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Static and Dynamic Analysis of Nano Beams based on Second Strain Gradient Theory
, M.Sc. Thesis Sharif University of Technology ; Eskandari, Morteza (Supervisor)
Abstract
In this thesis, static and dynamic analysis of nano beams based on second strain gradient theory is presented. Due to their small sizes, nano electro mechanical devices (NEMS) hold tremendous promise for novel, versatile and very sensitive devices for different applications ranging from actuators, transducers and also mass, force, light and frequency detectors. Therefore accurate modeling and analysis of such devices has an important role in their design and performance improvement. Neglecting the size effect, traditional theory of elasticity can not be suitable to predict mechanical behavior of these systems and so, it should be used non-classical theories which include size dependency...
Nonlinear Aeroelastic Analysis of Composite Wing at a Hale Flight Vehicle
, M.Sc. Thesis Sharif University of Technology ; Dehghani Firouz-Abadi, Roholla (Supervisor)
Abstract
The purpose of this study is aeroelastic stability analysis and nonlinear aeroelastic vibration of composite wing with nonlinear 1D beam model. Wing’s structure modelled as thin-walled composite single box beam in linear and nonlinear conditions. Thin-walled composite box beam developed by classical lamination theory and structural nonlinearity is von karman strain. Unsteady aerodynamic of wing modelled with modified strip theory. Aeroelastic equations of wing obtained from modal expansion (assumed mode) and Hamilton’s Principle. In order to stability analysis of wing, the linear aeroelastic equations in state space must be calculated and so with eigenvalue analysis instability speed will be...
Chatter instability analysis of spinning micro-end mill with process damping effect via semi-discretization approach
, Article Acta Mechanica ; Vol. 225, issue. 3 , 2014 , pp. 715-734 ; ISSN: 00015970 ; Movahhedy, M. R ; Akbari, J ; Sharif University of Technology
Abstract
In this paper, the stability of delay differential equations (DDEs), describing self-excited vibrations in a micro-milling process, is investigated based on semi-discretization (SD) method. Due to the stubby geometry of micro-tools, the shear deformation and rotary inertia effects are considered for modeling the structure. The extended Hamilton's principle is used to derive a detailed dynamical model of the spinning micro-tool with the support of misalignment in which the gyroscopic effects cause coupling of equations. Considering the actual geometry of the micro-end mill, exact dynamic stiffness (DS) formulations are developed to investigate the tool's free vibration characteristics. The...
Nonlinear dynamic analysis of a timoshenko beam resting on a viscoelastic foundation and traveled by a moving mass
, Article Shock and Vibration ; Vol. 2014 , 2014 ; ISSN: 10709622 ; Kargarnovin, M. H ; Sharif University of Technology
Abstract
The dynamic response of a Timoshenko beam with immovable ends resting on a nonlinear viscoelastic foundation and subjected to motion of a traveling mass moving with a constant velocity is studied. Primarily, the beam's nonlinear governing coupled PDEs of motion for the lateral and longitudinal displacements as well as the beam's cross-sectional rotation are derived using Hamilton's principle. On deriving these nonlinear coupled PDEs the stretching effect of the beam's neutral axis due to the beam's fixed end conditions in conjunction with the von-Karman strain-displacement relations is considered. To obtain the dynamic responses of the beam under the act of a moving mass, derived nonlinear...
Magnetoelastic instability of a long graphene nano-ribbon carrying electric current
, Article Advances in Applied Mathematics and Mechanics ; Vol. 6, issue. 3 , 2014 , pp. 299-306 ; ISSN: 20700733 ; Mohammadkhani, H ; Sharif University of Technology
Abstract
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
Effects of the van der Waals force, squeeze-film damping, and contact bounce on the dynamics of electrostatic microcantilevers before and after pull-in
, Article Nonlinear Dynamics ; Vol. 77, issue. 1-2 , 2014 , p. 87-98 ; Vossoughi, G ; Meghdari, A ; Sharif University of Technology
Abstract
The operational range of microcantilever beams under electrostatic force can be extended beyond pull-in in the presence of an intermediate dielectric layer. In this paper, a systematic method for deriving dynamic equation of microcantilevers under electrostatic force is presented. This model covers the behavior of the microcantilevers before and after the pull-in including the effects of van der Waals force, squeeze-film damping, and contact bounce. First, a polynomial approximate shape function with a time-dependent variable for each configuration is defined. Using Hamilton's principle, dynamic equations of microcantilever in all configurations have been derived. Comparison between modeling...
