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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...
Flexural vibration characteristics of micro-rotors based on the strain gradient theory
, Article International Journal of Applied Mechanics ; Volume 7, Issue 5 , October , 2015 ; 17588251 (ISSN) ; Hashemi, M ; Sharif University of Technology
World Scientific Publishing Co. Pte Ltd
2015
Abstract
In this paper, the coupled three-dimensional flexural vibration of micro-rotors is investigated by taking into account the small-scale effects utilizing the strain gradient theory, which is a powerful nonclassical continuum theory in capturing small-scale effects. A micro-rotor consists mainly of a flexible micro-rotating shaft and a disk. With the aid of Hamilton's principle, governing equations of motion are derived and then transformed to the complex form. By implementing the Galerkin's method, a coupled ordinary differential equation is attained for the system. Expressions for the first two natural frequencies of the spinning micro-rotors are obtained with truncated two-term equation....
Dynamics and stability analysis of rotating cylindrical shells in annular fluid medium
, Article International Journal of Structural Stability and Dynamics ; Volume 20, Issue 8 , 2020 ; Firouz Abadi, R. D ; Rahmanian, M ; Sharif University of Technology
World Scientific
2020
Abstract
Stability and dynamics of rotating coaxial cylindrical shells conveying incompressible and inviscid fluid are investigated. The interior shell is assumed to be flexible while the exterior cylinder is rigid. Using Sander's-Koiter theory assumptions and following Hamilton's principle, governing equations of motion are determined in their integral form. Employing the extended Galerkin method of solution, the integral equations of motion are projected to their equivalent system of algebraic equations. Fluid equations are fundamentally based on the linearized inviscid Navier-Stokes equations. Impermeability condition on the fluid and structure interface as well as the zero radial velocity...
Vibration analysis of spinning cylindrical shell made of functionally graded material using higher order shear deformation theory
, Article 7th European Conference on Structural Dynamics, EURODYN 2008, 7 July 2008 through 9 July 2008 ; 2008 ; 9780854328826 (ISBN) ; Mehrparvar, M ; Najafizadeh, A ; Sharif University of Technology
University of Southampton, Institute of Sound Vibration and Research
2008
Abstract
In this paper the vibration of a spinning cylindrical shell made of functional graded material (FGM) made is investigated. After a brief introduction of FG materials, by employing higher order theory for shell deformation, constitutive relationships are derived. In the next step by utilizing energy method and Hamilton's principle governing deferential equation of spinning cylindrical shell is obtained. By making use of the principle of minimum potential energy, the characteristic equation of natural frequencies is derived. After verification of the results, the effect of changing different parameters such as material grade, L/R, h/R, and spinning velocity on the natural frequency are...
Free vibrations of functionally graded material cylindrical shell closed with two spherical caps
, Article Ships and Offshore Structures ; 2021 ; 17445302 (ISSN) ; Kiani, Y ; Bagheri, N ; Eslami, M. R ; Sharif University of Technology
Taylor and Francis Ltd
2021
Abstract
Free vibration response of a cylindrical shell closed with two hemispherical caps at the ends (hermit capsule) is analysed in this research. It is assumed that the system of joined shell is made from functionally graded materials (FGM). Properties of the shells are assumed to be graded through the thickness. Cylindrical and hemispherical shells are unified in thickness. To capture the effects of through-the-thickness shear deformations and rotary inertias, first order theory of shells is used. Donnell type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton's principle. The resulting...
Free vibrations of functionally graded material cylindrical shell closed with two spherical caps
, Article Ships and Offshore Structures ; Volume 17, Issue 4 , 2022 , Pages 939-951 ; 17445302 (ISSN) ; Kiani, Y ; Bagheri, N ; Eslami, M. R ; Sharif University of Technology
Taylor and Francis Ltd
2022
Abstract
Free vibration response of a cylindrical shell closed with two hemispherical caps at the ends (hermit capsule) is analysed in this research. It is assumed that the system of joined shell is made from functionally graded materials (FGM). Properties of the shells are assumed to be graded through the thickness. Cylindrical and hemispherical shells are unified in thickness. To capture the effects of through-the-thickness shear deformations and rotary inertias, first order theory of shells is used. Donnell type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton's principle. The resulting...
