Program,
Proceedings Of The Institution Of Mechanical Engineers, Part N: Journal Of Nanomaterials, Nanoengineering And Nanosystems, Nov 21, 2022
The primary objective of this paper is to propose a novel method to derive Differential Quadratur... more The primary objective of this paper is to propose a novel method to derive Differential Quadrature Method matrices with several degrees of freedom at the boundaries that can be used to build Strong Quadrature Elements to solve fourth and higher-order equations of motion. The proposed method, referred to as Locally adaptive Strong Quadrature Element Method, is applied to higher-order equations of motion for nonlinear graded Timoshenko and Euler-Bernoulli nanobeams formulated using the Second Strain Gradient Theory or the Nonlocal Strain Gradient Theory. To limit the formulation complexity, the proposed approach is based on the regular formulation of the differential quadrature method combined with custom-built transfer matrices. Moreover, it does not require a different formulation for fourth and sixth-order equations and can be extended beyond sixth-order equations. Validation was carried out using examples from the literature as well as data obtained using the classical Locally adaptive Quadrature Element Method. Both linear and nonlinear frequencies were evaluated for a large number of configurations and boundary conditions. The proposed approach resulted in good accuracy and a convergence speed comparable to the conventional Locally adaptive Quadrature Element Method.
Acta Mechanica
A novel formulation of the weak form quadrature element method, referred to as the locally adapti... more A novel formulation of the weak form quadrature element method, referred to as the locally adaptive weak quadrature element method, is proposed to develop elements for nonlinear graded strain gradient Timoshenko and Euler–Bernoulli nanobeams. The equations of motion are obtained based on Hamilton principle while accounting for the position of the physical neutral axis. The proposed elements use Gauss quadrature points to ensure full integration of the variational statement. The proposed formulation develops matrices based on the differential quadrature method which employs Lagrange-based polynomials. These matrices can be modified to accommodate any number of extra derivative degrees of freedom including third-order beams and higher-order strain gradient beams without requiring an entirely new formulation. The performance of the proposed method is evaluated based on the free vibration response of the linear and nonlinear strain gradient Timoshenko and Euler–Bernoulli nanobeams. Both...
Composites Part B: Engineering, 2019
The free and forced vibration of a nonlocal Timoshenko graded nanobeam resting on a nonlinear ela... more The free and forced vibration of a nonlocal Timoshenko graded nanobeam resting on a nonlinear elastic foundation is investigated in this paper. The Timoshenko beam theory along with the von Kármán geometric nonlinearity is formulated while accounting for Eringen's nonlocal elasticity differential model. A power-law distribution is used to model the material distribution along the beam thickness. The equations of motion are derived using Hamilton's principle and then solved analytically using the Method of Multiple Scale (MMS) and numerically using the Differential Quadrature Method (DQM) and the Harmonic Quadrature Method (HQM). The considered boundary conditions include both Hinged-Hinged and Clamped-Clamped. The obtained nonlocal nonlinear frequencies of the nanobeam are first validated based on published analytical results that use linear mode shapes. A frequency response analysis is also conducted utilizing both MMS and DQM. The time discretization in DQM solution is performed using Spectral Method (SPM) and HQM. The primary objective of this study is to investigate the effects of the nonlocal parameter, power-law index, linear and nonlinear stiffnesses of the elastic foundation as well as the boundary conditions on the dynamic response of the nanobeam.
Composite Structures, 2017
This paper presents a study of the free vibration response of a nonlocal nonlinear functionally g... more This paper presents a study of the free vibration response of a nonlocal nonlinear functionally graded (FG) EulerBernoulli nanobeam resting on a nonlinear elastic foundation. A power-law distribution is used to describe the material distribution along the thickness of the beam. Eringen's nonlocal elasticity model with a material length scale is adopted to account for material behavior at the nano-scale along with a modied version of the von Kármán geometric nonlinearity that in turn accounts for moderate rotations. The derived equation of motion is solved using the well-known Dierential Quadrature Method (DQM) in addition to the more numerically stable Locally adaptive Dierential Quadrature Method (LaDQM). The obtained nonlocal nonlinear frequencies of the nanobeam are rst validated based on published analytical results that use linear mode shapes. The use of LaDQM is helpful in assessing the eect of the nonlinearities on the modes shapes which in turn was used to explain the discrepancy between the numerical and analytical results. This study aims to investigate the eects of the nonlocal parameter, and power-law index as well as linear and the nonlinear stinesses of the elastic foundation on the nonlinear fundamental frequency of the nanobeam for the selected boundary conditions.
Applied condition monitoring, 2023
Conventional clad core fiber optic technology has relied on a concentric structure of glass of di... more Conventional clad core fiber optic technology has relied on a concentric structure of glass of different refraction indices. These conventional fibers suffer from constraints and limitations related to thermal expansion compatibility between the core and the glass. The new fiber technology broadly characterized as Microstructured Optic Fibers (MOFs) is intended to lift the limitations of conventional clad core fibers and also extend the range of application of fiber optics. Photonic Cristal Fibers(PCFs) are a special family of Microstructured Optic Fibers characterized by the presence of holes in the cross section of the fiber that are organized in a hexagonal pattern. In order to manufacture these fibers, a preform with the same cross section has to be prepared which can later be drawn into fiber. For such complex geometry, glass extrusion at a viscosity higher than that for extrusion of solid glass preforms has proven to give better results. Despite these merits, the numerical mod...
Springer Tracts in Mechanical Engineering, 2021
Journal of the American Ceramic Society, 2014
ABSTRACT Computational simulations of glass extrusion are performed to quantify the effects of ma... more ABSTRACT Computational simulations of glass extrusion are performed to quantify the effects of material behavior and slip at the die/glass interface on the die swell. Experimental data for three glass types are used to guide the computational study, which considers glass material to be viscous with and without shear thinning and viscoelastic using the Maxwell upper-convected model. The study starts with assuming no-slip at the glass/die interface to see if material behavior alone can explain the die swell results, and then considers slip using the Navier model where interface shear is directly proportional to the relative slip speed at the interface. Consistent with the possibility of slip and intended high viscosity applications, viscosity ranging from 107.4–108.8 Pa·s was used. Based on optimization of the various input parameters required to achieve the measured die swell and ram force values, the study concludes that interface slip occurred as only extreme values of the shear thinning parameters provided an alternative.
Journal of Lightwave Technology, Jan 15, 2015
Authors and/or their employers shall have the right to post the accepted version of IEEE-copyrigh... more Authors and/or their employers shall have the right to post the accepted version of IEEE-copyrighted articles on their own personal servers or the servers of their institutions or employers without permission from IEEE, provided that the posted version includes a prominently displayed IEEE copyright notice (as shown in 8.1.9.B, above) and, when published, a full citation to the original IEEE publication, including a Digital Object Identifier (DOI). Authors shall not post the final, published versions of their articles.
Journal of Non-Crystalline Solids
Journal of Non-Crystalline Solids
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Papers by mohamed trabelssi