Nonlinear dynamic analysis of an axially loaded rotating Timoshenko beam with extensional condition included subjected to general type of force moving along the beam length
, Article JVC/Journal of Vibration and Control ; Volume 19, Issue 16 , 2013 , Pages 2448-2458 ; 10775463 (ISSN) ; Kargarnovin, M. H ; Sharif University of Technology
2013
Abstract
In this paper the non-planar nonlinear dynamic responses of an axially loaded rotating Timoshenko beam subjected to a three-directional force traveling with a constant velocity is studied. On deriving the nonlinear coupled partial differential equations (PDEs) of motion the stretching effect of the beam's neutral axis due to the pinned-pinned ends' condition in conjunction with the von Karman strain-displacement relation are considered. The beam's nonlinear governing coupled PDEs of motion for the bending rotations of warped cross-section, longitudinal and lateral displacements are derived using Hamilton's principle. To obtain the dynamic responses of the beam, derived PDEs of motion are...
Size dependent vibrations of micro-end mill incorporating strain gradient elasticity theory
, Article Journal of Sound and Vibration ; Volume 332, Issue 15 , 2013 , Pages 3922-3944 ; 0022460X (ISSN) ; Movahhedy, M. R ; Akbari, J ; Sharif University of Technology
2013
Abstract
In this paper, a size-dependent formulation is presented for vibration analysis of micro-end mill tool. The formulation is developed based on the strain gradient elasticity theory in order to enhance the modeling capability of micro-size structures. Due to stubby geometry of micro-tool, the shear deformation and rotary inertia effects are considered in the derivation of equations. Hence, based on the strain gradient Timoshenko beam theory, the extended Hamilton's principle is used to formulate a detailed dynamical model of the rotating micro-tool. The dynamical model includes a set of partial differential equations with gyroscopic coupling produced due to the spindle rotation. The governing...
Bending-torsional flutter of a cantilevered pipe conveying fluid with an inclined terminal nozzle
, Article Journal of Sound and Vibration ; Volume 332, Issue 12 , 2013 , Pages 3002-3014 ; 0022460X (ISSN) ; Askarian, A. R ; Kheiri, M ; Sharif University of Technology
2013
Abstract
Stability analysis of a horizontal cantilevered pipe conveying fluid with an inclined terminal nozzle is considered in this paper. The pipe is modelled as a cantilevered Euler-Bernoulli beam, and the flow-induced inertia, Coriolis and centrifugal forces along the pipe as well as the follower force induced by the jet-flow are taken into account. The governing equations of the coupled bending-torsional vibrations of the pipe are obtained using extended Hamilton's principle and are then discretized via the Galerkin method. The resulting eigenvalue problem is then solved, and several cases are examined to determine the effect of nozzle inclination angle, nozzle aspect ratio, mass ratio and...
Longitudinal behavior of strain gradient bars
, Article International Journal of Engineering Science ; Volume 66-67 , May , 2013 , Pages 44-59 ; 00207225 (ISSN) ; Asghari, M ; Ahmadian, M. T ; Sharif University of Technology
2013
Abstract
In this paper, the strain gradient theory, a non-classical continuum theory capable of capturing the size effect observed in micro-scale structures, is employed in order to investigate the size-dependent mechanical behavior of microbars. For a strain gradient bar, the governing equation of motion and classical and non-classical boundary conditions are derived using Hamilton's principle. Closed form solutions have been analytically obtained for static deformation, natural frequencies and mode shapes of strain gradient bars. The static deformation and natural frequencies of a clamped-clamped microbar subjected to a uniform axial distributed force are derived analytically and the results are...
