Sharif Digital Repository

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for this work. The shaft is modeled as a beam and the Euler-Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6 degrees of freedom. In order to solve these equations... 

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed and analyzed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for the present work. The shaft is modeled as a beam with a circular cross-section and the Euler Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6° of freedom.... 

This paper aims to revisit the effect of sloshing on the flutter characteristics of a partially liquid-filled cylinder. A computational fluid-structure interaction model within the framework of the finite element method is developed to capture fluid-structure interactions arising from the sloshing of the internal fluid and the flexibility of its containing structure exposed to an external supersonic airflow. The internal liquid sloshing is represented by a more sophisticated model, referred to as the liquid sloshing model, and the shell structure is modeled by Sanders' shell theory. The aerodynamic pressure loading is approximated by the first-order piston theory. The initial geometric... 

In this paper, numerical investigation of the statical and dynamical stability of aligned and misaligned viscoelastic cantilevered beam is performed with a terminal nozzle in the presence of gravity in two cases: (1) effect of fluid velocity on the flutter boundary of beam conveying fluid and (2) effect of gravity on the buckling boundary of beam conveying fluid. The beam is assumed to have a large width-to-thickness ratio, so the out-of-plane bending rigidity is far higher than the in-plane bending and torsional rigidities. Gravity vector is considered in the vertical direction. Thus, deflection of the beam because of the gravity effect couples the in-plane bending and torsional equations.... 

An efficient two-dimensional reduced-order hydroelastic model for studying supercavitation phenomenonwith zero cavitation number is proposed. In order to compute fluid eigenmodes, unsteady hydrodynamic model is derived using the finite-element method along with the potential flow assumption. This model takes advantage of a new real time, direct algorithm to compute the pressure distribution around the hydrofoil, which avoids any iterative scheme to find cavity extent as like as conventional method. The present approach starts by specifying the steady cavitation domain for the zero cavitation number, then, it is assumed that unsteady cavitation flow around the steady-state leads to small... 

A general reduced-order aeroelastic model for 3-D complex geometries in subsonic incompressible flow regimes in the continuous-time domain was developed. A boundary element method (BEM) based fluid eigenanalysis solver was integrated with a finite element method (FEM) based modal technique of structural modeling. A body assumed to be a closed surface with known solid boundaries submerged in a potential flow is considered. The wake is considered to be thin and no aerodynamic loads will be supported by it. domain. The modal formulation of the aerodynamic system must be modified with a static correction method to include at least the quasi-static contribution of the higher truncated modes. The... 

In the present study, free vibrations and stability of rotating single walled carbon nanotubes (SWCNT) is investigated by nonlocal theory of elasticity; while the CNT is partially resting on an elastic foundation. The governing equations of motion are presented by using Love's shell assumptions. An exact series expansion method of solution is employed and very accurate results are obtained. Some parameter studies including the effects of rotating speed, foundation stiffness, slenderness ratio and nonlocal parameter on the natural frequency and stability margins of the current model are studied. The studies show that rotation rates and foundation elasticity can contribute significantly in the... 

Carbon nanotubes (CNTs) have been recently taken into consideration as mechanical resonators of distinguished capabilities. This study aims at investigating the free vibration characteristics of a single-walled CNT in the vicinity of a fully constrained graphene sheet. Using a molecular structural mechanics model and considering nonlinear van-der-Waals interactions, the static deformation of the nanotube is obtained using an iterative procedure. Then, the governing equations of motion are linearized about the static equilibrium state and the natural frequencies are obtained. The molecular structural mechanics model is verified using established results in literature and then a survey is... 

In this study, the instability of spinning cylindrical shells partially filled with viscous liquid is investigated. Based on the Navier-Stokes equations for the incompressible flow, a 2D model is developed for liquid motion at each section of the cylinder. The governing equations of the cylinder vibrations are obtained based on the first-order shear deformable shell theory. The nonpenetration and no-slip boundary conditions of the flow on the wetted surface of the cylinder relate the liquid motion to the shell vibrations. Also the liquid pressure exerted on the cylinder wall combines the vibrations of the rotary cylinder to the liquid motion. By using the obtained coupled liquid-structure... 

Carbon nanotubes are regarded as ideal fillers for polymeric materials due to their excellent mechanical properties. Mechanical analysis without consideration of nanotube–matrix interphase, may not give precise predictions. In this work, the impacts of interphase on the behavior of polymer-based nanocomposites are studied. For this purpose, a closed-form micromechanical interphase model considering the diameter of nanotube, the thickness of interphase, and mechanical properties of nanotube and polymer is proposed to estimate the overall mechanical properties of nanotube-reinforced polymer nanocomposites. Furthermore, the effective elastic constants of the nanocomposites for a wide range of... 