Vibration of rotating functionally graded timoshenko nano-beams with nonlinear thermal distribution
, Article Mechanics of Advanced Materials and Structures ; Volume 25, Issue 6 , 2018 , Pages 467-480 ; 15376494 (ISSN) ; Mirjavadi, S ; Shafiei, N ; Salem Hamouda, A. M ; Davari, E ; Sharif University of Technology
Taylor and Francis Inc
2018
Abstract
The vibration analysis of rotating, functionally graded Timoshenko nano-beams under an in-plane nonlinear thermal loading is studied for the first time. The formulation is based on Eringen's nonlocal elasticity theory. Hamilton's principle is used for the derivation of the equations. The governing equations are solved by the differential quadrature method. The nano-beam is under axial load due to the rotation and thermal effects, and the boundary conditions are considered as cantilever and propped cantilever. The thermal distribution is considered to be nonlinear and material properties are temperature-dependent and are changing continuously through the thickness according to the power-law...
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...
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...
Effect of size dependency on in-plane vibration of circular micro-rings
, Article Scientia Iranica ; Volume 24, Issue 4 , 2017 , Pages 1996-2008 ; 10263098 (ISSN) ; Ahmadian, M. T ; Rahaeifard, M ; Sharif University of Technology
Sharif University of Technology
2017
Abstract
In this paper, based on the modified couple stress theory, the size-dependent dynamic behavior of circular rings on elastic foundation is investigated. The ring is modeled by Euler-Bernoulli and Timoshenko beam theories, and Hamilton's principle is utilized to derive the equations of motion and boundary conditions. The formulation derived is a general form of the equation of motion of circular rings and can be reduced to the classical form by eliminating the size-dependent terms. On this basis, the size-dependent natural frequencies of a circular ring are calculated based on the non-classical Euler-Bernoulli and Timoshenko beam theories. The findings are compared with classical beam...
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...
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...
Nonlinear dynamic analysis of a rectangular plate subjected to accelerated/decelerated moving load
, Article Journal of Theoretical and Applied Mechanics ; Volume 53, Issue 1 , 2015 , Pages 151-166 ; 14292955 (ISSN) ; Mohsenzadeh, R ; Kargarnovin, M. H ; Sharif University of Technology
Polish Society of Theoretical and Allied Mechanics
2015
Abstract
In this paper, nonlinear dynamical behavior of a rectangular plate traveled by a moving mass as well as an equivalent concentrated force with non-constant velocity is studied. The nonlinear governing coupled partial differential equations (PDEs) of motion are derived by energy method using Hamilton's principle based on the large deflection theory in conjuncture with the von-Karman strain-displacement relations. Then Galerkin's method is used to transform the equations of motion into a set of three coupled nonlinear ordinary differential equations (ODEs) which then is solved in a semi-analytical way to get the dynamical response of the plate. Also, by using the Finite Element Method (FEM)...
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...
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...
Nonlinear dynamics of extensible viscoelastic cantilevered pipes conveying pulsatile flow with an end nozzle
, Article International Journal of Non-Linear Mechanics ; Volume 91 , 2017 , Pages 22-35 ; 00207462 (ISSN) ; Haddadpour, H ; Dehghani Firouz Abadi, R ; Abtahi, H ; Sharif University of Technology
Elsevier Ltd
2017
Abstract
Nonlinear dynamics of an extensible cantilevered pipe conveying pulsating flow is considered in this paper. The fluid flow fluctuates harmonically and exhausts via a nozzle attached to the end of the pipe. Taking into account the extensibility assumption, the coupled nonlinear lateral–longitudinal equations of motion are derived using Hamilton's principle and discretized via Galerkin's method. The adaptive time step Adams algorithm is applied to extract the time response, and then the bifurcation, power spectral density and phase plane maps are plotted for some case studies. Effects of some geometrical parameters such as flow mass, pulsating flow frequency, gravity, nozzle mass and nozzle...
Vibration analysis of pipes conveying fluid resting on a fractional Kelvin-Voigt viscoelastic foundation with general boundary conditions
, Article International Journal of Mechanical Sciences ; Volume 179 , 2020 ; Permoon, M. R ; Shakouri, M ; Sharif University of Technology
Elsevier Ltd
2020
Abstract
In this paper, the stability of pipes conveying fluid with viscoelastic fractional foundation is investigated. The pipe is fixed at the beginning while the pipe end is constrained with two lateral and rotational springs. The fluid flow effect is modeled as a lateral distributed force, containing the fluid inertia, Coriolis and centrifugal forces. The pipe is modeled using the Euler-Bernoulli beam theory and a fractional Kelvin-Voigt model is employed to describe the viscoelastic foundation. The equation of motion is derived using the extended Hamilton's principle. Presenting the derived equation in Laplace domain and applying the Galerkin method, a set of algebraic equations is extracted....
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...
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...