Strain gradient formulation of functionally graded nonlinear beams
, Article International Journal of Engineering Science ; Volume 65 , 2013 , Pages 49-63 ; 00207225 (ISSN) ; Kahrobaiyan, M. H ; Ahmadian, M. T ; Firoozbakhsh, K ; Sharif University of Technology
2013
Abstract
In this paper size-dependent static and dynamic behavior of nonlinear Euler-Bernoulli beams made of functionally graded materials (FGMs) is investigated on the basis of the strain gradient theory. The volume fraction of the material constituents is assumed to be varying through the thickness of the beam based on a power law. As a consequence, the material properties of the microbeam (including length scales) are varying in the direction of the beam thickness. To develop the model, the usual simplifying assumption which considers the length scale parameter to be constant through the thickness is avoided and equivalent length scale parameters are introduced for functionally graded microbeams...
Dynamic analysis of a functionally graded simply supported Euler-Bernoulli beam subjected to a moving oscillator
, Article Acta Mechanica ; Volume 224, Issue 2 , 2013 , Pages 425-446 ; 00015970 (ISSN) ; Kargarnovin, M. H ; Gharini, M ; Sharif University of Technology
2013
Abstract
The dynamic behavior of a functionally graded (FG) simply supported Euler-Bernoulli beam subjected to a moving oscillator has been investigated in this paper. The Young's modulus and the mass density of the FG beam vary continuously in the thickness direction according to the power-law model. The system of equations of motion is derived by using Hamilton's principle. By employing Petrov-Galerkin method, the system of fourth-order partial differential equations of motion has been reduced to a system of second-order ordinary differential equations. The resulting equations are solved using Runge-Kutta numerical scheme. In this study, the effect of the various parameters such as power-law...
Dynamic response of Timoshenko beam under moving mass
, Article Scientia Iranica ; Volume 20, Issue 1 , 2013 , Pages 50-56 ; 10263098 (ISSN) ; Mofid, M ; Khoraskani, R. A ; Sharif University of Technology
2013
Abstract
In this article, the dynamic responses of a Timoshenko beam subjected to a moving mass, and a moving sprung mass are analyzed. By making recourse to Hamilton's principle, governing differential equations for beam vibration are derived. By using the modal superposition method, the partial differential equations of the system are transformed into a set of Ordinary Differential Equations (ODEs). The resulted set of ODEs is represented in state-space form, and solved by means of a numerical technique. The accuracy of the results has been ascertained through comparing the results of our approach with those available from previous studies; moreover, a reasonable agreement has been obtained. The...
Vibration and dynamic analysis of oil well drillstring considering coupled axial and torsional effects using cylindrical superelement
, Article ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) ; Volume 14 , November , 2013 ; 9780791856437 (ISBN) ; Ghorbani, Sh ; Firoozbakhsh, K ; Barari, A ; ASME ; Sharif University of Technology
American Society of Mechanical Engineers (ASME)
2013
Abstract
In this paper axial and torsional vibrations of a drillstring are studied using cylindrical superelement. Drillstring vibration equation is derived by calculating kinetic and potential energy and work done by external forces on drillstring, and utilizing Hamilton's principle. The model is analyzed by implementing finite element technique with consideration drillstring weight, centrifugal force due to rotation of drillstring, axial force resulting from bit with the formation contact and torsional torque caused by the stick-slip phenomenon. To calculate the vibrational response of drillstring, a computational finite element scheme was developed. For a typical case of oil well drillstring, the...
In-plane and transverse eigenmodes of high-speed rotating composite disks
, Article Journal of Applied Mechanics, Transactions ASME ; Volume 80, Issue 1 , 2013 ; 00218936 (ISSN) ; Abbas Jalali, M ; Sharif University of Technology
2013
Abstract
We apply Hamilton's principle and model the coupled in-plane and transverse vibrations of high-speed spinning disks, which are fiber-reinforced circumferentially. We search for eigenmodes in the linear regime using a collocation scheme, and compare the mode shapes of composite and isotropic disks. As the azimuthal wavenumber varies, the radial nodes of in-plane waves are remarkably displaced in isotropic disks while they resist such displacements in composite disks. The reverse of this phenomenon happens for transversal waves and the radial nodes move toward the outer disk edge as the azimuthal wavenumber is increased in composite disks. This result is in accordance with the predictions of...