Carbon nanotubes are regarded as ideal fillers for polymeric materials due to their excellent mechanical properties. Mechanical analysis without consideration of nanotube–matrix interphase, may not give precise predictions. In this work, the impacts of interphase on the behavior of polymer-based nanocomposites are studied. For this purpose, a closed-form micromechanical interphase model considering the diameter of nanotube, the thickness of interphase, and mechanical properties of nanotube and polymer is proposed to estimate the overall mechanical properties of nanotube-reinforced polymer nanocomposites. Furthermore, the effective elastic constants of the nanocomposites for a wide range of... 

In the current work, the effect of interphase region on the mechanical properties of polymer nanocomposites reinforced with nanoparticles is studied. For this purpose, a closed-form interphase model as a function of radial distance based on finite-size representative volume element is suggested to estimate the mechanical properties of particle-reinforced nanocomposites. The effective Young’s and shear moduli of thermoplastic polycarbonate-based nanocomposites for a wide range of sizes and volume fractions of silicon carbide nanoparticles are investigated using the proposed interphase model and molecular dynamics simulations. In order to investigate the effect of particle size, several unit... 

This paper aims at investigating the resonance frequencies and stability of a long Graphene Nano-Ribbon (GNR) carrying electric current. The governing equation of motion is obtained based on the Euler-Bernoulli beam model along with Hamilton's principle. The transverse force distribution on the GNR due to the interaction of the electric current with its own magnetic field is determined by the Biot-Savart and Lorentz force laws. Using Galerkin's method, the governing equation is solved and the effect of current strength and dimensions of the GNR on the stability and resonance frequencies are investigated  

This paper aims at investigating the interaction of two flexible permanent magnet beams facing each other. The governing equations of motion are obtained based on the Euler-Bernoulli beam model along with Hamiltons principle. Assuming that the beams tips are far enough, each magnet beam is considered as a series of dipole segments and the external force and moment distributions over each beam due to the magnetic field of the other one is calculated in the deformed configuration. The transverse deflections of the beams are written as series expansions of the mode shapes of an unloaded cantilever beam and the Galerkin method is applied to determine the stability and resonance frequencies.... 

This paper deals with the flexural instability of flexible spinning cylinders partially filled with viscous fluid. Using the linearized Navier-Stokes equations for the incompressible flow, a two-dimensional model is developed for fluid motion. The resultant force exerted on the flexible cylinder wall as the result of the fluid motion is calculated as a function of lateral acceleration of the cylinder axis in the Laplace domain. Applying the Hamilton principle, the governing equations of flexural motion of the rotary flexible cylinder mounted on general viscoelastic supports are derived. Then combining the equations describing the fluid force on the flexible cylinder with the structural... 

Since the efficiency of non-classical continuum theories is strongly dependent on the recognition of the suitable values of small length scale parameters and there is still uncertainty about them, a novel approach, equivalent lattice stiffness method is developed here. This approach without the characteristic length scale parameter which arises in non-classical continuum theories, such as nonlocal theory and strain gradient theory, is capable to capture size effect more easily and accurately. This method is proposed based on the concept of lattice dynamics but a Taylor series expansion is involved to approximate the displacements of the continuous domain; accordingly, this approach is in... 

Since the efficiency of non-classical continuum theories is strongly dependent on the recognition of the suitable values of small length scale parameters and there is still uncertainty about them, a novel approach, equivalent lattice stiffness method is developed here. This approach without the characteristic length scale parameter which arises in non-classical continuum theories, such as nonlocal theory and strain gradient theory, is capable to capture size effect more easily and accurately. This method is proposed based on the concept of lattice dynamics but a Taylor series expansion is involved to approximate the displacements of the continuous domain; accordingly, this approach is in... 

In this paper, the aeroelastic behavior and flutter instability of aircraft wings in subsonic incompressible flight speed regime are investigated. Quasi-steady and unsteady aerodynamic models are used for aerodynamic modeling and the obtained aeroelastic predictions are compared to those available in the specialized literature. Based on a number of test cases, it is shown that the quasi-steady aerodynamic models are inadequate for the determination of aeroelastic behavior and flutter boundary of aircraft wings in the incompressible flight speed range. © 2006 Elsevier Ltd. All rights reserved  

A numerical model based on the boundary element method is proposed for the sloshing of a flowing liquid in a three-dimensional tank. Assuming a mean flow in the tank in addition to a perturbation flow, the nonlinear boundary conditions of the liquid free-surface are linearized. Using the boundary element method along with the modal analysis technique a reduced order model is obtained which is used to calculate the fundamental sloshing frequencies and modes in the tank with an inlet and outlet. The obtained results for a test case are compared with the literature data to validate the proposed model. The results are in a very good agreement with analytical results and show an acceptable... 

Purpose: The purpose of this paper is to analyze the stability of aeroelastic systems using a novel reduced order aeroelastic model. Design/methodology/approach: The proposed aeroelastic model is a reduced-order model constructed based on the aerodynamic model identification using the generalized aerodynamic force response and the unsteady boundary element method in various excitation frequency values. Due to the low computational cost and acceptable accuracy of the boundary element method, this method is selected to determine the unsteady time response of the aerodynamic model. Regarding the structural model, the elastic mode shapes of the shell are used. Findings: Three case studies are...