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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...
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...
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 oscillations of viscoelastic microcantilever beam based on modified strain gradient theory
, Article Scientia Iranica ; Volume 28, Issue 2 , 2021 , Pages 785-794 ; 10263098 (ISSN) ; Ahmadian, M. T ; Firoozbakhsh, K ; Sharif University of Technology
Sharif University of Technology
2021
Abstract
A viscoelastic microcantilever beam is analytically analyzed based on the modified strain gradient theory. Kelvin-Voigt scheme is used to model beam viscoelasticity. By applying Euler-Bernoulli inextensibility of the centerline condition based on Hamilton's principle, the nonlinear equation of motion and the related boundary conditions are derived from shortening effect theory and discretized by Galerkin method. Inner damping, nonlinear curvature effect, and nonlinear inertia terms are also taken into account. In the present study, the generalized derived formulation allows modeling any nonlinear combination such as nonlinear terms that arise due to inertia, damping, and stiffness, as well...
An analytical method for free vibration analysis of functionally graded beams
, Article Materials and Design ; Volume 30, Issue 3 , 2009 , Pages 741-747 ; 02641275 (ISSN) ; Navazi, H. M ; Haddadpour, H ; Sharif University of Technology
2009
Abstract
A new beam theory different from the traditional first-order shear deformation beam theory is used to analyze free vibration of functionally graded beams. The beam properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. It is assumed that the lateral normal stress of the beam is zero and the governing equations of motion are derived using Hamilton's principle. Resulting system of ordinary differential equations of free vibration analysis is solved using an analytical method. Different boundary conditions are considered and comparisons are made among different beam theories. Also, the effects of...
Influence of system parameters on buckling and frequency analysis of a spinning cantilever cylindrical 3D shell coupled with piezoelectric actuator
, Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science ; Volume 234, Issue 2 , 2020 , Pages 512-529 ; Safarpour, H ; Habibi, M ; Sharif University of Technology
SAGE Publications Ltd
2020
Abstract
In this research, buckling and vibrational characteristics of a spinning cylindrical moderately thick shell covered with piezoelectric actuator carrying spring-mass systems are performed. This structure rotates about axial direction and the formulations include the Coriolis and centrifugal effects. In addition, various cases of thermal (uniform, linear, and nonlinear) distributions are studied. The modeled cylindrical moderately thick shell covered with piezoelectric actuator, its equations of motion, and boundary conditions are derived by the Hamilton's principle and based on a moderately cylindrical thick shell theory. For the first time in the present study, attached mass-spring systems...
Frequency characteristics of a GPL-reinforced composite microdisk coupled with a piezoelectric layer
, Article European Physical Journal Plus ; Volume 135, Issue 2 , January , 2020 ; Ebrahimi, F ; Supeni, E. E. B ; Habibi, M ; Safarpour, H ; Sharif University of Technology
Springer
2020
Abstract
This is the first research on the frequency analysis of a graphene nanoplatelet composite (GPLRC) microdisk in the framework of a numerical-based generalized differential quadrature method. The stresses and strains are obtained using the higher-order shear deformable theory. Rule of mixture is employed to obtain varying mass density, thermal expansion, and Poisson’s ratio, while module of elasticity is computed by modified Halpin–Tsai model. Governing equations and boundary conditions of the GPLRC microdisk covered with piezoelectric layer are obtained by implementing Hamilton’s principle. Regarding perfect bonding between the piezoelectric layer and core, the compatibility conditions are...
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...
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...
Vibration analysis of electrostatically actuated nonlinear microbridges based on the modified couple stress theory
, Article Applied Mathematical Modelling ; Volume 39, Issue 21 , November , 2015 , Pages 6694-6704 ; 0307904X (ISSN) ; Ahmadian, M. T ; Firoozbakhsh, K ; Sharif University of Technology
Elsevier Inc
2015
Abstract
In this paper natural frequency of electrostatically actuated microbridges is investigated based on the modified couple stress theory. Nonlinear formulation of Euler-Bernoulli microbeam is derived using Hamilton's principle. By considering the von-Karman strain, the nonlinearities caused by the mid-plane stretching are included in the formulation. To confirm the model, results of static deflection and natural frequency of microbeams are calculated using modified couple stress theory and compared to those evaluated based on the classical theory and experimental observations. At first, from experimental results of static deflection of a microcantilever, estimation for length scale parameter of...