Investigation of the effects of process damping on chatter instability in micro end milling
, Article Procedia CIRP ; Volume 1, Issue 1 , 2012 , Pages 156-161 ; 22128271 (ISSN) ; Movahhedy, M. R ; Akbari, J ; Sharif University of Technology
2012
Abstract
In this paper, chatter instability of micro end mill tools is studied by taking into account the process damping effect. The actual geometry of the micro tool including shank, taper part and fluted section is considered in the analysis. Timoshenko beam theory is utilized to consider the shear deformation and rotary inertia effects due to short and thick beam-type structures of each parts of the micro tool. The extended Hamilton's Principle is used to formulate a detailed dynamical model of the rotating micro end mill. The governing equations are solved by assumed mode model expansion. An exact dynamic stiffness method is developed to investigate modal characteristics of the tool including...
Nonlinear dynamic analysis of an inclined Timoshenko beam subjected to a moving mass/force with beam's weight included
, Article Shock and Vibration ; Volume 18, Issue 6 , 2011 , Pages 875-891 ; 10709622 (ISSN) ; Kargarnovin, M. H ; Sharif University of Technology
2011
Abstract
In this study, the nonlinear vibrations analysis of an inclined pinned-pinned self-weight Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity is investigated. The nonlinear coupled partial differential equations of motion for the rotation of warped cross section, longitudinal and transverse displacements are derived using the Hamilton's principle. These nonlinear coupled PDEs are solved by applying the Galerkin's method to obtain dynamic responses of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various...
Dynamic analysis of an inclined Timoshenko beam traveled by successive moving masses/forces with inclusion of geometric nonlinearities
, Article Acta Mechanica ; Volume 218, Issue 1-2 , 2011 , Pages 9-29 ; 00015970 (ISSN) ; Kargarnovin, M. H ; Sharif University of Technology
2011
Abstract
In the first part of this paper, the nonlinear coupled governing partial differential equations of vibrations by including the bending rotation of cross section, longitudinal and transverse displacements of an inclined pinned-pinned Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity are derived. To do this, the energy method (Hamilton's principle) based on the large deflection theory in conjuncture with the von-Karman strain-displacement relations is used. These equations are solved using the Galerkin's approach via numerical integration methods to obtain dynamic...
Flutter of wings involving a locally distributed flexible control surface
, Article Journal of Sound and Vibration ; Volume 357 , November , 2015 , Pages 377-408 ; 0022460X (ISSN) ; Firouz Abadi, R. D ; Roshanian, J ; Sharif University of Technology
Academic Press
2015
Abstract
This paper undertakes to facilitate appraisal of aeroelastic interaction of a locally distributed, flap-type control surface with aircraft wings operating in a subsonic potential flow field. The extended Hamilton's principle serves as a framework to ascertain the Euler-Lagrange equations for coupled bending-torsional-flap vibration. An analytical solution to this boundary-value problem is then accomplished by assumed modes and the extended Galerkin's method. The developed aeroelastic model considers both the inherent flexibility of the control surface displaced on the wing and the inertial coupling between these two flexible bodies. The structural deformations also obey the Euler-Bernoulli...
Dynamic modeling of scratch drive actuators
, Article Journal of Microelectromechanical Systems ; Volume 24, Issue 5 , April , 2015 , Pages 1370-1383 ; 10577157 (ISSN) ; Vossoughi, G ; Meghdari, A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2015
Abstract
There has been much research in developing scratch drive actuators (SDAs), but because of their dynamic complexity, these microelectromechanical system-based actuators have not been dynamically analyzed up to now. In this paper, a comprehensive model is presented to describe the dynamic behavior of SDA and its components during stepwise motion. In this model, Hamilton's principle and Newton's method are used to extract dynamic equations of the SDA plate and dynamic equation for the linear motion of SDA. This model presents a good insight into the operating principles of SDA by predicting the variation of different variables, such as bushing angle, contact length, horizontal position, and...