Loading...
Search for:
hamilton’s-principle
0.007 seconds
Total 53 records
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...
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
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...
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...
Closed-form solution of natural frequencies of a cantilever beam under longitudinal rotation of the support
, Article DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, CA, 24 September 2005 through 28 September 2005 ; Volume 1 A , 2005 , Pages 145-151 ; 0791847381 (ISBN); 9780791847381 (ISBN) ; Durali, M ; Jalili, N ; Sharif University of Technology
American Society of Mechanical Engineers
2005
Abstract
This paper presents the modeling steps towards development of frequency equations for a cantilever beam with a tip mass under general base excitations. More specifically, the beam is considered to vibrate in all the three directions, while subjected to a base rotational motion around its longitudinal direction. This is a common configuration utilized in many vibrating beam gyroscopes and well drilling systems. The governing equations are derived using Extended Hamilton's Principle with general 6-DOF base motion. The natural frequency equations are then extracted in closed-form for the case where the base undergoes longitudinal rotation. For validation purposes, the resulting natural...
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...
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...
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...
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...
Stresses in thin-walled beams subjected to atraversing mass under a pulsating force
, Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science ; Volume 224, Issue 11 , April , 2010 , Pages 2363-2372 ; 09544062 (ISSN) ; Vafai, A ; Mofid, M ; Sharif University of Technology
2010
Abstract
An analytical-numerical method to determine the dynamic response of beams with various boundary conditions subjected to a moving mass under a pulsating force is explained. Governing partial differential equations of the system are changed to a convenience type of ordinary differential equations to be solved through a Runge-Kutta scheme. Pulsating force specifications influenced the dynamic response of the beam depending on the moving mass properties. Results showed the significant effect of the boundary conditions on the dynamic response of the beam, which was considered rarely in the past. Stiffening the constraints reduces the maximum stresses in the beams. Results for identical...
Full operational range dynamic modeling of microcantilever beams
, Article Journal of Microelectromechanical Systems ; Volume 22, Issue 5 , May , 2013 , Pages 1190-1198 ; 10577157 (ISSN) ; Vossoughi, G ; Meghdari, A ; Sharif University of Technology
Abstract
Microcantilever beams are frequently utilized in microelectromechanical systems. The operational range of microcantilever beams under electrostatic force can be extended beyond pull-in in the presence of an intermediate dielectric layer, which has a significant effect on the behavior of the system. Three possible configurations of the beam over the operational voltage range are floating, pinned, and flat configurations. In this paper, a systematic method for deriving dynamic equation of microcantilevers for all configurations is presented. First, a static study is performed on deflection profile of the microcantilever under electrostatic force. After that, a polynomial approximate shape...
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...
Vibration of rotating functionally graded timoshenko nano-beams with nonlinear thermal distribution
, Article Mechanics of Advanced Materials and Structures ; 2017 , Pages 1-14 ; 15376494 (ISSN) ; Mirjavadi, S. S ; Shafiei, N ; Hamouda, A. M. S ; Davari, E ; Sharif University of Technology
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...
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...