On pull-in instabilities of microcantilevers
, Article International Journal of Engineering Science ; Volume 87 , February , 2015 , Pages 23-31 ; 00207225 (ISSN) ; Ahmadian, M. T ; Sharif University of Technology
Elsevier Ltd
2015
Abstract
In this paper the static deflection and pull-in instability of electrostatically actuated microcantilevers is investigated based on the strain gradient theory. The equation of motion and boundary conditions are derived using Hamilton's principle and solved numerically. It is shown that the strain gradient theory predicts size dependent normalized static deflection and pull-in voltage for the microbeam while according to the classical theory the normalized behavior of the microbeam is independent of its size. The results of strain gradient theory are compared with those of classical and modified couple stress theories and also experimental observations. According to this comparison, the...
Vibration analysis of a rotating FGM cantilever ARM
, Article ASME International Mechanical Engineering Congress and Exposition, Proceedings, 13 November 2009 through 19 November 2009 ; Volume 15 , 2010 , Pages 359-365 ; 9780791843888 (ISBN) ; Moeini, S. A ; Kahrobaiyan, M. H ; Ahmadian, M. T ; Sharif University of Technology
Abstract
Functionally graded materials (FGMs) are inhomogeneous composites which are usually made of a mixture of metals and ceramics. Properties of these kinds of materials vary continuously and smoothly from a ceramic surface to a metallic surface in a specified direction of the structure. The gradient compositional variation of the constituents from one surface to the other provides an elegant solution to the problem of high transverse shear stresses that are induced when two dissimilar materials with large differences in material properties are bonded. FGMs have extracted much attention as advanced structural materials in recent years. In this paper, free vibration of a rotating FGM cantilever...
Nonlinear cylindrical bending analysis of shear deformable functionally graded plates under different loadings using analytical methods
, Article International Journal of Mechanical Sciences ; Volume 50, Issue 12 , 2008 , Pages 1650-1657 ; 00207403 (ISSN) ; Haddadpour, H ; Sharif University of Technology
2008
Abstract
An exact solution is presented for the nonlinear cylindrical bending and postbuckling of shear deformable functionally graded plates in this paper. A simple power law function and the Mori-Tanaka scheme are used to model the through-the-thickness continuous gradual variation of the material properties. The von Karman nonlinear strains are used and then the nonlinear equilibrium equations and the relevant boundary conditions are obtained using Hamilton's principle. The Navier equations are reduced to a linear ordinary differential equation for transverse deflection with nonlinear boundary conditions, which can be solved by exact methods. Finally, by solving some numeral examples for simply...
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...
Application of nonlocal strain–stress gradient theory and GDQEM for thermo-vibration responses of a laminated composite nanoshell
, Article Engineering with Computers ; 14 March , 2020 ; Ebrahimi, F ; Habibi, M ; Safarpour, H ; Foong, L. K ; Sharif University of Technology
Springer
2020
Abstract
In this article, thermal buckling and frequency analysis of a size-dependent laminated composite cylindrical nanoshell in thermal environment using nonlocal strain–stress gradient theory are presented. The thermodynamic equations of the laminated cylindrical nanoshell are based on first-order shear deformation theory, and generalized differential quadrature element method is implemented to solve these equations and obtain natural frequency and critical temperature of the presented model. The results show that by considering C–F boundary conditions and every even layers’ number, in lower value of length scale parameter, by increasing the length scale parameter, the frequency of the structure...
Nonlinear dynamics and stability analysis of a parametrically excited CNT-reinforced MRE viscoelastic cantilever beam
, Article Smart Materials and Structures ; Volume 27, Issue 10 , 2018 ; 09641726 (ISSN) ; Jalali, A ; Sharif University of Technology
Abstract
This paper investigates the dynamic response of a clamped-free CNT-reinforced-MRE beam which is actuated by the combination of a constant and a harmonic time-dependent magnetic field. Using Hamilton's principle, the equation of motion has been obtained and discretized using the Galerkin method. This procedure transforms the governing PDE equation of motion into a nonlinear ODE equation in the form of the nonlinear Mathieu equation with cubic damping. Then, the method of multiple scales is employed to obtain the dynamic response of the system. Furthermore, a stability analysis is also performed and the effects of a magnetic field on the dynamic response and stability of the system is...
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...
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...